#3252 ⟨a, b, c | bb=aa, abcc=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 ⋅ b²(c²b)² = b and b ⋅ 1 = b, however b²(c²b)² ≠ 1
Not right cancellative, because right multiplication by b(bc²)² is not injective:
- b²(c²b)² ⋅ b(bc²)² = b(bc²)² and 1 ⋅ b(bc²)² = b(bc²)², however b²(c²b)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(b) = 0, c < b; deg(a) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:bb=aa,abcc=1 cb/a - -
bbbbbcc=bbbccbb
bbbccbcc=1
bbbccbbbcc=bb
a=bbbcc