#8 ⟨a, b, c | ab=a, ac=1⟩

Properties

Sum of relation sides is 5
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 c is not injective:
- ca ⋅ c = c and 1 ⋅ c = c, however ca ≠ 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

#	Rule	Proof
1.	ab ⇒ a	[1]
2.	ac ⇒ 1	[2]

# abc:ab=a,ac=1 abc - -
ab=a
ac=1

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

4 total

Σ	#	Presentation	Mapping
6	101	⟨a, b, c \| ab=a, abc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
7	781	⟨a, b, c \| ab=a, abbc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	1795	⟨a, b, c \| aba=aa, abc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	4797	⟨a, b, c \| ab=a, abbbc=1⟩	φ(a) = a, φ(b) = b, φ(c) = c