#1118 ⟨a, b | ababab=aab⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ babc = ac and a ⋅ c = ac, however babc ≠ c
Not right cancellative, because right multiplication by c is not injective:
- aba ⋅ c = c² and c ⋅ c = c², however aba ≠ c

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

# ab:ababab=aab bc/a aab=c magic:0
cab=abc
cac=acc
aab=c
aac=abcc
abac=cc
ababc=ac
ababab=c