#2594 ⟨a, b, c | aba=b, aaac=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 ⋅ a²ca = a and a ⋅ 1 = a, however a²ca ≠ 1
Not right cancellative, because right multiplication by a²c is not injective:
- a²ca ⋅ a²c = a²c and 1 ⋅ a²c = a²c, however a²ca ≠ 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(a) = deg(b) = 0, a < b; deg(c) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:aba=b,aaac=1 ab/c - -
aba=b
bba=abb
bc=aaab
bac=aab
aaac=1
baac=ab