#3078 ⟨a, b | aababbaabba=1⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of same group
  4. Isomorphic instances
  5. 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 [41]
2. cd ⇒ 1 [35]
3. cb ⇒ bc [5]
4. db ⇒ bd [40]
5. b2 ⇒ c [2]
6. a3b ⇒ dabaca [54]
7. abacab ⇒ ca3c [56]
8. abaca2c ⇒ b(aca)2 [53]
9. (aca)2d ⇒ bdabaca2 [63]
10. abaca2bc ⇒ b(aca)2b [58]
11. (aca)2bd ⇒ bdabaca2b [62]
12. a(ca2)2d ⇒ bda2baca2 [68]
13. a(ca2)2b ⇒ ba2ca3c [66]
14. a2baca2b ⇒ ca2ca3 [61]
15. a3(ca)2b ⇒ dabac2a3c [57]
16. aca2ca3 ⇒ bd [46]
17. a3caca2c ⇒ d(ab)2c(aca)2 [59]
18. a3caca2bc ⇒ d(ab)2c(aca)2b [70]
19. a2ca4cab ⇒ da2b(ac)2a3c [71]
20. (a2ca2)2c ⇒ da(ab)2ca(ca2)2 [74]
21. (a2ca2)2b ⇒ da2bac2a2ca3 [73]
22. (a2ca)2ca2b ⇒ bda(ca2c)2a3 [76]
# ab:aababbaabba=1 reversed:cdb/a bb=c,aabbaaaba=d magic:1
dc=1
cd=1
cb=bc
db=bd
bb=c
aaab=dabaca
abacab=caaac
abacaac=bacaaca
acaacad=bdabacaa
abacaabc=bacaacab
acaacabd=bdabacaab
acaacaad=bdaabacaa
acaacaab=baacaaac
aabacaab=caacaaa
aaacacab=dabaccaaac
acaacaaa=bd
aaacacaac=dababcacaaca
aaacacaabc=dababcacaacab
aacaaaacab=daabacacaaac
aacaaaacaac=daababcacaacaa
aacaaaacaab=daabaccaacaaa
aacaaacacaab=bdacaaccaacaaa

Other submonoids of same group

1 unique, 1 total

Σ#PresentationProperties
113782⟨a, b | ababbaabba=b⟩Can Inf

Isomorphic instances

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

2 total

Σ#PresentationMapping
113274⟨a, b | abbaaababba=1⟩φ(a) = a, φ(b) = bacaacaaab
113281⟨a, b | abbaabbaaab=1⟩φ(a) = a, φ(b) = bacaacaaab

Anti-isomorphic instances

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

4 total

Σ#PresentationMapping
113111⟨a, b | aabbaabbaba=1⟩φ(a) = a, φ(b) = abbacaacaa
113117⟨a, b | aabbabaaabb=1⟩φ(a) = a, φ(b) = abbacaacaa
113261⟨a, b | ababbbaabba=1⟩φ(a) = abbacaacaa, φ(b) = a
113280⟨a, b | abbaababbba=1⟩φ(a) = abbacaacaa, φ(b) = a