#7411 ⟨a, b, c | ab=1, acac=bb⟩

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 ⋅ a²(ca)² = a and a ⋅ 1 = a, however a²(ca)² ≠ 1
Not right cancellative, because right multiplication by a(ac)² is not injective:
- a²(ca)² ⋅ a(ac)² = a(ac)² and 1 ⋅ a(ac)² = a(ac)², however a²(ca)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(c) = deg(a) = 0, c < a; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:ab=1,acac=bb ca/b - -
aaacac=1
aacacacac=acacaacac
aacacaacac=acac
b=aacac