#5388 ⟨a, b | abbaaab=abbb⟩

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 ⋅ b²a³b = ab³ and a ⋅ b³ = ab³, however b²a³b ≠ b³
Not right cancellative, because right multiplication by b is not injective:
- ab²a³ ⋅ b = ab³ and ab² ⋅ b = ab³, however ab²a³ ≠ ab²

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 = abbb
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:abbaaab=abbb ac/b abbb=c magic:0
cbb=abbaac
cbaaab=abbaac
abbb=c
abbaaab=c