#12514 ⟨a, b | abab=aa, bbba=a⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ bab = a² and a ⋅ a = a², however bab ≠ a
Not right cancellative, because right multiplication by a is not injective:
- b³ ⋅ a = a and 1 ⋅ a = a, however b³ ≠ 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:abab=aa,bbba=a ab - -
abaa=aaab
abab=aa
bbba=a
aabba=aaab
aaaabb=aaaba