#5123 ⟨a, b | aabaaab=abba⟩

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 ⋅ aba³b = ab²a and a ⋅ b²a = ab²a, however aba³b ≠ b²a

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 = abba
Reduction order:
- Left-to-right recursive path with deg(a) = 0; deg(b) = deg(c) = 1, b < c
Certificate: derivations of all rewriting rules from the defining relations.

# ab:aabaaab=abba a/bc abba=c magic:0
abba=c
aabaaab=c
cba=aabaac
caaab=aabac
cbba=abbc
cabaaab=abbc