#7224 ⟨a, b, c | aa=1, bacb=bb⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element ab has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ acb = b² and b ⋅ b = b², however acb ≠ b
Not right cancellative, because right multiplication by b is not injective:
- bac ⋅ b = b² and b ⋅ b = b², however bac ≠ 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.	a² ⇒ 1	[1]
2.	bacb ⇒ b²	[2]

# abc:aa=1,bacb=bb abc - -
aa=1
bacb=bb