#3248 ⟨a, b, c | bb=aa, abac=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 ⋅ a⁵c²a = a and a ⋅ 1 = a, however a⁵c²a ≠ 1
Not right cancellative, because right multiplication by a⁵c² is not injective:
- a⁵c²a ⋅ a⁵c² = a⁵c² and 1 ⋅ a⁵c² = a⁵c², however a⁵c²a ≠ 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:bb=aa,abac=1 ca/b - -
aaaaaacc=1
aaaaaaac=aaaaacaa
aaaaacaac=a
aaaaacaaaac=aaa
aaaaacaaaaaac=aaaaa
aaaaacaaaaacca=aaaaac
b=aaaaacaaaaacc