diff --git a/examples/Chapter2.ipynb b/examples/Chapter2.ipynb
index f1b3997..2b443f3 100644
--- a/examples/Chapter2.ipynb
+++ b/examples/Chapter2.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 1,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -24,7 +24,7 @@
        "(:KENZO)"
       ]
      },
-     "execution_count": 1,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -35,7 +35,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 2,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -54,7 +54,7 @@
        "NIL"
       ]
      },
-     "execution_count": 2,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -72,7 +72,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 3,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -120,7 +120,7 @@
        "-----------------------------------------------------------------------------\""
       ]
      },
-     "execution_count": 3,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -138,7 +138,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -168,7 +168,7 @@
        "------------------------------------------------------------------------------\""
       ]
      },
-     "execution_count": 4,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -186,7 +186,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -230,7 +230,7 @@
        "------------------------------------------------------------------------------\""
       ]
      },
-     "execution_count": 5,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -241,7 +241,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -260,7 +260,7 @@
        "------------------------------------------------------------------------------\""
       ]
      },
-     "execution_count": 6,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -278,7 +278,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -289,7 +289,7 @@
        "CDELTA"
       ]
      },
-     "execution_count": 7,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -319,7 +319,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -330,7 +330,7 @@
        "MAKE-F"
       ]
      },
-     "execution_count": 8,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -353,7 +353,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -364,7 +364,7 @@
        "MAKE-G"
       ]
      },
-     "execution_count": 9,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -380,7 +380,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -391,7 +391,7 @@
        "MAKE-H"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -416,7 +416,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -427,7 +427,7 @@
        "MAKE-RDCT"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -444,7 +444,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -455,7 +455,7 @@
        "[K8 Reduction K1 => K3]"
       ]
      },
-     "execution_count": 12,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -466,7 +466,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -477,7 +477,7 @@
        "(REDUCTION DELTA 6 3)"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -488,7 +488,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -507,7 +507,7 @@
        "NIL"
       ]
      },
-     "execution_count": 14,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -518,7 +518,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -535,7 +535,7 @@
        "------------------------------------------------------------------------------\n"
       ]
      },
-     "execution_count": 15,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -546,7 +546,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -560,7 +560,7 @@
        "------------------------------------------------------------------------------\n"
       ]
      },
-     "execution_count": 16,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -571,7 +571,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -648,7 +648,7 @@
        "NIL"
       ]
      },
-     "execution_count": 17,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -659,7 +659,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -670,7 +670,7 @@
        "[K35 Reduction K1 => K30]"
       ]
      },
-     "execution_count": 18,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -681,7 +681,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -692,7 +692,7 @@
        "[K39 Reduction K30 => K3]"
       ]
      },
-     "execution_count": 19,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -703,7 +703,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -714,7 +714,7 @@
        "[K45 Reduction K1 => K3]"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -725,7 +725,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -744,7 +744,7 @@
        "NIL"
       ]
      },
-     "execution_count": 21,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -755,7 +755,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -832,7 +832,7 @@
        "NIL"
       ]
      },
-     "execution_count": 22,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -851,7 +851,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -862,7 +862,7 @@
        "[K66 Homotopy-Equivalence K30 <= K30 => K30]"
       ]
      },
-     "execution_count": 23,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -873,7 +873,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -884,7 +884,7 @@
        "[K74 Homotopy-Equivalence K69 <= K69 => K69]"
       ]
      },
-     "execution_count": 24,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -895,7 +895,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -908,7 +908,7 @@
        "------------------------------------------------------------------------------\n"
       ]
      },
-     "execution_count": 25,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -926,7 +926,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -945,7 +945,7 @@
        "------------------------------------------------------------------------------\n"
       ]
      },
-     "execution_count": 26,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -957,7 +957,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -968,7 +968,7 @@
        "((2 . <BcnB B1>) (4 . <BcnB B1>) (6 . <BcnB B3>) (3 . <BcnB C1>) (5 . <BcnB C1>) (7 . <BcnB D1>))"
       ]
      },
-     "execution_count": 27,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -987,7 +987,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -1003,7 +1003,7 @@
        "------------------------------------------------------------------------------\n"
       ]
      },
-     "execution_count": 28,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1014,7 +1014,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -1029,7 +1029,7 @@
        "------------------------------------------------------------------------------\n"
       ]
      },
-     "execution_count": 29,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1040,7 +1040,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -1054,7 +1054,7 @@
        "------------------------------------------------------------------------------\n"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1065,7 +1065,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -1084,7 +1084,7 @@
        "------------------------------------------------------------------------------\n"
       ]
      },
-     "execution_count": 31,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1095,7 +1095,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -1111,7 +1111,7 @@
        "------------------------------------------------------------------------------\n"
       ]
      },
-     "execution_count": 32,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1122,7 +1122,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -1137,7 +1137,7 @@
        "------------------------------------------------------------------------------\n"
       ]
      },
-     "execution_count": 33,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1148,7 +1148,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -1162,7 +1162,7 @@
        "------------------------------------------------------------------------------\n"
       ]
      },
-     "execution_count": 34,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1173,7 +1173,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 64,
    "metadata": {
     "collapsed": false
    },
@@ -1199,7 +1199,7 @@
        ")"
       ]
      },
-     "execution_count": 35,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1209,6 +1209,1058 @@
     "    (cat:dispatch-bicn-cmbn comb-bic)\n",
     "    (list b c d))"
    ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 2.6 Construction of abicone from 2 reductions\n",
+    "#### Example"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "---done---"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:cat-init)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "CDELTA"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(defun cdelta (dmns)\n",
+    "    (cat:build-chcm\n",
+    "     :cmpr #'cat:l-cmpr\n",
+    "     :basis #'(lambda (n)\n",
+    "                      (mapcar #'cat:dlop-int-ext (funcall (cat:delta-n-basis dmns) n)))\n",
+    "     :bsgn '(0)\n",
+    "     :intr-dffr\n",
+    "         #'(lambda (degr gmsm)\n",
+    "            (cat:make-cmbn\n",
+    "             :degr (1- degr)\n",
+    "             :list (do ((rslt cat:+empty-list+\n",
+    "                              (cons (cons sign\n",
+    "                                          (append\n",
+    "                                           (subseq gmsm 0 nark)\n",
+    "                                           (subseq gmsm (1+ nark))))\n",
+    "                                    rslt))\n",
+    "                        (sign 1 (- sign))\n",
+    "                        (nark 0 (1+ nark)))\n",
+    "                       ((> nark degr) rslt))))\n",
+    "     :strt :gnrt\n",
+    "     :orgn `(Effective version of C_* delta ,dmns)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K1 Chain-Complex]"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:def delta3 (cdelta 3))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((0) (1) (2) (3))"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:basis delta3 0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((0 1) (0 2) (1 2) (0 3) (1 3) (2 3))"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:basis delta3 1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((0 1 2) (0 1 3) (0 2 3) (1 2 3))"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:basis delta3 2)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "((0 1 2 3))"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:basis delta3 3)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:basis delta3 4)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K15 Chain-Complex]"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:def bic (cat:bicone (make-rdct 3 2) (make-rdct 4 2)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(<BcnB (0)> <BcnB (1)> <BcnB (2)> <BcnB (3)> <BcnC (0 1)> <BcnC (0 2)> <BcnC (1 2)> <BcnD (0)> <BcnD (1)> <BcnD (2)> ...)"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:basis bic 0)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(<BcnB (0 1)> <BcnB (0 2)> <BcnB (1 2)> <BcnB (0 3)> <BcnB (1 3)> <BcnB (2 3)> <BcnC (0 1 2)> <BcnD (0 1)> <BcnD (0 2)> <BcnD (1 2)> ...)"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:basis bic 1)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "(<BcnD (0 1 2 3 4)>)"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:basis bic 4)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 1}\n",
+       "<3 * <BcnB (0 1)>>\n",
+       "<-3 * <BcnB (0 3)>>\n",
+       "<3 * <BcnB (1 3)>>\n",
+       "<12 * <BcnC (0 1 2)>>\n",
+       "<-4 * <BcnC (0 1 3)>>\n",
+       "<4 * <BcnC (0 2 3)>>\n",
+       "<-4 * <BcnC (1 2 3)>>\n",
+       "<5 * <BcnD (0 1)>>\n",
+       "<-5 * <BcnD (0 4)>>\n",
+       "<5 * <BcnD (1 4)>>\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:? bic (cat:cmbn 2 3 (cat:bcnb '(0 1 3)) 4 (cat:bcnc '(0 1 2 3)) 5 (cat:bcnd '(0 1 4))))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 0}\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:? bic (cat:? bic (cat:cmbn 2 3 (cat:bcnb '(0 1 3)) 4 (cat:bcnc '(0 1 2 3)) 5 (cat:bcnd '(0 1 4)))))"
+   ]
+  },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "## 2.7 Composition of homotopy equivalences\n",
+    "#### Example"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "---done---"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:cat-init)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K1 Chain-Complex]"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:def c (cat:build-chcm\n",
+    "            :cmpr #'cat:s-cmpr\n",
+    "            :basis #'(lambda (dmns) (declare (ignore dmns)) '(a))\n",
+    "            :bsgn 'a\n",
+    "            :intr-dffr #'cat:zero-intr-dffr\n",
+    "            :strt :cmbn\n",
+    "            :orgn '(c)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K6 Homotopy-Equivalence K1 <= K1 => K1]"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:def h1 (cat:trivial-hmeq c))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K17 Homotopy-Equivalence K1 <= K7 => K1]"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:def h2 (cat:cmps h1 h1))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "---done---"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:pre-check-rdct (cat:lrdct h2))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 3}\n",
+       "<1 * <BcnB A>>\n",
+       "<10 * <BcnC A>>\n",
+       "<100 * <BcnD A>>\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(setf cat:*tc* (cat:cmbn 3 1 (cat:bcnb 'a) 10 (cat:bcnc 'a) 100 (cat:bcnd 'a)))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 3}\n",
+       "<1 * A>\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(setf cat:*bc* (cat:cmbn 3 1 'a))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "*TC* => \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "<1 * <BcnB A>>\n",
+      "<10 * <BcnC A>>\n",
+      "<100 * <BcnD A>>\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "*BC* => \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "<1 * A>\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *TDD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 1}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *BDD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 1}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *DF-FD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 2}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *DG-GD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 2}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *ID-FG* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *ID-GF-DH-HD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *HH* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 5}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *FH* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 4}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *HG* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 4}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "---done---"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:check-rdct-no-wait)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "---done---"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:pre-check-rdct (cat:rrdct h2))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "*TC* => \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "<1 * <BcnB A>>\n",
+      "<10 * <BcnC A>>\n",
+      "<100 * <BcnD A>>\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "*BC* => \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "<1 * A>\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *TDD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 1}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *BDD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 1}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *DF-FD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 2}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *DG-GD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 2}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *ID-FG* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *ID-GF-DH-HD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *HH* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 5}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *FH* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 4}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *HG* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 4}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "---done---"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:check-rdct-no-wait)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "[K65 Homotopy-Equivalence K1 <= K55 => K1]"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:def h3 (cat:cmps h2 h2))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "\n",
+       "----------------------------------------------------------------------{CMBN 3}\n",
+       "<1 * <BcnB <BcnB A>>>\n",
+       "<10 * <BcnB <BcnC A>>>\n",
+       "<100 * <BcnB <BcnD A>>>\n",
+       "<1000 * <BcnC A>>\n",
+       "<10000 * <BcnD <BcnB A>>>\n",
+       "<5234 * <BcnD <BcnC A>>>\n",
+       "<223 * <BcnD <BcnD A>>>\n",
+       "------------------------------------------------------------------------------\n"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(setf cat:*tc* (cat:cmbn 3 1 (cat:bcnb (cat:bcnb 'a)) 10 (cat:bcnb (cat:bcnc 'a)) 100 (cat:bcnb (cat:bcnd 'a))\n",
+    "                         1000 (cat:bcnc 'a)\n",
+    "                         10000 (cat:bcnd (cat:bcnb 'a)) 5234 (cat:bcnd (cat:bcnc 'a))\n",
+    "                         223 (cat:bcnd (cat:bcnd 'a))))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "---done---"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:pre-check-rdct (cat:lrdct h3))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "*TC* => \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "<1 * <BcnB <BcnB A>>>\n",
+      "<10 * <BcnB <BcnC A>>>\n",
+      "<100 * <BcnB <BcnD A>>>\n",
+      "<1000 * <BcnC A>>\n",
+      "<10000 * <BcnD <BcnB A>>>\n",
+      "<5234 * <BcnD <BcnC A>>>\n",
+      "<223 * <BcnD <BcnD A>>>\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "*BC* => \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "<1 * A>\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *TDD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 1}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *BDD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 1}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *DF-FD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 2}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *DG-GD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 2}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *ID-FG* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *ID-GF-DH-HD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *HH* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 5}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *FH* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 4}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *HG* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 4}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "---done---"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:check-rdct-no-wait)"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "---done---"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:pre-check-rdct (cat:rrdct h3))"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 64,
+   "metadata": {
+    "collapsed": false
+   },
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "\n",
+      "*TC* => \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "<1 * <BcnB <BcnB A>>>\n",
+      "<10 * <BcnB <BcnC A>>>\n",
+      "<100 * <BcnB <BcnD A>>>\n",
+      "<1000 * <BcnC A>>\n",
+      "<10000 * <BcnD <BcnB A>>>\n",
+      "<5234 * <BcnD <BcnC A>>>\n",
+      "<223 * <BcnD <BcnD A>>>\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "*BC* => \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "<1 * A>\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *TDD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 1}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *BDD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 1}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *DF-FD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 2}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *DG-GD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 2}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *ID-FG* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *ID-GF-DH-HD* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 3}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *HH* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 5}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *FH* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 4}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "Checking *HG* = 0\n",
+      "Result: \n",
+      "----------------------------------------------------------------------{CMBN 4}\n",
+      "------------------------------------------------------------------------------\n",
+      "\n",
+      "---done---"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "NIL"
+      ]
+     },
+     "execution_count": 64,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "(cat:check-rdct-no-wait)"
+   ]
   }
  ],
  "metadata": {