#7659 ⟨a, b, c | aa=1, bbb=bac⟩

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 ⋅ ac = b³ and b ⋅ b² = b³, however ac ≠ b²

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.	bac ⇒ b³	[2]

# abc:aa=1,bbb=bac bac - -
aa=1
bac=bbb