#7761 ⟨a, b, c | ab=1, bbb=aac⟩

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 ⋅ a⁴ca = a and a ⋅ 1 = a, however a⁴ca ≠ 1
Not right cancellative, because right multiplication by a⁴c is not injective:
- a⁴ca ⋅ a⁴c = a⁴c and 1 ⋅ a⁴c = a⁴c, however a⁴ca ≠ 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(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:ab=1,bbb=aac ac/b - -
aaaaac=1
aacaaac=aaacaac
aacaaaac=aaaacaac
b=aaaac