#12386 ⟨a, b | aaba=ba, abbb=a⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element ab has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b³ = a and a ⋅ 1 = a, however b³ ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a³ ⋅ a = a² and a ⋅ a = a², however a³ ≠ a

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:aaba=ba,abbb=a ab - -
aaaa=aa
aaba=ba
abbb=a
baaa=ba
bbba=aaa
aabba=bba