#3304 ⟨a, b, c | bb=ac, cbaa=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 c is not injective:
- c ⋅ (ac)²a³c = c and c ⋅ 1 = c, however (ac)²a³c ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- b ⋅ a = (ac)²a² and a(ca)² ⋅ a = (ac)²a², however b ≠ a(ca)²

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:bb=ac,cbaa=1 ca/b - -
cacaaca=cacacaa
cacacaaa=1
ba=acacaa
cb=cacaac
bb=ac