#1573 ⟨a, b, c | aaa=bb, bac=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 ⋅ a³(ca)² = a and a ⋅ 1 = a, however a³(ca)² ≠ 1
Not right cancellative, because right multiplication by a³cac is not injective:
- a³(ca)² ⋅ a³cac = a³cac and 1 ⋅ a³cac = a³cac, however a³(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:aaa=bb,bac=1 ca/b - -
aaaacac=1
aaaaaaac=aaaacaaa
aaaacaaaac=aaa
b=aaaac