#2085 ⟨a, b | abbbaaab=aa⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b³a³b = a² and a ⋅ a = a², however b³a³b ≠ a

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:
- Right-to-left recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:abbbaaab=aa reversed:ac/b abbb=c morph:4/3
cacacaac=aa
aaacacaac=cacacaaaa
aab=cacaac
caacb=ac
aaaacb=cacacaaac
abbb=c