#3213 ⟨a, b, c | ba=ac, abcb=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 ⋅ bcba = a and a ⋅ 1 = a, however bcba ≠ 1
Not right cancellative, because right multiplication by bcb is not injective:
- bcba ⋅ bcb = bcb and 1 ⋅ bcb = bcb, however bcba ≠ 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.	ac ⇒ ba	[1]
2.	abcb ⇒ 1	[2]

# abc:ba=ac,abcb=1 bac - -
ac=ba
abcb=1