#3914 ⟨a, b | aabb=ba, bbbb=1⟩

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Properties

Element profile

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. a5 ⇒ a
  2. a4ba ⇒ ba
  3. b2a ⇒ a2ba2
  4. (ba)2 ⇒ aba4
  5. ba2ba ⇒ a3ba3
  6. ba3ba ⇒ a2
  7. ab2 ⇒ a3ba
  8. b4 ⇒ 1 
# ab:aabb=ba,bbbb=1 a/b
aaaaa=a
aaaaba=ba
bba=aabaa
baba=abaaaa
baaba=aaabaaa
baaaba=aa
abb=aaaba
bbbb=1

Right Cayley graph

Left Cayley graph

Other isomorphic instances

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

3 total

Σ#PresentationMapping
103992⟨a, b | babb=aa, bbbb=1⟩φ(a) = a, φ(b) = b
104090⟨a, b | baa=abb, aaaa=1⟩φ(a) = bbb, φ(b) = a
1111090⟨a, b | babb=aba, bbbb=1⟩φ(a) = aa, φ(b) = b

Other anti-isomorphic instances

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

4 total

Σ#PresentationMapping
105707⟨a, b | aaaa=1, aabba=b⟩φ(a) = bbb, φ(b) = a
1111005⟨a, b | abab=bba, bbbb=1⟩φ(a) = ab, φ(b) = bbb
1117107⟨a, b | aaaa=1, aababa=b⟩φ(a) = bbb, φ(b) = ab
1117636⟨a, b | aaaa=1, aabab=ba⟩φ(a) = b, φ(b) = aa