#255 ⟨a, b, c | ab=1, bcc=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,bcc=c cab - -
ac=cc
ab=1
bcc=c

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

10 total

Σ	#	Presentation	Mapping
7	1361	⟨a, b, c \| ab=1, bcac=c⟩	φ(a) = a, φ(b) = b, φ(c) = bc
8	6877	⟨a, b, c \| ab=1, abbcc=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	6986	⟨a, b, c \| ab=1, babcc=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7016	⟨a, b, c \| ab=1, bbacc=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7045	⟨a, b, c \| ab=1, bcaac=c⟩	φ(a) = a, φ(b) = b, φ(c) = bbc
8	7048	⟨a, b, c \| ab=1, bcabc=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7057	⟨a, b, c \| ab=1, bcbac=c⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7537	⟨a, b, c \| ab=1, bbcc=bc⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7802	⟨a, b, c \| ab=1, bcc=abc⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	7824	⟨a, b, c \| ab=1, cab=bcc⟩	φ(a) = a, φ(b) = b, φ(c) = c