#77 ⟨a, b | ab=1, aabb=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. ab ⇒ 1 
# ab:ab=1,aabb=1 ab
ab=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.

108 total

Σ#PresentationMapping
679⟨a, b | ab=1, abab=1⟩φ(a) = a, φ(b) = b
698⟨a, b | ab=1, aab=a⟩φ(a) = a, φ(b) = b
6100⟨a, b | ab=1, aba=a⟩φ(a) = a, φ(b) = b
8514⟨a, b | aab=a, aabb=1⟩φ(a) = a, φ(b) = b
8546⟨a, b | aba=a, aabb=1⟩φ(a) = a, φ(b) = b
8547⟨a, b | aba=a, abab=1⟩φ(a) = a, φ(b) = b
81067⟨a, b | ab=1, aaabbb=1⟩φ(a) = a, φ(b) = b
81071⟨a, b | ab=1, aababb=1⟩φ(a) = a, φ(b) = b
81073⟨a, b | ab=1, aabbab=1⟩φ(a) = a, φ(b) = b
81079⟨a, b | ab=1, ababab=1⟩φ(a) = a, φ(b) = b
81142⟨a, b | ab=1, aaabb=a⟩φ(a) = a, φ(b) = b
81146⟨a, b | ab=1, aabab=a⟩φ(a) = a, φ(b) = b
81148⟨a, b | ab=1, aabba=a⟩φ(a) = a, φ(b) = b
81152⟨a, b | ab=1, abaab=a⟩φ(a) = a, φ(b) = b
81154⟨a, b | ab=1, ababa=a⟩φ(a) = a, φ(b) = b
81208⟨a, b | ab=1, aaab=aa⟩φ(a) = a, φ(b) = b
81212⟨a, b | ab=1, aaba=aa⟩φ(a) = a, φ(b) = b
81217⟨a, b | ab=1, aabb=ab⟩φ(a) = a, φ(b) = b
81219⟨a, b | ab=1, abaa=aa⟩φ(a) = a, φ(b) = b
81224⟨a, b | ab=1, abab=ab⟩φ(a) = a, φ(b) = b
81228⟨a, b | ab=1, abba=ba⟩φ(a) = a, φ(b) = b
81236⟨a, b | ab=1, baba=ba⟩φ(a) = a, φ(b) = b
81260⟨a, b | ab=1, aba=aab⟩φ(a) = a, φ(b) = b
103778⟨a, b | aaab=aa, aabb=1⟩φ(a) = a, φ(b) = b
103833⟨a, b | aaba=aa, aabb=1⟩φ(a) = a, φ(b) = b
103840⟨a, b | aaba=aa, baba=1⟩φ(a) = b, φ(b) = a
103842⟨a, b | aaba=aa, bbaa=1⟩φ(a) = b, φ(b) = a
103935⟨a, b | abab=ab, baba=1⟩φ(a) = b, φ(b) = a
103937⟨a, b | abab=ab, bbaa=1⟩φ(a) = b, φ(b) = a
103964⟨a, b | abba=ab, bbaa=1⟩φ(a) = b, φ(b) = a
105593⟨a, b | aabb=1, aaabbb=1⟩φ(a) = a, φ(b) = b
105599⟨a, b | aabb=1, aabbab=1⟩φ(a) = a, φ(b) = b
105633⟨a, b | abab=1, aababb=1⟩φ(a) = a, φ(b) = b
105641⟨a, b | abab=1, ababab=1⟩φ(a) = a, φ(b) = b
106045⟨a, b | aab=a, aaabbb=1⟩φ(a) = a, φ(b) = b
106049⟨a, b | aab=a, aababb=1⟩φ(a) = a, φ(b) = b
106173⟨a, b | aba=a, aaabbb=1⟩φ(a) = a, φ(b) = b
106176⟨a, b | aba=a, aababb=1⟩φ(a) = a, φ(b) = b
106178⟨a, b | aba=a, aabbab=1⟩φ(a) = a, φ(b) = b
106183⟨a, b | aba=a, abaabb=1⟩φ(a) = a, φ(b) = b
106184⟨a, b | aba=a, ababab=1⟩φ(a) = a, φ(b) = b
109535⟨a, b | ab=1, aaaabbbb=1⟩φ(a) = a, φ(b) = b
109543⟨a, b | ab=1, aaababbb=1⟩φ(a) = a, φ(b) = b
109547⟨a, b | ab=1, aaabbabb=1⟩φ(a) = a, φ(b) = b
109549⟨a, b | ab=1, aaabbbab=1⟩φ(a) = a, φ(b) = b
109561⟨a, b | ab=1, aabababb=1⟩φ(a) = a, φ(b) = b
109563⟨a, b | ab=1, aababbab=1⟩φ(a) = a, φ(b) = b
109568⟨a, b | ab=1, aabbaabb=1⟩φ(a) = a, φ(b) = b
109570⟨a, b | ab=1, aabbabab=1⟩φ(a) = a, φ(b) = b
109588⟨a, b | ab=1, abaabbab=1⟩φ(a) = a, φ(b) = b
109594⟨a, b | ab=1, abababab=1⟩φ(a) = a, φ(b) = b
109814⟨a, b | ab=1, aaaabbb=a⟩φ(a) = a, φ(b) = b
109822⟨a, b | ab=1, aaababb=a⟩φ(a) = a, φ(b) = b
109826⟨a, b | ab=1, aaabbab=a⟩φ(a) = a, φ(b) = b
109828⟨a, b | ab=1, aaabbba=a⟩φ(a) = a, φ(b) = b
109836⟨a, b | ab=1, aabaabb=a⟩φ(a) = a, φ(b) = b
109840⟨a, b | ab=1, aababab=a⟩φ(a) = a, φ(b) = b
109842⟨a, b | ab=1, aababba=a⟩φ(a) = a, φ(b) = b
109846⟨a, b | ab=1, aabbaab=a⟩φ(a) = a, φ(b) = b
109848⟨a, b | ab=1, aabbaba=a⟩φ(a) = a, φ(b) = b
109853⟨a, b | ab=1, aabbbab=b⟩φ(a) = a, φ(b) = b
109864⟨a, b | ab=1, abaabab=a⟩φ(a) = a, φ(b) = b
109866⟨a, b | ab=1, abaabba=a⟩φ(a) = a, φ(b) = b
109870⟨a, b | ab=1, ababaab=a⟩φ(a) = a, φ(b) = b
109872⟨a, b | ab=1, abababa=a⟩φ(a) = a, φ(b) = b
1010076⟨a, b | ab=1, aaaabb=aa⟩φ(a) = a, φ(b) = b
1010084⟨a, b | ab=1, aaabab=aa⟩φ(a) = a, φ(b) = b
1010088⟨a, b | ab=1, aaabba=aa⟩φ(a) = a, φ(b) = b
1010093⟨a, b | ab=1, aaabbb=ab⟩φ(a) = a, φ(b) = b
1010099⟨a, b | ab=1, aabaab=aa⟩φ(a) = a, φ(b) = b
1010103⟨a, b | ab=1, aababa=aa⟩φ(a) = a, φ(b) = b
1010108⟨a, b | ab=1, aababb=ab⟩φ(a) = a, φ(b) = b
1010110⟨a, b | ab=1, aabbaa=aa⟩φ(a) = a, φ(b) = b
1010115⟨a, b | ab=1, aabbab=ab⟩φ(a) = a, φ(b) = b
1010120⟨a, b | ab=1, aabbba=ba⟩φ(a) = a, φ(b) = b
1010126⟨a, b | ab=1, abaaab=aa⟩φ(a) = a, φ(b) = b
1010130⟨a, b | ab=1, abaaba=aa⟩φ(a) = a, φ(b) = b
1010134⟨a, b | ab=1, ababaa=aa⟩φ(a) = a, φ(b) = b
1010139⟨a, b | ab=1, ababab=ab⟩φ(a) = a, φ(b) = b
1010143⟨a, b | ab=1, ababba=ba⟩φ(a) = a, φ(b) = b
1010151⟨a, b | ab=1, abbaab=ba⟩φ(a) = a, φ(b) = b
1010154⟨a, b | ab=1, abbaba=ba⟩φ(a) = a, φ(b) = b
1010178⟨a, b | ab=1, baabba=ba⟩φ(a) = a, φ(b) = b
1010185⟨a, b | ab=1, bababa=ba⟩φ(a) = a, φ(b) = b
1010352⟨a, b | ab=1, aaaab=aaa⟩φ(a) = a, φ(b) = b
1010360⟨a, b | ab=1, aaaba=aaa⟩φ(a) = a, φ(b) = b
1010369⟨a, b | ab=1, aaabb=aab⟩φ(a) = a, φ(b) = b
1010370⟨a, b | ab=1, aaabb=aba⟩φ(a) = a, φ(b) = b
1010376⟨a, b | ab=1, aabaa=aaa⟩φ(a) = a, φ(b) = b
1010385⟨a, b | ab=1, aabab=aab⟩φ(a) = a, φ(b) = b
1010386⟨a, b | ab=1, aabab=aba⟩φ(a) = a, φ(b) = b
1010393⟨a, b | ab=1, aabba=aab⟩φ(a) = a, φ(b) = b
1010394⟨a, b | ab=1, aabba=aba⟩φ(a) = a, φ(b) = b
1010400⟨a, b | ab=1, abaaa=aaa⟩φ(a) = a, φ(b) = b
1010409⟨a, b | ab=1, abaab=aab⟩φ(a) = a, φ(b) = b
1010410⟨a, b | ab=1, abaab=aba⟩φ(a) = a, φ(b) = b
1010417⟨a, b | ab=1, ababa=aab⟩φ(a) = a, φ(b) = b
1010418⟨a, b | ab=1, ababa=aba⟩φ(a) = a, φ(b) = b
1010428⟨a, b | ab=1, abbaa=baa⟩φ(a) = a, φ(b) = b
1010438⟨a, b | ab=1, abbba=bba⟩φ(a) = a, φ(b) = b
1010452⟨a, b | ab=1, baaba=baa⟩φ(a) = a, φ(b) = b
1010460⟨a, b | ab=1, babaa=baa⟩φ(a) = a, φ(b) = b
1010540⟨a, b | ab=1, aaba=aaab⟩φ(a) = a, φ(b) = b
1010545⟨a, b | ab=1, abaa=aaab⟩φ(a) = a, φ(b) = b
1010546⟨a, b | ab=1, abaa=aaba⟩φ(a) = a, φ(b) = b
1010551⟨a, b | ab=1, abab=aabb⟩φ(a) = a, φ(b) = b
1010575⟨a, b | ab=1, baab=abba⟩φ(a) = a, φ(b) = b
1010583⟨a, b | ab=1, baba=abba⟩φ(a) = a, φ(b) = b