#787 ⟨a, b, c | ab=a, acac=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 a is not injective:
- a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
Not right cancellative, because right multiplication by cac is not injective:
- (ca)² ⋅ cac = cac and 1 ⋅ cac = cac, however (ca)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

#	Rule	Proof
1.	ab ⇒ a	[1]
2.	(ac)² ⇒ 1	[2]

# abc:ab=a,acac=1 abc - -
ab=a
acac=1

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

2 total

Σ	#	Presentation	Mapping
8	4803	⟨a, b, c \| ab=a, abcac=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	4815	⟨a, b, c \| ab=a, acabc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c