#477 ⟨a, b, c | ba=ac, bbc=1⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ bcb = b and b ⋅ 1 = b, however bcb ≠ 1
Not right cancellative, because right multiplication by bc is not injective:
- bcb ⋅ bc = bc and 1 ⋅ bc = bc, however bcb ≠ 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.	ba ⇒ ac	[1]
2.	b²c ⇒ 1	[2]

# abc:ba=ac,bbc=1 abc - -
ba=ac
bbc=1