#1576 ⟨a, b, c | aaa=bb, bcc=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 ⋅ a²c⁴a = a and a ⋅ 1 = a, however a²c⁴a ≠ 1
Not right cancellative, because right multiplication by a²c⁴ is not injective:
- a²c⁴a ⋅ a²c⁴ = a²c⁴ and 1 ⋅ a²c⁴ = a²c⁴, however a²c⁴a ≠ 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(c) = deg(a) = 0, c < a; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:aaa=bb,bcc=1 ca/b - -
aaacccc=1
aaaaaacc=aaaccaaa
aaaccaaacc=aaa
b=aaacc