#501 ⟨a, b, c | bb=ac, caa=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 c is not injective:
- c ⋅ a²c = c and c ⋅ 1 = c, however a²c ≠ 1
Not right cancellative, because right multiplication by a² is not injective:
- a²c ⋅ a² = a² and 1 ⋅ a² = a², however a²c ≠ 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:bb=ac,caa=1 abc - -
bb=ac
bac=acb
caa=1
cbaa=caba
acaba=ba
cbaba=ca