#4756 ⟨a, b | abaaaaab=abb⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ba⁵b = ab² and a ⋅ b² = ab², however ba⁵b ≠ b²
Not right cancellative, because right multiplication by b is not injective:
- aba⁵ ⋅ b = ab² and ab ⋅ b = ab², however aba⁵ ≠ ab

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.

# ab:abaaaaab=abb ac/b abb=c magic:0
cb=abaaaac
caaaaab=abaaaac
abb=c
abaaaaab=c