#2968 ⟨a, b | ab=a, baaaa=a⟩

Up:Monoids with two generators and two relations
Prev:#2936 ⟨a, b | ab=a, aaaaa=a⟩
Next:#2984 ⟨a, b | ab=a, bbaaa=a⟩

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. ba ⇒ a
  3. a4 ⇒ a 
# ab:ab=a,baaaa=a ab
ab=a
ba=a
aaaa=a

Staircase diagram

Right Cayley graph (truncated)

Other isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

23 total

Σ#PresentationMapping
108778⟨a, b | ab=a, baaaab=a⟩φ(a) = a, φ(b) = b
108780⟨a, b | ab=a, baaaba=a⟩φ(a) = a, φ(b) = b
108784⟨a, b | ab=a, baabaa=a⟩φ(a) = a, φ(b) = b
108792⟨a, b | ab=a, babaaa=a⟩φ(a) = a, φ(b) = b
109049⟨a, b | ab=a, baaaa=ab⟩φ(a) = a, φ(b) = b
1115577⟨a, b | aab=aa, baaaa=a⟩φ(a) = a, φ(b) = b
1115704⟨a, b | aab=ba, abbbb=b⟩φ(a) = b, φ(b) = a
1115872⟨a, b | aba=ab, abbbb=b⟩φ(a) = b, φ(b) = a
1124466⟨a, b | ab=a, baaaabb=a⟩φ(a) = a, φ(b) = b
1124470⟨a, b | ab=a, baaabab=a⟩φ(a) = a, φ(b) = b
1124472⟨a, b | ab=a, baaabba=a⟩φ(a) = a, φ(b) = b
1124478⟨a, b | ab=a, baabaab=a⟩φ(a) = a, φ(b) = b
1124480⟨a, b | ab=a, baababa=a⟩φ(a) = a, φ(b) = b
1124484⟨a, b | ab=a, baabbaa=a⟩φ(a) = a, φ(b) = b
1124494⟨a, b | ab=a, babaaab=a⟩φ(a) = a, φ(b) = b
1124496⟨a, b | ab=a, babaaba=a⟩φ(a) = a, φ(b) = b
1124500⟨a, b | ab=a, bababaa=a⟩φ(a) = a, φ(b) = b
1124508⟨a, b | ab=a, babbaaa=a⟩φ(a) = a, φ(b) = b
1124993⟨a, b | ab=a, baaaab=ab⟩φ(a) = a, φ(b) = b
1124997⟨a, b | ab=a, baaaba=ab⟩φ(a) = a, φ(b) = b
1125005⟨a, b | ab=a, baabaa=ab⟩φ(a) = a, φ(b) = b
1125021⟨a, b | ab=a, babaaa=ab⟩φ(a) = a, φ(b) = b
1125535⟨a, b | ab=a, baaaa=abb⟩φ(a) = a, φ(b) = b