#5872 ⟨a, b | ababab=abbba⟩

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 ⋅ b(ab)² = ab³a and a ⋅ b³a = ab³a, however b(ab)² ≠ b³a

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 = abbba
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:ababab=abbba ac/b abbba=c magic:0
cab=abc
cbba=ababc
abbba=c
ababab=c
cbbba=abbbc
cbabab=abbbc