#27141 ⟨a, b | aa=1, abbabab=bb⟩

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  1. Properties
  2. Rewriting system
  3. Anti-isomorphic instances

Properties

Rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
#RuleProof
1. b7 ⇒ b3 [8]
2. bab6 ⇒ bab2 [9]
3. b4ab2 ⇒ ab6 [11]
4. a2 ⇒ 1 [1]
5. abab2 ⇒ b2ab3 [5]
6. (ab2)2 ⇒ bab5 [10]
7. ab3ab2 ⇒ b3ab4 [13]
8. b2(ab)2 ⇒ ab2 [3]
# ab:aa=1,abbabab=bb b/a
bbbbbbb=bbb
babbbbbb=babb
bbbbabb=abbbbbb
aa=1
ababb=bbabbb
abbabb=babbbbb
abbbabb=bbbabbbb
bbabab=abb

Anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1127732⟨a, b | aa=1, bababb=bba⟩φ(a) = a, φ(b) = b