#12563 ⟨a, b | abba=aa, babb=b⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element ba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ab² = b and b ⋅ 1 = b, however ab² ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- bab ⋅ b = b and 1 ⋅ b = b, however bab ≠ 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

# ab:abba=aa,babb=b ab - -
aaa=aa
baa=ba
aabb=abb
abba=aa
babb=b