#1568 ⟨a, b, c | aaa=bb, aac=1⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ bcb²c²b = b and b ⋅ 1 = b, however bcb²c²b ≠ 1
Not right cancellative, because right multiplication by bcb²c² is not injective:
- bcb²c²b ⋅ bcb²c² = bcb²c² and 1 ⋅ bcb²c² = bcb²c², however bcb²c²b ≠ 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(b) = 0, c < b; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:aaa=bb,aac=1 cb/a - -
bbbbc=bbcbb
bbcbbcc=1
bbcbbcbbc=bb
a=bbc