#1844 ⟨a, b, c | aba=ac, cbc=1⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b(ab)² = a and a ⋅ 1 = a, however b(ab)² ≠ 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

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

# abc:aba=ac,cbc=1 ba/c - -
aab=aba
ababab=a
bc=cb
ac=aba
ccb=1