#256 ⟨a, b, c | ab=1, cac=a⟩

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

# abc:ab=1,cac=a cab - -
ab=1
cac=a
aac=caa

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

7 total

Σ	#	Presentation	Mapping
8	2599	⟨a, b, c \| aba=b, abac=1⟩	φ(a) = c, φ(b) = a, φ(c) = b
8	6883	⟨a, b, c \| ab=1, abcac=a⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7078	⟨a, b, c \| ab=1, caabc=a⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7084	⟨a, b, c \| ab=1, cabac=a⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7544	⟨a, b, c \| ab=1, bcac=ba⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7826	⟨a, b, c \| ab=1, cac=aab⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7828	⟨a, b, c \| ab=1, cac=aba⟩	φ(a) = a, φ(b) = b, φ(c) = c