#2452 ⟨a, b | aaa=1, bbabb=a⟩

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Contents

  1. Properties
  2. Rewriting system
  3. 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. a3 ⇒ 1 [1]
2. b2a ⇒ ab2 [5]
3. b4 ⇒ 1 [6]
# ab:aaa=1,bbabb=a ab - -
aaa=1
bba=abb
bbbb=1

Isomorphic instances

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

13 total

Σ#PresentationMapping
107233⟨a, b | aaa=1, aabbabb=1⟩φ(a) = a, φ(b) = b
107251⟨a, b | aaa=1, abbaabb=1⟩φ(a) = a, φ(b) = b
107253⟨a, b | aaa=1, abbabba=1⟩φ(a) = a, φ(b) = b
107266⟨a, b | aaa=1, baabbab=1⟩φ(a) = a, φ(b) = b
107542⟨a, b | aaa=1, babbab=a⟩φ(a) = a, φ(b) = baa
1121162⟨a, b | aaa=1, aababbab=1⟩φ(a) = a, φ(b) = baa
1121186⟨a, b | aaa=1, abaababb=1⟩φ(a) = a, φ(b) = baa
1121196⟨a, b | aaa=1, ababbaba=1⟩φ(a) = a, φ(b) = baa
1121206⟨a, b | aaa=1, abbabaab=1⟩φ(a) = a, φ(b) = baa
1121236⟨a, b | aaa=1, babaabab=1⟩φ(a) = a, φ(b) = baa
1121768⟨a, b | aaa=1, babaabb=a⟩φ(a) = a, φ(b) = ba
1122277⟨a, b | aaa=1, abbabb=aa⟩φ(a) = a, φ(b) = b
1122318⟨a, b | aaa=1, bbaabb=aa⟩φ(a) = a, φ(b) = b