#1812 ⟨a, b, c | aba=ab, bbc=1⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by d is not injective:
- d ⋅ d²c = d and d ⋅ 1 = d, however d²c ≠ 1
Not right cancellative, because right multiplication by bc is not injective:
- bcb ⋅ bc = bc and 1 ⋅ bc = bc, however bcb ≠ 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(c) = deg(d) = 0, c < d; deg(b) = deg(a) = 1, b < a
Certificate: derivations of all rewriting rules from the defining relations.
Morphocompletion: how the auxiliary generators were found.

# abc:aba=ab,bbc=1 cd/ba ab=d morph:2/1
dddc=d
db=dd
ddcb=d
a=ddc
bbc=1