#6073 ⟨a, b, c | ab=c, bac=cc⟩

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 c is not injective:
- ba ⋅ c = c² and c ⋅ c = c², however ba ≠ c

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

# abc:ab=c,bac=cc dca/b cac=d morph:3/1
cd=dc
cad=dac
cac=d
add=dad
adc=dac
acc=d
bd=ccc
bad=dc
bac=cc
ab=c