#920 ⟨a, b | ab=a, aaaa=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 ⇒ a
  2. a4 ⇒ a 
# ab:ab=a,aaaa=a ab
ab=a
aaaa=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.

66 total

Σ#PresentationMapping
92938⟨a, b | ab=a, aaaab=a⟩φ(a) = a, φ(b) = b
92940⟨a, b | ab=a, aaaba=a⟩φ(a) = a, φ(b) = b
92944⟨a, b | ab=a, aabaa=a⟩φ(a) = a, φ(b) = b
92952⟨a, b | ab=a, abaaa=a⟩φ(a) = a, φ(b) = b
93073⟨a, b | ab=a, aaaa=ab⟩φ(a) = a, φ(b) = b
105094⟨a, b | aab=aa, aaaa=a⟩φ(a) = a, φ(b) = b
108718⟨a, b | ab=a, aaaabb=a⟩φ(a) = a, φ(b) = b
108722⟨a, b | ab=a, aaabab=a⟩φ(a) = a, φ(b) = b
108724⟨a, b | ab=a, aaabba=a⟩φ(a) = a, φ(b) = b
108730⟨a, b | ab=a, aabaab=a⟩φ(a) = a, φ(b) = b
108732⟨a, b | ab=a, aababa=a⟩φ(a) = a, φ(b) = b
108736⟨a, b | ab=a, aabbaa=a⟩φ(a) = a, φ(b) = b
108746⟨a, b | ab=a, abaaab=a⟩φ(a) = a, φ(b) = b
108748⟨a, b | ab=a, abaaba=a⟩φ(a) = a, φ(b) = b
108752⟨a, b | ab=a, ababaa=a⟩φ(a) = a, φ(b) = b
108760⟨a, b | ab=a, abbaaa=a⟩φ(a) = a, φ(b) = b
108989⟨a, b | ab=a, aaaab=ab⟩φ(a) = a, φ(b) = b
108993⟨a, b | ab=a, aaaba=ab⟩φ(a) = a, φ(b) = b
109001⟨a, b | ab=a, aabaa=ab⟩φ(a) = a, φ(b) = b
109017⟨a, b | ab=a, abaaa=ab⟩φ(a) = a, φ(b) = b
109259⟨a, b | ab=a, aaaa=abb⟩φ(a) = a, φ(b) = b
1114331⟨a, b | aaaa=a, aaaab=a⟩φ(a) = a, φ(b) = b
1115547⟨a, b | aab=aa, aaaab=a⟩φ(a) = a, φ(b) = b
1115549⟨a, b | aab=aa, aaaba=a⟩φ(a) = a, φ(b) = b
1115553⟨a, b | aab=aa, aabaa=a⟩φ(a) = a, φ(b) = b
1115561⟨a, b | aab=aa, abaaa=a⟩φ(a) = a, φ(b) = b
1115803⟨a, b | aba=aa, aaaab=a⟩φ(a) = a, φ(b) = b
1115888⟨a, b | aba=ab, babbb=b⟩φ(a) = b, φ(b) = a
1115896⟨a, b | aba=ab, bbabb=b⟩φ(a) = b, φ(b) = a
1115900⟨a, b | aba=ab, bbbab=b⟩φ(a) = b, φ(b) = a
1115902⟨a, b | aba=ab, bbbba=b⟩φ(a) = b, φ(b) = a
1124346⟨a, b | ab=a, aaaabbb=a⟩φ(a) = a, φ(b) = b
1124354⟨a, b | ab=a, aaababb=a⟩φ(a) = a, φ(b) = b
1124358⟨a, b | ab=a, aaabbab=a⟩φ(a) = a, φ(b) = b
1124360⟨a, b | ab=a, aaabbba=a⟩φ(a) = a, φ(b) = b
1124370⟨a, b | ab=a, aabaabb=a⟩φ(a) = a, φ(b) = b
1124374⟨a, b | ab=a, aababab=a⟩φ(a) = a, φ(b) = b
1124376⟨a, b | ab=a, aababba=a⟩φ(a) = a, φ(b) = b
1124382⟨a, b | ab=a, aabbaab=a⟩φ(a) = a, φ(b) = b
1124384⟨a, b | ab=a, aabbaba=a⟩φ(a) = a, φ(b) = b
1124388⟨a, b | ab=a, aabbbaa=a⟩φ(a) = a, φ(b) = b
1124402⟨a, b | ab=a, abaaabb=a⟩φ(a) = a, φ(b) = b
1124406⟨a, b | ab=a, abaabab=a⟩φ(a) = a, φ(b) = b
1124408⟨a, b | ab=a, abaabba=a⟩φ(a) = a, φ(b) = b
1124414⟨a, b | ab=a, ababaab=a⟩φ(a) = a, φ(b) = b
1124416⟨a, b | ab=a, abababa=a⟩φ(a) = a, φ(b) = b
1124420⟨a, b | ab=a, ababbaa=a⟩φ(a) = a, φ(b) = b
1124430⟨a, b | ab=a, abbaaab=a⟩φ(a) = a, φ(b) = b
1124432⟨a, b | ab=a, abbaaba=a⟩φ(a) = a, φ(b) = b
1124436⟨a, b | ab=a, abbabaa=a⟩φ(a) = a, φ(b) = b
1124444⟨a, b | ab=a, abbbaaa=a⟩φ(a) = a, φ(b) = b
1124873⟨a, b | ab=a, aaaabb=ab⟩φ(a) = a, φ(b) = b
1124881⟨a, b | ab=a, aaabab=ab⟩φ(a) = a, φ(b) = b
1124885⟨a, b | ab=a, aaabba=ab⟩φ(a) = a, φ(b) = b
1124897⟨a, b | ab=a, aabaab=ab⟩φ(a) = a, φ(b) = b
1124901⟨a, b | ab=a, aababa=ab⟩φ(a) = a, φ(b) = b
1124909⟨a, b | ab=a, aabbaa=ab⟩φ(a) = a, φ(b) = b
1124929⟨a, b | ab=a, abaaab=ab⟩φ(a) = a, φ(b) = b
1124933⟨a, b | ab=a, abaaba=ab⟩φ(a) = a, φ(b) = b
1124941⟨a, b | ab=a, ababaa=ab⟩φ(a) = a, φ(b) = b
1124957⟨a, b | ab=a, abbaaa=ab⟩φ(a) = a, φ(b) = b
1125415⟨a, b | ab=a, aaaab=abb⟩φ(a) = a, φ(b) = b
1125423⟨a, b | ab=a, aaaba=abb⟩φ(a) = a, φ(b) = b
1125439⟨a, b | ab=a, aabaa=abb⟩φ(a) = a, φ(b) = b
1125471⟨a, b | ab=a, abaaa=abb⟩φ(a) = a, φ(b) = b
1125813⟨a, b | ab=a, abbb=aaaa⟩φ(a) = a, φ(b) = b