#1475 ⟨a, b | aaa=bb, bbbb=1⟩

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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. a3 ⇒ b2
  2. b2a ⇒ ab2
  3. b4 ⇒ 1 
# ab:aaa=bb,bbbb=1 ab
aaa=bb
bba=abb
bbbb=1

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.

7 total

Σ#PresentationMapping
104805⟨a, b | aaa=bb, aaabb=1⟩φ(a) = a, φ(b) = b
104808⟨a, b | aaa=bb, aabba=1⟩φ(a) = a, φ(b) = b
104816⟨a, b | aaa=bb, baaab=1⟩φ(a) = a, φ(b) = b
1110781⟨a, b | aaab=bbb, bbbb=1⟩φ(a) = a, φ(b) = b
1113437⟨a, b | aaabb=1, aaaaaa=1⟩φ(a) = a, φ(b) = b
1113601⟨a, b | aabba=1, aaaaaa=1⟩φ(a) = a, φ(b) = b
1114973⟨a, b | aaa=bb, aaaaaa=1⟩φ(a) = a, φ(b) = b