#2697 ⟨a, b, c | abc=a, acbc=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 a is not injective:
- a ⋅ bc = a and a ⋅ 1 = a, however bc ≠ 1
Not right cancellative, because right multiplication by cbc is not injective:
- cbca ⋅ cbc = cbc and 1 ⋅ cbc = cbc, however cbca ≠ 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.	abc ⇒ a	[1]
2.	acbc ⇒ 1	[2]

# abc:abc=a,acbc=1 abc - -
abc=a
acbc=1