#8614 ⟨a, b | aa=a, abbbab=a⟩

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  1. Properties
  2. Rewriting system
  3. 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. a2 ⇒ a [1]
2. aba ⇒ ab [9]
3. ab2a ⇒ ab2 [10]
4. ab3a ⇒ ab3 [11]
5. ab4 ⇒ a [8]
# ab:aa=a,abbbab=a ab
aa=a
aba=ab
abba=abb
abbba=abbb
abbbb=a

Isomorphic instances

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

6 total

Σ#PresentationMapping
1115871⟨a, b | aba=ab, abbbb=a⟩φ(a) = a, φ(b) = b
1124098⟨a, b | aa=a, aabbbab=a⟩φ(a) = a, φ(b) = b
1124122⟨a, b | aa=a, ababbab=a⟩φ(a) = a, φ(b) = b
1124132⟨a, b | aa=a, abbabab=a⟩φ(a) = a, φ(b) = b
1124138⟨a, b | aa=a, abbbaab=a⟩φ(a) = a, φ(b) = b
1124677⟨a, b | aa=a, abbbab=aa⟩φ(a) = a, φ(b) = b