#569 ⟨a, b | aaa=a, bab=a⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element ac has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a² = a and a ⋅ 1 = a, however a² ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a² ⋅ a = a and 1 ⋅ a = a, however a² ≠ 1

Format:	Pretty Plain
Word:
	Enter a word above to compute its normal form. Tips: Lowercase letters stand for generators. Spaces are ignored. Numbers repeat the previous letter, e.g. `b90`.
Strategy:	Leftmost Rightmost
Result:	1 1

Auxiliary generators:
1. c = abb
Reduction order:
- Left-to-right recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:aaa=a,bab=a ac/b abb=c morph:3/1
cc=aa
aaa=a
aac=c
caa=c
ab=bc
cb=bcac
bba=aca
bbc=a

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

8 total

Σ	#	Presentation	Mapping
10	6266	⟨a, b \| aaa=a, baaab=a⟩	φ(a) = a, φ(b) = b
10	6507	⟨a, b \| aba=b, ababb=b⟩	φ(a) = b, φ(b) = a
10	6511	⟨a, b \| aba=b, abbba=b⟩	φ(a) = b, φ(b) = a
10	6519	⟨a, b \| aba=b, babab=b⟩	φ(a) = b, φ(b) = a
10	6785	⟨a, b \| aba=b, abbb=ab⟩	φ(a) = b, φ(b) = a
10	6793	⟨a, b \| aba=b, babb=ba⟩	φ(a) = b, φ(b) = a
10	6801	⟨a, b \| aaa=a, bab=aaa⟩	φ(a) = a, φ(b) = b
10	6841	⟨a, b \| aba=b, bbb=aba⟩	φ(a) = b, φ(b) = a