#1586 ⟨a, b | aaa=ab, aab=a⟩

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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. a4 ⇒ a
  2. ab ⇒ a3 
# ab:aaa=ab,aab=a a/b
aaaa=a
ab=aaa

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.

45 total

Σ#PresentationMapping
91588⟨a, b | aaa=ab, aba=a⟩φ(a) = a, φ(b) = b
92020⟨a, b | aab=a, aaaa=a⟩φ(a) = a, φ(b) = b
92034⟨a, b | aab=a, abbb=a⟩φ(a) = a, φ(b) = b
105042⟨a, b | aaa=ab, aaaa=a⟩φ(a) = a, φ(b) = b
1112459⟨a, b | aabb=ab, abbb=a⟩φ(a) = a, φ(b) = b
1112568⟨a, b | abba=ab, abbb=a⟩φ(a) = a, φ(b) = b
1118834⟨a, b | aab=a, aaaaab=a⟩φ(a) = a, φ(b) = b
1118836⟨a, b | aab=a, aaaaba=a⟩φ(a) = a, φ(b) = b
1118840⟨a, b | aab=a, aaabaa=a⟩φ(a) = a, φ(b) = b
1118848⟨a, b | aab=a, aabaaa=a⟩φ(a) = a, φ(b) = b
1118862⟨a, b | aab=a, aabbbb=a⟩φ(a) = a, φ(b) = b
1118864⟨a, b | aab=a, abaaaa=a⟩φ(a) = a, φ(b) = b
1118878⟨a, b | aab=a, ababbb=a⟩φ(a) = a, φ(b) = b
1118886⟨a, b | aab=a, abbabb=a⟩φ(a) = a, φ(b) = b
1118890⟨a, b | aab=a, abbbab=a⟩φ(a) = a, φ(b) = b
1118892⟨a, b | aab=a, abbbba=a⟩φ(a) = a, φ(b) = b
1119090⟨a, b | aba=a, aaaaab=a⟩φ(a) = a, φ(b) = b
1119134⟨a, b | aba=a, abbbab=a⟩φ(a) = a, φ(b) = b
1119376⟨a, b | aab=a, aaaaa=aa⟩φ(a) = a, φ(b) = b
1119381⟨a, b | aab=a, aaaab=ab⟩φ(a) = a, φ(b) = b
1119385⟨a, b | aab=a, aaaba=ab⟩φ(a) = a, φ(b) = b
1119393⟨a, b | aab=a, aabaa=ab⟩φ(a) = a, φ(b) = b
1119404⟨a, b | aab=a, aabbb=aa⟩φ(a) = a, φ(b) = b
1119409⟨a, b | aab=a, abaaa=ab⟩φ(a) = a, φ(b) = b
1119420⟨a, b | aab=a, ababb=aa⟩φ(a) = a, φ(b) = b
1119428⟨a, b | aab=a, abbab=aa⟩φ(a) = a, φ(b) = b
1119432⟨a, b | aab=a, abbba=aa⟩φ(a) = a, φ(b) = b
1119437⟨a, b | aab=a, abbbb=ab⟩φ(a) = a, φ(b) = b
1119442⟨a, b | aab=a, baaaa=ba⟩φ(a) = a, φ(b) = b
1119470⟨a, b | aab=a, babbb=ba⟩φ(a) = a, φ(b) = b
1119640⟨a, b | aba=a, aaaba=ab⟩φ(a) = a, φ(b) = b
1119648⟨a, b | aba=a, aabaa=ab⟩φ(a) = a, φ(b) = b
1119921⟨a, b | aab=a, aaaa=aab⟩φ(a) = a, φ(b) = b
1119922⟨a, b | aab=a, aaaa=aba⟩φ(a) = a, φ(b) = b
1119931⟨a, b | aab=a, aaab=abb⟩φ(a) = a, φ(b) = b
1119939⟨a, b | aab=a, aaba=abb⟩φ(a) = a, φ(b) = b
1119944⟨a, b | aab=a, aabb=aaa⟩φ(a) = a, φ(b) = b
1119955⟨a, b | aab=a, abaa=abb⟩φ(a) = a, φ(b) = b
1119960⟨a, b | aab=a, abab=aaa⟩φ(a) = a, φ(b) = b
1119968⟨a, b | aab=a, abba=aaa⟩φ(a) = a, φ(b) = b
1119977⟨a, b | aab=a, abbb=aab⟩φ(a) = a, φ(b) = b
1119978⟨a, b | aab=a, abbb=aba⟩φ(a) = a, φ(b) = b
1119989⟨a, b | aab=a, baaa=bab⟩φ(a) = a, φ(b) = b
1120012⟨a, b | aab=a, babb=baa⟩φ(a) = a, φ(b) = b
1120206⟨a, b | aba=a, abab=aaa⟩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.

5 total

Σ#PresentationMapping
91649⟨a, b | aab=bb, abb=b⟩φ(a) = b, φ(b) = a
105193⟨a, b | aab=bb, aaab=b⟩φ(a) = b, φ(b) = a
1112613⟨a, b | abbb=bb, bbbb=b⟩φ(a) = b, φ(b) = a
1119641⟨a, b | aba=a, aaaba=ba⟩φ(a) = a, φ(b) = b
1120187⟨a, b | aba=a, aaab=bab⟩φ(a) = a, φ(b) = b