#12374 ⟨a, b | aaba=ab, bbba=a⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a³ = a² and a ⋅ a = a², however a³ ≠ 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:aaba=ab,bbba=a ab - -
aba=aab
aaaa=aa
aaab=ab
abba=aabb
abbb=aaa
bbba=a