#1010 ⟨a, b | ab=a, baa=ba⟩

Properties

Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element b 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:
- a² ⋅ a = a² and a ⋅ a = a², however a² ≠ a

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

# ab:ab=a,baa=ba ab - -
ab=a
aaa=aa
baa=ba

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

19 total

Σ	#	Presentation	Mapping
9	3110	⟨a, b \| ab=a, baab=ba⟩	φ(a) = a, φ(b) = b
9	3114	⟨a, b \| ab=a, baba=ba⟩	φ(a) = a, φ(b) = b
9	3186	⟨a, b \| ab=a, bab=baa⟩	φ(a) = a, φ(b) = b
10	9062	⟨a, b \| ab=a, baabb=ba⟩	φ(a) = a, φ(b) = b
10	9070	⟨a, b \| ab=a, babab=ba⟩	φ(a) = a, φ(b) = b
10	9074	⟨a, b \| ab=a, babba=ba⟩	φ(a) = a, φ(b) = b
10	9333	⟨a, b \| ab=a, baab=bab⟩	φ(a) = a, φ(b) = b
10	9341	⟨a, b \| ab=a, baba=bab⟩	φ(a) = a, φ(b) = b
10	9348	⟨a, b \| ab=a, babb=baa⟩	φ(a) = a, φ(b) = b
11	25018	⟨a, b \| ab=a, baabbb=ba⟩	φ(a) = a, φ(b) = b
11	25034	⟨a, b \| ab=a, bababb=ba⟩	φ(a) = a, φ(b) = b
11	25042	⟨a, b \| ab=a, babbab=ba⟩	φ(a) = a, φ(b) = b
11	25046	⟨a, b \| ab=a, babbba=ba⟩	φ(a) = a, φ(b) = b
11	25561	⟨a, b \| ab=a, baabb=bab⟩	φ(a) = a, φ(b) = b
11	25577	⟨a, b \| ab=a, babab=bab⟩	φ(a) = a, φ(b) = b
11	25585	⟨a, b \| ab=a, babba=bab⟩	φ(a) = a, φ(b) = b
11	25592	⟨a, b \| ab=a, babbb=baa⟩	φ(a) = a, φ(b) = b
11	25856	⟨a, b \| ab=a, babb=baab⟩	φ(a) = a, φ(b) = b
11	25857	⟨a, b \| ab=a, babb=baba⟩	φ(a) = a, φ(b) = b