#2796 ⟨a, b, c | abc=b, caca=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 ⋅ (ac)² = c and c ⋅ 1 = c, however (ac)² ≠ 1
Not right cancellative, because right multiplication by aca is not injective:
- (ac)² ⋅ aca = aca and 1 ⋅ aca = aca, however (ac)² ≠ 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

# abc:abc=b,caca=1 abc - -
abc=b
baca=ab
bacb=abbc
caca=1
cacb=bc