#572 ⟨a, b, c | aaa=1, babc=1⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element ba² has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ abcb = b and b ⋅ 1 = b, however abcb ≠ 1
Not right cancellative, because right multiplication by abc is not injective:
- abcb ⋅ abc = abc and 1 ⋅ abc = abc, however abcb ≠ 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.	a³ ⇒ 1	[1]
2.	babc ⇒ 1	[2]

# abc:aaa=1,babc=1 abc - -
aaa=1
babc=1