#258 ⟨a, b, c | ab=1, cac=c⟩

Properties

Sum of relation sides is 6
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

#	Rule	Proof
1.	ab ⇒ 1	[1]
2.	cac ⇒ c	[2]

# abc:ab=1,cac=c abc - -
ab=1
cac=c

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

6 total

Σ	#	Presentation	Mapping
8	6885	⟨a, b, c \| ab=1, abcac=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7080	⟨a, b, c \| ab=1, caabc=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7086	⟨a, b, c \| ab=1, cabac=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7546	⟨a, b, c \| ab=1, bcac=bc⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7830	⟨a, b, c \| ab=1, cac=abc⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7844	⟨a, b, c \| ab=1, cac=cab⟩	φ(a) = a, φ(b) = b, φ(c) = c