#5587 ⟨a, b, c | ab=c, bcac=c⟩

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:
- c² ⋅ d = d and 1 ⋅ d = d, however c² ≠ 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 = ac
Reduction order:
- Left-to-right recursive path with deg(b) = deg(c) = deg(d) = 0, b < c < d; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# abc:ab=c,bcac=c bcd/a ac=d morph:2/1
bcd=c
ccd=d
ab=c
ac=d
ad=dcd