#3070 ⟨a, b | aabababbaba=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. b2abc ⇒ a(ab)3 [14]
7. b(ab)2d ⇒ adb2ab [11]
8. babcba ⇒ cb(ab)2 [19]
9. b(ba)2c ⇒ a2(ba)3 [16]
10. (ba)3d ⇒ adb(ba)2 [12]
11. b2aba2 ⇒ a2dbabcb [26]
12. (ba)3a ⇒ dba(bc)2 [24]
13. (ba)2b2a ⇒ adbcb(ab)2 [17]
14. bc(ba)2b2 ⇒ a2d [20]
15. (ba)2b2cba ⇒ dbabc2b(ab)2 [27]
# ab:aabababbaba=1 reversed:cda/b aaa=c,bababbab=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
bbabc=aababab
bababd=adbbab
babcba=cbabab
bbabac=aabababa
bababad=adbbaba
bbabaa=aadbabcb
bababaa=dbabcbc
bababba=adbcbabab
bcbababb=aad
bababbcba=dbabccbabab

Other submonoids of same group

5 unique, 5 total

Σ#PresentationProperties
8431⟨a, b | aaabaa=bb⟩Can Inf
91038⟨a, b | aaabaa=bab⟩Can Inf
102430⟨a, b | aaabaa=baab⟩Can Inf
113775⟨a, b | abababbaba=b⟩Can Inf
115550⟨a, b | aaabaa=baaab⟩Can Inf

Other submonoids of anti-isomorphic group

4 unique, 4 total

Σ#PresentationProperties
8366⟨a, b | aaabbaa=b⟩Can Inf
9769⟨a, b | aaababaa=b⟩Can Inf
101616⟨a, b | aaabaabaa=b⟩Can Inf
113434⟨a, b | aaabaaabaa=b⟩Can Inf

Isomorphic instances

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

1 total

Σ#PresentationMapping
113255⟨a, b | ababbabaaab=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
113080⟨a, b | aababbababa=1⟩φ(a) = a, φ(b) = abaad
113248⟨a, b | abababbbaba=1⟩φ(a) = abaad, φ(b) = a
113262⟨a, b | ababbbabaab=1⟩φ(a) = abaad, φ(b) = a
113287⟨a, b | abbababaaab=1⟩φ(a) = a, φ(b) = abaad