#1970 ⟨a, b, c | abc=ba, bac=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 b is not injective:
- b ⋅ acb = b and b ⋅ 1 = b, however acb ≠ 1
Not right cancellative, because right multiplication by ac is not injective:
- acb ⋅ ac = ac and 1 ⋅ ac = ac, however acb ≠ 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.	abc ⇒ ba	[1]
2.	bac ⇒ 1	[2]

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