#252 ⟨a, b, c | ab=1, bca=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

# abc:ab=1,bca=c bdac ac=d morph:2/1
bd=c
db=c
ab=1
ad=da
ac=d
cb=bc
cd=dc
ca=d

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

4 total

Σ	#	Presentation	Mapping
8	6871	⟨a, b, c \| ab=1, abbca=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6983	⟨a, b, c \| ab=1, babca=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7528	⟨a, b, c \| ab=1, bbca=bc⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7784	⟨a, b, c \| ab=1, bca=abc⟩	φ(a) = a, φ(b) = b, φ(c) = c