#34 ⟨a, b, c | ab=aa, bc=1⟩

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 b is not injective:
- b ⋅ cb = b and b ⋅ 1 = b, however cb ≠ 1
Not right cancellative, because right multiplication by c is not injective:
- cb ⋅ c = c and 1 ⋅ c = c, however cb ≠ 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=aa,bc=1 abc - -
ab=aa
bc=1
aac=a

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

3 total

Σ	#	Presentation	Mapping
8	7379	⟨a, b, c \| ab=1, abca=cc⟩	φ(a) = b, φ(b) = c, φ(c) = a
8	7395	⟨a, b, c \| ab=1, abcc=ca⟩	φ(a) = b, φ(b) = c, φ(c) = a
8	7812	⟨a, b, c \| ab=1, bcc=bca⟩	φ(a) = b, φ(b) = c, φ(c) = a