#302 ⟨a, b | aa=1, bbbbb=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. a2 ⇒ 1
  2. b5 ⇒ 1 
# ab:aa=1,bbbbb=1 ab
aa=1
bbbbb=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.

47 total

Σ#PresentationMapping
91939⟨a, b | aab=b, bbbbb=1⟩φ(a) = a, φ(b) = b
93229⟨a, b | aa=1, aabbbbb=1⟩φ(a) = a, φ(b) = b
93250⟨a, b | aa=1, abbbbba=1⟩φ(a) = a, φ(b) = b
93259⟨a, b | aa=1, baabbbb=1⟩φ(a) = a, φ(b) = b
93267⟨a, b | aa=1, bbaabbb=1⟩φ(a) = a, φ(b) = b
93386⟨a, b | aa=1, abbbbb=a⟩φ(a) = a, φ(b) = b
93541⟨a, b | aa=1, bbbbb=aa⟩φ(a) = a, φ(b) = b
1111948⟨a, b | aabb=aa, aaaaa=1⟩φ(a) = b, φ(b) = a
1112076⟨a, b | abba=aa, aaaaa=1⟩φ(a) = b, φ(b) = a
1118173⟨a, b | aaa=a, aabbbbb=1⟩φ(a) = a, φ(b) = b
1118194⟨a, b | aaa=a, abbbbba=1⟩φ(a) = a, φ(b) = b
1118203⟨a, b | aaa=a, baabbbb=1⟩φ(a) = a, φ(b) = b
1118211⟨a, b | aaa=a, bbaabbb=1⟩φ(a) = a, φ(b) = b
1118447⟨a, b | aab=b, aabbbbb=1⟩φ(a) = a, φ(b) = b
1118478⟨a, b | aab=b, abbbbba=1⟩φ(a) = a, φ(b) = b
1118495⟨a, b | aab=b, baabbbb=1⟩φ(a) = a, φ(b) = b
1118519⟨a, b | aab=b, bbaabbb=1⟩φ(a) = a, φ(b) = b
1118531⟨a, b | aab=b, bbbaabb=1⟩φ(a) = a, φ(b) = b
1118537⟨a, b | aab=b, bbbbaab=1⟩φ(a) = a, φ(b) = b
1118540⟨a, b | aab=b, bbbbbaa=1⟩φ(a) = a, φ(b) = b
1125943⟨a, b | aa=1, aaaabbbbb=1⟩φ(a) = a, φ(b) = b
1125972⟨a, b | aa=1, aaabbbbba=1⟩φ(a) = a, φ(b) = b
1125987⟨a, b | aa=1, aabaabbbb=1⟩φ(a) = a, φ(b) = b
1126007⟨a, b | aa=1, aabbaabbb=1⟩φ(a) = a, φ(b) = b
1126017⟨a, b | aa=1, aabbbaabb=1⟩φ(a) = a, φ(b) = b
1126021⟨a, b | aa=1, aabbbbaab=1⟩φ(a) = a, φ(b) = b
1126024⟨a, b | aa=1, aabbbbbaa=1⟩φ(a) = a, φ(b) = b
1126050⟨a, b | aa=1, abaabbbba=1⟩φ(a) = a, φ(b) = b
1126082⟨a, b | aa=1, abbaabbba=1⟩φ(a) = a, φ(b) = b
1126119⟨a, b | aa=1, baaaabbbb=1⟩φ(a) = a, φ(b) = b
1126130⟨a, b | aa=1, baabaabbb=1⟩φ(a) = a, φ(b) = b
1126135⟨a, b | aa=1, baabbaabb=1⟩φ(a) = a, φ(b) = b
1126138⟨a, b | aa=1, baabbbaab=1⟩φ(a) = a, φ(b) = b
1126165⟨a, b | aa=1, bbaaaabbb=1⟩φ(a) = a, φ(b) = b
1126168⟨a, b | aa=1, bbaabaabb=1⟩φ(a) = a, φ(b) = b
1126500⟨a, b | aa=1, aaabbbbb=a⟩φ(a) = a, φ(b) = b
1126552⟨a, b | aa=1, aabbbbba=a⟩φ(a) = a, φ(b) = b
1126578⟨a, b | aa=1, abaabbbb=a⟩φ(a) = a, φ(b) = b
1126610⟨a, b | aa=1, abbaabbb=a⟩φ(a) = a, φ(b) = b
1126624⟨a, b | aa=1, abbbaabb=a⟩φ(a) = a, φ(b) = b
1126630⟨a, b | aa=1, abbbbaab=a⟩φ(a) = a, φ(b) = b
1127080⟨a, b | aa=1, aabbbbb=aa⟩φ(a) = a, φ(b) = b
1127161⟨a, b | aa=1, abbbbba=aa⟩φ(a) = a, φ(b) = b
1127194⟨a, b | aa=1, baabbbb=aa⟩φ(a) = a, φ(b) = b
1127223⟨a, b | aa=1, bbaabbb=aa⟩φ(a) = a, φ(b) = b
1127688⟨a, b | aa=1, abbbbb=aaa⟩φ(a) = a, φ(b) = b
1128286⟨a, b | aa=1, bbbbb=aaaa⟩φ(a) = a, φ(b) = b