#5299 ⟨a, b | aaa=aa, aba=ab⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element c has infinite order
Not left cancellative, because left multiplication by c is not injective:
- c ⋅ a = c and c ⋅ 1 = c, however a ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a² ⋅ a = a² and a ⋅ a = a², however a² ≠ 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 = abb
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.
Morphocompletion: how the auxiliary generators were found.

# ab:aaa=aa,aba=ab ac/b abb=c morph:3/1
ca=c
aaa=aa
aac=ac
aba=ab
cb=abc
abb=c