#3475 ⟨a, b, c | ba=ac, cbb=b⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not right cancellative, because right multiplication by d is not injective:
- cb ⋅ d = d and 1 ⋅ d = d, however cb ≠ 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. d = ab
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.

# abc:ba=ac,cbb=b d/bac ab=d morph:2/0
ddb=bdd
ad=bdd
cd=db
bdb=d
ab=d
ac=ba
cbd=d
cbb=b