#13227 ⟨a, b | baa=aab, bba=ba⟩

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 b is not injective:
- b ⋅ ba = ba and b ⋅ a = ba, however ba ≠ a
Not right cancellative, because right multiplication by a is not injective:
- b² ⋅ a = ba and b ⋅ a = ba, however b² ≠ b

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

#	Rule	Proof
1.	b²a ⇒ ba	[2]
2.	a²b ⇒ ba²	[1]

# ab:baa=aab,bba=ba ba - -
bba=ba
aab=baa