#3470 ⟨a, b, c | ba=ac, bcb=b⟩

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 b is not injective:
- b ⋅ cb = b and b ⋅ 1 = b, however cb ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- bc ⋅ b = b and 1 ⋅ b = b, however bc ≠ 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.	bcb ⇒ b	[2]

# abc:ba=ac,bcb=b bac - -
ac=ba
bcb=b