#2302 ⟨a, b | aaa=1, abbabb=1⟩

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Quick links

  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. a3 ⇒ 1 [1]
2. bab2a ⇒ ab2ab [6]
3. b2ab2 ⇒ a2 [3]
4. b2aba2 ⇒ a2bab2 [4]
# ab:aaa=1,abbabb=1 ab
aaa=1
babba=abbab
bbabb=aa
bbabaa=aababb

Isomorphic instances

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

10 total

Σ#PresentationMapping
92311⟨a, b | aaa=1, babbab=1⟩φ(a) = a, φ(b) = b
107818⟨a, b | aaa=1, bbabb=aa⟩φ(a) = a, φ(b) = b
1113823⟨a, b | aaaa=a, abbabb=1⟩φ(a) = a, φ(b) = b
1113832⟨a, b | aaaa=a, babbab=1⟩φ(a) = a, φ(b) = b
1113964⟨a, b | aaab=b, abbabb=1⟩φ(a) = a, φ(b) = b
1113982⟨a, b | aaab=b, babbab=1⟩φ(a) = a, φ(b) = b
1113991⟨a, b | aaab=b, bbabba=1⟩φ(a) = a, φ(b) = b
1121698⟨a, b | aaa=1, aabbabb=a⟩φ(a) = a, φ(b) = b
1121726⟨a, b | aaa=1, ababbab=a⟩φ(a) = a, φ(b) = b
1121738⟨a, b | aaa=1, abbabba=a⟩φ(a) = a, φ(b) = b