#944 ⟨a, b | ab=a, bbaa=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. a2 ⇒ a
  2. ab ⇒ a
  3. b2a ⇒ a 
# ab:ab=a,bbaa=a ab
aa=a
ab=a
bba=a

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.

44 total

Σ#PresentationMapping
92044⟨a, b | aab=a, bbaa=a⟩φ(a) = a, φ(b) = b
92986⟨a, b | ab=a, bbaab=a⟩φ(a) = a, φ(b) = b
92988⟨a, b | ab=a, bbaba=a⟩φ(a) = a, φ(b) = b
93121⟨a, b | ab=a, bbaa=ab⟩φ(a) = a, φ(b) = b
105118⟨a, b | aab=aa, bbaa=a⟩φ(a) = a, φ(b) = b
108814⟨a, b | ab=a, bbaabb=a⟩φ(a) = a, φ(b) = b
108818⟨a, b | ab=a, bbabab=a⟩φ(a) = a, φ(b) = b
108820⟨a, b | ab=a, bbabba=a⟩φ(a) = a, φ(b) = b
109085⟨a, b | ab=a, bbaab=ab⟩φ(a) = a, φ(b) = b
109089⟨a, b | ab=a, bbaba=ab⟩φ(a) = a, φ(b) = b
109355⟨a, b | ab=a, bbaa=abb⟩φ(a) = a, φ(b) = b
1112234⟨a, b | aaab=aa, bbaa=a⟩φ(a) = a, φ(b) = b
1112578⟨a, b | abba=ab, bbaa=a⟩φ(a) = a, φ(b) = b
1114715⟨a, b | aabb=a, bbaab=a⟩φ(a) = a, φ(b) = b
1114779⟨a, b | abab=a, bbaab=a⟩φ(a) = a, φ(b) = b
1114781⟨a, b | abab=a, bbaba=a⟩φ(a) = a, φ(b) = b
1115595⟨a, b | aab=aa, bbaab=a⟩φ(a) = a, φ(b) = b
1118928⟨a, b | aab=a, bbaaaa=a⟩φ(a) = a, φ(b) = b
1118930⟨a, b | aab=a, bbaaab=a⟩φ(a) = a, φ(b) = b
1118932⟨a, b | aab=a, bbaaba=a⟩φ(a) = a, φ(b) = b
1118936⟨a, b | aab=a, bbabaa=a⟩φ(a) = a, φ(b) = b
1119472⟨a, b | aab=a, bbaaa=aa⟩φ(a) = a, φ(b) = b
1119473⟨a, b | aab=a, bbaaa=ab⟩φ(a) = a, φ(b) = b
1119477⟨a, b | aab=a, bbaab=ab⟩φ(a) = a, φ(b) = b
1119481⟨a, b | aab=a, bbaba=ab⟩φ(a) = a, φ(b) = b
1119950⟨a, b | aab=a, aabb=bba⟩φ(a) = a, φ(b) = b
1119966⟨a, b | aab=a, abab=bba⟩φ(a) = a, φ(b) = b
1119974⟨a, b | aab=a, abba=bba⟩φ(a) = a, φ(b) = b
1119982⟨a, b | aab=a, abbb=bba⟩φ(a) = a, φ(b) = b
1120017⟨a, b | aab=a, bbaa=aab⟩φ(a) = a, φ(b) = b
1120018⟨a, b | aab=a, bbaa=aba⟩φ(a) = a, φ(b) = b
1120019⟨a, b | aab=a, bbaa=abb⟩φ(a) = a, φ(b) = b
1120027⟨a, b | aab=a, bbab=abb⟩φ(a) = a, φ(b) = b
1120212⟨a, b | aba=a, abab=bba⟩φ(a) = a, φ(b) = b
1124538⟨a, b | ab=a, bbaabbb=a⟩φ(a) = a, φ(b) = b
1124546⟨a, b | ab=a, bbababb=a⟩φ(a) = a, φ(b) = b
1124550⟨a, b | ab=a, bbabbab=a⟩φ(a) = a, φ(b) = b
1124552⟨a, b | ab=a, bbabbba=a⟩φ(a) = a, φ(b) = b
1125065⟨a, b | ab=a, bbaabb=ab⟩φ(a) = a, φ(b) = b
1125073⟨a, b | ab=a, bbabab=ab⟩φ(a) = a, φ(b) = b
1125077⟨a, b | ab=a, bbabba=ab⟩φ(a) = a, φ(b) = b
1125607⟨a, b | ab=a, bbaab=abb⟩φ(a) = a, φ(b) = b
1125615⟨a, b | ab=a, bbaba=abb⟩φ(a) = a, φ(b) = b
1125865⟨a, b | ab=a, 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.

12 total

Σ#PresentationMapping
1112469⟨a, b | aabb=ba, abaa=a⟩φ(a) = a, φ(b) = b
1112472⟨a, b | aabb=ba, abba=a⟩φ(a) = a, φ(b) = b
1112476⟨a, b | aabb=ba, baaa=a⟩φ(a) = a, φ(b) = b
1112478⟨a, b | aabb=ba, baba=a⟩φ(a) = a, φ(b) = b
1112481⟨a, b | aabb=ba, bbaa=a⟩φ(a) = a, φ(b) = b
1114703⟨a, b | aabb=a, baabb=a⟩φ(a) = a, φ(b) = b
1114709⟨a, b | aabb=a, babba=a⟩φ(a) = a, φ(b) = b
1114823⟨a, b | abba=a, baabb=a⟩φ(a) = a, φ(b) = b
1115831⟨a, b | aba=aa, baabb=a⟩φ(a) = a, φ(b) = b
1119142⟨a, b | aba=a, baaabb=a⟩φ(a) = a, φ(b) = b
1119645⟨a, b | aba=a, aaabb=ba⟩φ(a) = a, φ(b) = b
1119671⟨a, b | aba=a, ababb=ba⟩φ(a) = a, φ(b) = b