#7796 ⟨a, b | aaa=1, abbab=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. b9 ⇒ b3 [10]
2. bab8 ⇒ bab2 [8]
3. b3ab ⇒ ab4 [4]
4. a2b2 ⇒ b2ab [3]
5. abab2 ⇒ bab6 [9]
6. ab2ab ⇒ b2 [2]
7. b2(ab)2 ⇒ ab2 [5]
8. a3 ⇒ 1 [1]
# ab:aaa=1,abbab=bb b/a
bbbbbbbbb=bbb
babbbbbbbb=babb
bbbab=abbbb
aabb=bbab
ababb=babbbbbb
abbab=bb
bbabab=abb
aaa=1

Anti-isomorphic instances

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

1 total

Σ#PresentationMapping
1123317⟨a, b | aaa=1, bbaa=babb⟩φ(a) = a, φ(b) = b