#3109 ⟨a, b | aabbaababba=1⟩

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Contents

  1. Properties
  2. Rewriting system
  3. Other submonoids of anti-isomorphic 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. cb ⇒ bc [8]
2. bc2 ⇒ 1 [9]
3. cab2a ⇒ ba2bc [13]
4. cabca ⇒ ab2ac4 [20]
5. b2a2 ⇒ abcab2c [16]
6. b2ca2 ⇒ ab2ac [10]
7. a2bca ⇒ c4 [18]
8. cabab2a ⇒ ab2ac3ab2 [26]
9. a2bab2a ⇒ c3ab2 [24]
# ab:aabbaababba=1 bc/a abbaa=c morph:5/0
cb=bc
bcc=1
cabba=baabc
cabca=abbacccc
bbaa=abcabbc
bbcaa=abbac
aabca=cccc
cababba=abbacccabb
aababba=cccabb

Other submonoids of anti-isomorphic group

1 unique, 1 total

Σ#PresentationProperties
113808⟨a, b | abbaababba=b⟩Can Inf

Isomorphic instances

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

3 total

Σ#PresentationMapping
113252⟨a, b | ababbaaabba=1⟩φ(a) = a, φ(b) = abcabbab
113275⟨a, b | abbaaabbaab=1⟩φ(a) = a, φ(b) = abcabbab
113286⟨a, b | abbabaabbba=1⟩φ(a) = abcabbab, φ(b) = a

Anti-isomorphic instances

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

2 total

Σ#PresentationMapping
113119⟨a, b | aabbabaabba=1⟩φ(a) = a, φ(b) = ababcabb
113254⟨a, b | ababbaabbba=1⟩φ(a) = ababcabb, φ(b) = a