#1193 ⟨a, b | aa=1, abbb=bb⟩

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Properties

Complete 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
  1. a2 ⇒ 1
  2. ab2 ⇒ b3
  3. b4 ⇒ b2 
# ab:aa=1,abbb=bb ba
aa=1
abb=bbb
bbbb=bb

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

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

11 total

Σ#PresentationMapping
81256⟨a, b | aa=1, bbb=abb⟩φ(a) = a, φ(b) = b
109958⟨a, b | aa=1, aaabbb=bb⟩φ(a) = a, φ(b) = b
109996⟨a, b | aa=1, abaabb=bb⟩φ(a) = a, φ(b) = b
1010012⟨a, b | aa=1, abbaab=bb⟩φ(a) = a, φ(b) = b
1010229⟨a, b | aa=1, aaabb=bbb⟩φ(a) = a, φ(b) = b
1010255⟨a, b | aa=1, aabbb=abb⟩φ(a) = a, φ(b) = b
1010267⟨a, b | aa=1, abaab=bbb⟩φ(a) = a, φ(b) = b
1010313⟨a, b | aa=1, baabb=abb⟩φ(a) = a, φ(b) = b
1010494⟨a, b | aa=1, abbb=aabb⟩φ(a) = a, φ(b) = b
1010508⟨a, b | aa=1, baab=abbb⟩φ(a) = a, φ(b) = b
1010524⟨a, b | aa=1, bbaa=abbb⟩φ(a) = a, φ(b) = b

Other anti-isomorphic instances

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

6 total

Σ#PresentationMapping
109981⟨a, b | aa=1, aabbba=bb⟩φ(a) = a, φ(b) = b
1010251⟨a, b | aa=1, aabba=bbb⟩φ(a) = a, φ(b) = b
1010258⟨a, b | aa=1, aabbb=bba⟩φ(a) = a, φ(b) = b
1010293⟨a, b | aa=1, abbba=abb⟩φ(a) = a, φ(b) = b
1010316⟨a, b | aa=1, baabb=bba⟩φ(a) = a, φ(b) = b
1010497⟨a, b | aa=1, abbb=abba⟩φ(a) = a, φ(b) = b