#1282 ⟨a, b, c | ab=1, aabc=a⟩

Properties

Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ c = a and a ⋅ 1 = a, however c ≠ 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

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

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

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

6 total

Σ	#	Presentation	Mapping
7	1296	⟨a, b, c \| ab=1, abac=a⟩	φ(a) = a, φ(b) = b, φ(c) = c
7	1440	⟨a, b, c \| ab=1, aab=ac⟩	φ(a) = a, φ(b) = b, φ(c) = c
7	1454	⟨a, b, c \| ab=1, aba=ac⟩	φ(a) = a, φ(b) = b, φ(c) = c
7	1468	⟨a, b, c \| ab=1, aca=aa⟩	φ(a) = a, φ(b) = b, φ(c) = c
7	1500	⟨a, b, c \| ab=1, bac=ba⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	1939	⟨a, b, c \| abc=ab, bca=1⟩	φ(a) = b, φ(b) = a, φ(c) = c