#271 ⟨a, b | ab=a, bba=a⟩

Up:Monoids with two generators and two relations
Prev:#268 ⟨a, b | ab=a, baa=b⟩
Next:#274 ⟨a, b | ab=a, bbb=b⟩

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. b2a ⇒ a 
# ab:ab=a,bba=a ab
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.

24 total

Σ#PresentationMapping
8946⟨a, b | ab=a, bbab=a⟩φ(a) = a, φ(b) = b
81017⟨a, b | ab=a, bba=ab⟩φ(a) = a, φ(b) = b
92057⟨a, b | aab=b, aaba=b⟩φ(a) = b, φ(b) = a
92990⟨a, b | ab=a, bbabb=a⟩φ(a) = a, φ(b) = b
93125⟨a, b | ab=a, bbab=ab⟩φ(a) = a, φ(b) = b
93190⟨a, b | ab=a, bba=abb⟩φ(a) = a, φ(b) = b
105247⟨a, b | aba=ab, aaba=b⟩φ(a) = b, φ(b) = a
108822⟨a, b | ab=a, bbabbb=a⟩φ(a) = a, φ(b) = b
109093⟨a, b | ab=a, bbabb=ab⟩φ(a) = a, φ(b) = b
109318⟨a, b | ab=a, abbb=bba⟩φ(a) = a, φ(b) = b
109363⟨a, b | ab=a, bbab=abb⟩φ(a) = a, φ(b) = b
1112243⟨a, b | aaab=ab, aaba=b⟩φ(a) = b, φ(b) = a
1114610⟨a, b | aaba=b, aabaa=b⟩φ(a) = b, φ(b) = a
1115850⟨a, b | aba=ab, aabaa=b⟩φ(a) = b, φ(b) = a
1118965⟨a, b | aab=b, aaaaba=b⟩φ(a) = b, φ(b) = a
1119510⟨a, b | aab=b, aaaab=ba⟩φ(a) = b, φ(b) = a
1119513⟨a, b | aab=b, aaaba=ab⟩φ(a) = b, φ(b) = a
1120058⟨a, b | aab=b, aaab=aba⟩φ(a) = b, φ(b) = a
1120065⟨a, b | aab=b, aaba=aab⟩φ(a) = b, φ(b) = a
1124554⟨a, b | ab=a, bbabbbb=a⟩φ(a) = a, φ(b) = b
1125081⟨a, b | ab=a, bbabbb=ab⟩φ(a) = a, φ(b) = b
1125530⟨a, b | ab=a, abbbb=bba⟩φ(a) = a, φ(b) = b
1125623⟨a, b | ab=a, bbabb=abb⟩φ(a) = a, φ(b) = b
1125877⟨a, b | ab=a, bbab=abbb⟩φ(a) = a, φ(b) = b