#4491 ⟨a, b, c | abc=1, aaba=b⟩

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 ⋅ bca = a and a ⋅ 1 = a, however bca ≠ 1
Not right cancellative, because right multiplication by bc is not injective:
- bca ⋅ bc = bc and 1 ⋅ bc = bc, however bca ≠ 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:
- Right-to-left recursive path with deg(a) = deg(c) = 0, a < c; deg(b) = 1
Certificate: derivations of all rewriting rules from the defining relations.

# abc:abc=1,aaba=b reversed:ac/b - -
aaba=b
abc=1
bba=aaaabb
baba=aabb
bbc=aab