#1674 ⟨a, b, c | aab=ba, ccb=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 c is not injective:
- c ⋅ cbc = c and c ⋅ 1 = c, however cbc ≠ 1
Not right cancellative, because right multiplication by cb is not injective:
- cbc ⋅ cb = cb and 1 ⋅ cb = cb, however cbc ≠ 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.	a²b ⇒ ba	[1]
2.	c²b ⇒ 1	[2]

# abc:aab=ba,ccb=1 abc - -
aab=ba
ccb=1