A0  A1   B0  B1   C0  C1   D0  D1   E0  E1
C1L D1R  H1L D0R  D1R A1L  B0R E0R  A0L E1L    id=5502432 dm_0

List of the shift rules:
(sr0)     *(+-)<A*  -->  *<A(++)*
(sr1)     *(-+)<C*  -->  *<C(++)*  (not used)
(sr2)     *D>(-+)*  -->  *(--)D>*
(sr3)     *B>(+-)*  -->  *(--)B>*  (not used)
(sr4)     *(+)<E*   -->  *<E(+)*   (not used)

No approved shift rules !!!

Lemma:

The following transactions are true for any k:

(1)  *(k|--)<A-* --> *(k|+-)<A-*
(2)  *+D>(++|k)* --> *+(k|--)D>*

---------

Lemma proof (induction on length of sequences (xx|k) ):

a) (1) and (2) are trivialy true for k=0.

b) Let (1) and (2) are proved for k.

   (1)/k+1 proof:
                     *--(k|--)<A-*
      (1)/k; sr0 --> *--<A(++|k)-*                 
      2 steps    --> *+D>+(++|k)-*
      repack     --> *+D>(++|k)+-*
      (2)/k      --> *+(k|--)D>+-*
      2 steps    --> *+(k|--)-<A-*
      repack     --> *+-(k|--)<A-*
      (1)/k      --> *+-(k|+-)<A-*  --pack--> OK!

   (2)/k+1 proof:
                     *+D>(++|k)++*
      (2)/k      --> *+(k|--)D>--*
      3 steps    --> *+(k|--)<A-+*
      (1)/k; sr0 --> *+<A(++|k)-+*
      step       --> *+D>(++|k)-+*
      (2)/k      --> *+(k|--)D>-+*
      sr2        --> *+(k|--)--D>*  --pack--> OK!

(1) applied to starting position .<A. follow that
position .(k|+-)<A. is reachable for any k - this
machine never stops !

k=1 is reached at step 4.
k=2 is reached at step 20.
k=3 is reached at step 72.
   
----- Simple History: -----
   0:    0 <A                                        ^.
   1:   -1 <C                                       ^+.
   2:    0 D>                                      .+#.
   3:    1 E>                                      .+-^
   4:    0 <A                                      .+=.
   5:   -1 <C                                      .#+.
   6:   -2 <A                                      ^++.
   7:   -3 <C                                     ^+++.
   8:   -2 D>                                    .+#++.
   9:   -1 E>                                    .+-#+.
  10:   -2 <E                                    .+=++.
  11:   -3 <A                                    .#-++.
  12:   -2 D>                                    .+=++.
  13:   -1 B>                                    .+-#+.
  14:    0 D>                                    .+--#.
  15:    1 E>                                    .+---^
  16:    0 <A                                    .+--=.
  17:   -1 <C                                    .+-=+.
  18:    0 D>                                    .+-+#.
  19:    1 E>                                    .+-+-^
  20:    0 <A                                    .+-+=.
  21:   -1 <C                                    .+-#+.
  22:   -2 <A                                    .+=++.
  23:   -3 <C                                    .#+++.
  24:   -4 <A                                    ^++++.
  25:   -5 <C                                   ^+++++.
  26:   -4 D>                                  .+#++++.
  27:   -3 E>                                  .+-#+++.
  28:   -4 <E                                  .+=++++.
  29:   -5 <A                                  .#-++++.
  30:   -4 D>                                  .+=++++.
  31:   -3 B>                                  .+-#+++.
  32:   -2 D>                                  .+--#++.
  33:   -1 E>                                  .+---#+.
  34:   -2 <E                                  .+--=++.
  35:   -3 <A                                  .+-=-++.
  36:   -4 <C                                  .+=+-++.
  37:   -3 D>                                  .++#-++.
  38:   -2 E>                                  .++-=++.
  39:   -3 <A                                  .++=-++.
  40:   -4 <C                                  .+#+-++.
  41:   -5 <A                                  .#++-++.
  42:   -4 D>                                  .+#+-++.
  43:   -3 E>                                  .+-#-++.
  44:   -4 <E                                  .+=+-++.
  45:   -5 <A                                  .#-+-++.
  46:   -4 D>                                  .+=+-++.
  47:   -3 B>                                  .+-#-++.
  48:   -2 D>                                  .+--=++.
  49:   -1 B>                                  .+---#+.
  50:    0 D>                                  .+----#.
  51:    1 E>                                  .+-----^
  52:    0 <A                                  .+----=.
  53:   -1 <C                                  .+---=+.
  54:    0 D>                                  .+---+#.
  55:    1 E>                                  .+---+-^
  56:    0 <A                                  .+---+=.
  57:   -1 <C                                  .+---#+.
  58:   -2 <A                                  .+--=++.
  59:   -3 <C                                  .+-=+++.
  60:   -2 D>                                  .+-+#++.
  61:   -1 E>                                  .+-+-#+.
  62:   -2 <E                                  .+-+=++.
  63:   -3 <A                                  .+-#-++.
  64:   -2 D>                                  .+-+=++.
  65:   -1 B>                                  .+-+-#+.
  66:    0 D>                                  .+-+--#.
  67:    1 E>                                  .+-+---^
  68:    0 <A                                  .+-+--=.
  69:   -1 <C                                  .+-+-=+.
  70:    0 D>                                  .+-+-+#.
  71:    1 E>                                  .+-+-+-^
  72:    0 <A                                  .+-+-+=.