#15954 ⟨a, b | aaa=aa, aaba=ba⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a² = a² and a ⋅ a = a², however a² ≠ a
Not right cancellative, because right multiplication by c is not injective:
- a ⋅ c = c and 1 ⋅ c = c, however a ≠ 1

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

# ab:aaa=aa,aaba=ba a/cb bba=c morph:3/1
aaa=aa
caa=ca
ac=c
aba=ba
bc=cba
bba=c