#6221 ⟨a, b, c | aa=1, bacabc=1⟩

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 ⋅ acabcb = b and b ⋅ 1 = b, however acabcb ≠ 1
Not right cancellative, because right multiplication by acabc is not injective:
- acabcb ⋅ acabc = acabc and 1 ⋅ acabc = acabc, however acabcb ≠ 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

#	Rule	Proof
1.	a² ⇒ 1	[1]
2.	bacabc ⇒ 1	[2]

# abc:aa=1,bacabc=1 abc - -
aa=1
bacabc=1