#3911 ⟨a, b | aabb=ba, baba=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. a2b2 ⇒ ba [1]
2. (ab)2 ⇒ 1 [6]
3. ba3 ⇒ a3b [7]
4. ba2b ⇒ ab2a [10]
5. (ba)2 ⇒ 1 [2]
6. b2a2 ⇒ ab [9]
7. b3a ⇒ ab3 [11]
8. ab2ab ⇒ b2a [12]
9. bab2a ⇒ ab2 [4]
# ab:aabb=ba,baba=1 ab
aabb=ba
abab=1
baaa=aaab
baab=abba
baba=1
bbaa=ab
bbba=abbb
abbab=bba
babba=abb

Isomorphic instances

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

3 total

Σ#PresentationMapping
105636⟨a, b | abab=1, aabbba=1⟩φ(a) = a, φ(b) = b
105646⟨a, b | abab=1, abbbaa=1⟩φ(a) = a, φ(b) = b
105657⟨a, b | abab=1, bbbaaa=1⟩φ(a) = a, φ(b) = b