#154 ⟨a, b, c | ab=a, ca=a⟩

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 a is not injective:
- c ⋅ a = a and 1 ⋅ a = a, however c ≠ 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.	ca ⇒ a	[2]

# abc:ab=a,ca=a abc - -
ab=a
ca=a

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

5 total

Σ	#	Presentation	Mapping
7	984	⟨a, b, c \| ab=a, cab=a⟩	φ(a) = a, φ(b) = b, φ(c) = c
7	1056	⟨a, b, c \| ab=a, ca=ab⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	5416	⟨a, b, c \| ab=a, cabb=a⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	5802	⟨a, b, c \| ab=a, abb=ca⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	5916	⟨a, b, c \| ab=a, cab=ab⟩	φ(a) = a, φ(b) = b, φ(c) = c