#7410 ⟨a, b, c | ab=1, acac=ba⟩

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 a is not injective:
- a ⋅ ba = a and a ⋅ 1 = a, however ba ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- ba ⋅ b = b and 1 ⋅ b = b, however ba ≠ 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:ab=1,acac=ba abc - -
ab=1
acac=ba
baac=acba
aacba=aac
aaccac=aacbba