#2256 ⟨a, b, c | abac=1, acab=1⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ baca = a and a ⋅ 1 = a, however baca ≠ 1
Not right cancellative, because right multiplication by bac is not injective:
- baca ⋅ bac = bac and 1 ⋅ bac = bac, however baca ≠ 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.	abac ⇒ 1	[1]
2.	acab ⇒ 1	[2]

# abc:abac=1,acab=1 abc - -
abac=1
acab=1