#588 ⟨a, b | aab=a, bab=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. ab ⇒ a2
  2. ba ⇒ a2
  3. a3 ⇒ a 
# ab:aab=a,bab=a ab
ab=aa
ba=aa
aaa=a

Staircase diagram

Right Cayley graph (truncated)

Other isomorphic instances

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

41 total

Σ#PresentationMapping
8599⟨a, b | aba=a, bab=a⟩φ(a) = a, φ(b) = b
8638⟨a, b | ab=aa, baa=a⟩φ(a) = a, φ(b) = b
8640⟨a, b | ab=aa, bab=a⟩φ(a) = a, φ(b) = b
104124⟨a, b | aab=aaa, baa=a⟩φ(a) = a, φ(b) = b
104160⟨a, b | abb=aab, bab=a⟩φ(a) = a, φ(b) = b
104166⟨a, b | abb=aba, bab=a⟩φ(a) = a, φ(b) = b
104178⟨a, b | baa=abb, bab=a⟩φ(a) = a, φ(b) = b
104181⟨a, b | baa=abb, bba=b⟩φ(a) = b, φ(b) = a
104191⟨a, b | bab=aba, bba=b⟩φ(a) = b, φ(b) = a
106350⟨a, b | aab=a, baaaa=a⟩φ(a) = a, φ(b) = b
106356⟨a, b | aab=a, baabb=a⟩φ(a) = a, φ(b) = b
106360⟨a, b | aab=a, babab=a⟩φ(a) = a, φ(b) = b
106362⟨a, b | aab=a, babba=a⟩φ(a) = a, φ(b) = b
106478⟨a, b | aba=a, babab=a⟩φ(a) = a, φ(b) = b
106493⟨a, b | aba=b, aaabb=b⟩φ(a) = b, φ(b) = a
106497⟨a, b | aba=b, aabab=b⟩φ(a) = b, φ(b) = a
106499⟨a, b | aba=b, aabba=b⟩φ(a) = b, φ(b) = a
106503⟨a, b | aba=b, abaab=b⟩φ(a) = b, φ(b) = a
106505⟨a, b | aba=b, ababa=b⟩φ(a) = b, φ(b) = a
106515⟨a, b | aba=b, baaab=b⟩φ(a) = b, φ(b) = a
106604⟨a, b | aab=a, aaab=ba⟩φ(a) = a, φ(b) = b
106608⟨a, b | aab=a, aaba=ba⟩φ(a) = a, φ(b) = b
106616⟨a, b | aab=a, abaa=ba⟩φ(a) = a, φ(b) = b
106628⟨a, b | aab=a, abbb=ba⟩φ(a) = a, φ(b) = b
106631⟨a, b | aab=a, baaa=ab⟩φ(a) = a, φ(b) = b
106634⟨a, b | aab=a, baab=aa⟩φ(a) = a, φ(b) = b
106638⟨a, b | aab=a, baba=aa⟩φ(a) = a, φ(b) = b
106643⟨a, b | aab=a, babb=ab⟩φ(a) = a, φ(b) = b
106731⟨a, b | aba=a, aaab=ba⟩φ(a) = a, φ(b) = b
106768⟨a, b | aba=b, aaab=bb⟩φ(a) = b, φ(b) = a
106772⟨a, b | aba=b, aaba=bb⟩φ(a) = b, φ(b) = a
106774⟨a, b | aba=b, aabb=ab⟩φ(a) = b, φ(b) = a
106775⟨a, b | aba=b, aabb=ba⟩φ(a) = b, φ(b) = a
106778⟨a, b | aba=b, abab=ab⟩φ(a) = b, φ(b) = a
106779⟨a, b | aba=b, abab=ba⟩φ(a) = b, φ(b) = a
106782⟨a, b | aba=b, abba=ab⟩φ(a) = b, φ(b) = a
106789⟨a, b | aba=b, baab=ab⟩φ(a) = b, φ(b) = a
106813⟨a, b | aab=a, bab=aab⟩φ(a) = a, φ(b) = b
106831⟨a, b | aba=a, bab=aba⟩φ(a) = a, φ(b) = b
106835⟨a, b | aba=b, abb=aba⟩φ(a) = b, φ(b) = a
106839⟨a, b | aba=b, bab=aba⟩φ(a) = b, φ(b) = a