#105 ⟨a, b, c | ab=a, bac=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 a is not injective:
- a ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
Not right cancellative, because right multiplication by ac is not injective:
- acb ⋅ ac = ac and 1 ⋅ ac = ac, however acb ≠ 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=a,bac=1 abc - -
ab=a
aac=a
bac=1

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

3 total

Σ	#	Presentation	Mapping
7	795	⟨a, b, c \| ab=a, babc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	1945	⟨a, b, c \| abc=ab, cba=1⟩	φ(a) = c, φ(b) = a, φ(c) = b
8	4843	⟨a, b, c \| ab=a, babbc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c