#4876 ⟨a, b | abbabbba=bab⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group

Properties

Rewriting system

Format:
Word:
Enter a word above to compute its normal form. Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Strategy:
Result: 1 
1
#RuleProof
1. ab ⇒ c [2]
2. acbda ⇒ c2 [6]
3. bc ⇒ cbda [5]
4. acbd2 ⇒ cdb [14]
5. acbdc ⇒ c2b [9]
6. ac2bd3 ⇒ cd2cb [22]
7. ac3bd3 ⇒ cdcbdc [26]
8. ac4bd3 ⇒ cd2c [35]
9. ac5bd3 ⇒ cdcbda [37]
10. c6bd3 ⇒ bd2a [42]
11. c2bdcda ⇒ dc [7]
12. bd2c ⇒ c4bd3 [32]
13. c2bdcd2 ⇒ d2b [15]
14. c2b(dc)2 ⇒ dcb [19]
15. cb2 ⇒ d [3]
16. bdb ⇒ cbd2 [11]
17. cbdcb ⇒ bd [8]
18. c2bd3b ⇒ bd3 [24]
19. b2d ⇒ cb(dc)2b [10]
20. bd2bd ⇒ c2bd4cb [25]
21. c2bdcdbd ⇒ d3cb [21]
22. bdcbda ⇒ c5bd3 [41]
23. cbdc2bda ⇒ bdc [12]
24. c2bd3cbda ⇒ bd3c [27]
25. bdcbd2 ⇒ cbd3b [18]
26. cbdc2bd2 ⇒ bd2b [16]
27. c2bd3cbd2 ⇒ bd4b [28]
28. (bdc)2 ⇒ c3bd3 [31]
29. (cbdc)2 ⇒ bdcb [20]
30. c2bd3cbdc ⇒ bd3cb [39]
31. bdc2bd3 ⇒ cbd4cb [23]
32. bdc3bd3 ⇒ cbd3cbdc [34]
33. (c2bd3)2 ⇒ bd5cb [29]
34. bdc4bd3 ⇒ cbd4c [36]
35. c2bd3c3bd3 ⇒ bd4cbdc [43]
36. bdc5bd3 ⇒ cbd3cbda [40]
37. c2bd3c4bd3 ⇒ bd5c [38]
38. c2bd3c5bd3 ⇒ bd4cbda [44]
# ab:abbabbba=bab reversed:a/dc/b ab=c,cbb=d morph:2/1,3/1
ab=c
acbda=cc
bc=cbda
acbdd=cdb
acbdc=ccb
accbddd=cddcb
acccbddd=cdcbdc
accccbddd=cddc
acccccbddd=cdcbda
ccccccbddd=bdda
ccbdcda=dc
bddc=ccccbddd
ccbdcdd=ddb
ccbdcdc=dcb
cbb=d
bdb=cbdd
cbdcb=bd
ccbdddb=bddd
bbd=cbdcdcb
bddbd=ccbddddcb
ccbdcdbd=dddcb
bdcbda=cccccbddd
cbdccbda=bdc
ccbdddcbda=bdddc
bdcbdd=cbdddb
cbdccbdd=bddb
ccbdddcbdd=bddddb
bdcbdc=cccbddd
cbdccbdc=bdcb
ccbdddcbdc=bdddcb
bdccbddd=cbddddcb
bdcccbddd=cbdddcbdc
ccbdddccbddd=bdddddcb
bdccccbddd=cbddddc
ccbdddcccbddd=bddddcbdc
bdcccccbddd=cbdddcbda
ccbdddccccbddd=bdddddc
ccbdddcccccbddd=bddddcbda

Other submonoids of same group

11 unique, 55 total

Σ#PresentationPropertiesφ
6104⟨a, b | aaba=bb⟩Can Inf
7145⟨a, b | aababba=1⟩Grp Inf44
7193⟨a, b | ababba=b⟩Can Inf
7252⟨a, b | aaba=bab⟩Can Inf
9842⟨a, b | abaababa=b⟩Can Inf
91126⟨a, b | ababba=bab⟩Can Inf
91273⟨a, b | abbba=babb⟩Can Inf
102633⟨a, b | abbbba=babb⟩Can Inf
113716⟨a, b | abaaabaaba=b⟩Can Inf
115415⟨a, b | abbbbba=babb⟩Can Inf
115898⟨a, b | ababba=babab⟩Can Inf

Other submonoids of anti-isomorphic group

7 unique, 7 total

Σ#PresentationProperties
687⟨a, b | aabba=b⟩Can Inf
7179⟨a, b | aababa=b⟩Can Inf
8374⟨a, b | aabaaba=b⟩Can Inf
8586⟨a, b | baab=aaba⟩Can Inf
9792⟨a, b | aabaaaba=b⟩Can Inf
101666⟨a, b | aabaaaaba=b⟩Can Inf
113536⟨a, b | aabaaaaaba=b⟩Can Inf