#1586 ⟨a, b, c | aaa=bc, acc=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 b is not injective:
- b ⋅ c⁷b = b and b ⋅ 1 = b, however c⁷b ≠ 1
Not right cancellative, because right multiplication by c is not injective:
- bc³b ⋅ c = bcbc³ and bcbc² ⋅ c = bcbc³, however bc³b ≠ bcbc²

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(c) = 0, b < c; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:aaa=bc,acc=1 bc/a - -
bcccbc=bcbccc
bcccccbc=bcbccccc
bccccccc=1
a=bccccc