#147 ⟨a, b, c | ab=a, ac=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

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 ⇒ a	[2]

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

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

5 total

Σ	#	Presentation	Mapping
7	950	⟨a, b, c \| ab=a, abc=a⟩	φ(a) = a, φ(b) = b, φ(c) = c
7	1054	⟨a, b, c \| ab=a, ac=ab⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	5300	⟨a, b, c \| ab=a, abbc=a⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	5800	⟨a, b, c \| ab=a, abb=ac⟩	φ(a) = a, φ(b) = b, φ(c) = c
8	5806	⟨a, b, c \| ab=a, abc=ab⟩	φ(a) = a, φ(b) = b, φ(c) = c