#22833 ⟨a, b | aaa=1, baabb=abb⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element ac has infinite order
Not right cancellative, because right multiplication by d is not injective:
- ba ⋅ d = d and 1 ⋅ d = d, however ba ≠ 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 = ab
2. d = cb
Reduction order:
- Left-to-right recursive path with deg(d) = 0; deg(b) = deg(a) = deg(c) = 1, b < a < c
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# ab:aaa=1,baabb=abb d/bac ab=c,cb=d morph:2/0,2/0
cd=dad
bad=d
ab=c
aad=bb
cb=d
cad=ad
aaa=1
aac=b