#5810 ⟨a, b | abaaab=aaaab⟩

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 ⋅ ba³b = a⁴b and a ⋅ a³b = a⁴b, however ba³b ≠ a³b
Not right cancellative, because right multiplication by b is not injective:
- aba³ ⋅ b = a⁴b and a⁴ ⋅ b = a⁴b, however aba³ ≠ a⁴

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

# ab:abaaab=aaaab b/ca aaaab=c magic:0
aaac=caaab
abaac=caaab
aaaab=c
abaaab=c