#3062 ⟨a, b | aababaabbba=1⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Other submonoids of anti-isomorphic group
  5. Isomorphic instances
  6. Anti-isomorphic instances

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. dc ⇒ 1 [10]
2. cd ⇒ 1 [8]
3. ca ⇒ ac [5]
4. da ⇒ ad [9]
5. a3 ⇒ c [2]
6. b(aba)2 ⇒ dbcbabc [23]
7. bcbaba2 ⇒ cbaba2b [20]
8. ba2b3c ⇒ a(ab)2a2b2 [14]
9. baba2b2d ⇒ adba2b3 [11]
10. ba2b3a ⇒ a2db2cbab [38]
11. baba2b2a ⇒ db2cbabc [36]
12. b3cba ⇒ (ab)2a2b2 [43]
13. b2c(ba)2 ⇒ a2b3cb [47]
14. baba2b3 ⇒ d [3]
15. (bcba)2aba ⇒ cbaba2dbcbabc [27]
16. bc(ba)2cb3c ⇒ (c(ba)2)2ab2 [26]
17. (bcba)2ab2d ⇒ cbab2a2b3 [25]
18. bc(ba)2cb3a ⇒ c(ba)2b2cbab [35]
19. (bcba)2ab2a ⇒ cbaba2db2cbabc [59]
20. b3cb2a2ba ⇒ adb2cbadbcbabc [49]
21. b2cbab2a2ba ⇒ aba2b2dbcbabc [34]
22. (bcba)2ab3 ⇒ cbaba2d [24]
23. b3cb4c ⇒ a2d(ba2b)2aba2b2 [61]
24. b3cbcb3c ⇒ adb(c(ba)2)2ab2 [56]
25. b2cbabcb3c ⇒ a2b3a2cbaba2b2 [58]
26. b3cb2a2b2d ⇒ adb2cba2dba2b3 [48]
27. b2cbab2a2b2d ⇒ aba2b2adba2b3 [32]
28. b3cb4a ⇒ a2dba2b2a2db2cbab [63]
29. b3cbcb3a ⇒ adbc(ba)2b2cbab [55]
30. b2cbabcb3a ⇒ a2b3a2b2cbab [57]
31. b3cb2a2b2a ⇒ a(db2cba)2bc [50]
32. b2cb(ab2a)2 ⇒ aba2b2db2cbabc [40]
33. b3cb2a2b3 ⇒ adb2cbad [42]
34. b2cbab2a2b3 ⇒ aba2b2d [31]
# ab:aababaabbba=1 reversed:cda/b aaa=c,babaabbb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
babaaba=dbcbabc
bcbabaa=cbabaab
baabbbc=aababaabb
babaabbd=adbaabbb
baabbba=aadbbcbab
babaabba=dbbcbabc
bbbcba=ababaabb
bbcbaba=aabbbcb
babaabbb=d
bcbabcbaaba=cbabaadbcbabc
bcbabacbbbc=cbabacbabaabb
bcbabcbaabbd=cbabbaabbb
bcbabacbbba=cbababbcbab
bcbabcbaabba=cbabaadbbcbabc
bbbcbbaaba=adbbcbadbcbabc
bbcbabbaaba=abaabbdbcbabc
bcbabcbaabbb=cbabaad
bbbcbbbbc=aadbaabbaababaabb
bbbcbcbbbc=adbcbabacbabaabb
bbcbabcbbbc=aabbbaacbabaabb
bbbcbbaabbd=adbbcbaadbaabbb
bbcbabbaabbd=abaabbadbaabbb
bbbcbbbba=aadbaabbaadbbcbab
bbbcbcbbba=adbcbababbcbab
bbcbabcbbba=aabbbaabbcbab
bbbcbbaabba=adbbcbadbbcbabc
bbcbabbaabba=abaabbdbbcbabc
bbbcbbaabbb=adbbcbad
bbcbabbaabbb=abaabbd

Other submonoids of same group

1 unique, 1 total

Σ#PresentationProperties
113748⟨a, b | abaabbabba=b⟩Can Inf

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationProperties
114247⟨a, b | abaaababa=bb⟩Can Inf

Isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

2 total

Σ#PresentationMapping
113146⟨a, b | aabbbababba=1⟩φ(a) = aadab, φ(b) = a
113220⟨a, b | abaabbbaaab=1⟩φ(a) = a, φ(b) = aadab

Anti-isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

4 total

Σ#PresentationMapping
113124⟨a, b | aabbababbba=1⟩φ(a) = abaad, φ(b) = a
113140⟨a, b | aabbbaababa=1⟩φ(a) = a, φ(b) = abaad
113197⟨a, b | abaaabbbaab=1⟩φ(a) = a, φ(b) = abaad
113232⟨a, b | ababaaabbba=1⟩φ(a) = a, φ(b) = abaad