#1581 ⟨a, b, c | aaa=bc, aac=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 ⋅ c²bc³b = b and b ⋅ 1 = b, however c²bc³b ≠ 1
Not right cancellative, because right multiplication by c is not injective:
- b(c²b)²c ⋅ c = bc and b ⋅ c = bc, however b(c²b)²c ≠ b

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

# abc:aaa=bc,aac=1 cb/a - -
bcbcc=bccbc
bccbccc=1
bccbccbcc=bc
a=bcc