#3104 ⟨a, b | ab=a, baaa=aa⟩

Properties

Sum of relation sides is 9
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,baaa=aa ab - -
ab=a
aaa=aa
baa=aa

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

20 total

Σ	#	Presentation	Mapping
10	9052	⟨a, b \| ab=a, baaab=aa⟩	φ(a) = a, φ(b) = b
10	9056	⟨a, b \| ab=a, baaba=aa⟩	φ(a) = a, φ(b) = b
10	9064	⟨a, b \| ab=a, babaa=aa⟩	φ(a) = a, φ(b) = b
10	9321	⟨a, b \| ab=a, baaa=aab⟩	φ(a) = a, φ(b) = b
10	9322	⟨a, b \| ab=a, baaa=aba⟩	φ(a) = a, φ(b) = b
11	25000	⟨a, b \| ab=a, baaabb=aa⟩	φ(a) = a, φ(b) = b
11	25008	⟨a, b \| ab=a, baabab=aa⟩	φ(a) = a, φ(b) = b
11	25012	⟨a, b \| ab=a, baabba=aa⟩	φ(a) = a, φ(b) = b
11	25024	⟨a, b \| ab=a, babaab=aa⟩	φ(a) = a, φ(b) = b
11	25028	⟨a, b \| ab=a, bababa=aa⟩	φ(a) = a, φ(b) = b
11	25036	⟨a, b \| ab=a, babbaa=aa⟩	φ(a) = a, φ(b) = b
11	25541	⟨a, b \| ab=a, baaab=aab⟩	φ(a) = a, φ(b) = b
11	25542	⟨a, b \| ab=a, baaab=aba⟩	φ(a) = a, φ(b) = b
11	25549	⟨a, b \| ab=a, baaba=aab⟩	φ(a) = a, φ(b) = b
11	25550	⟨a, b \| ab=a, baaba=aba⟩	φ(a) = a, φ(b) = b
11	25565	⟨a, b \| ab=a, babaa=aab⟩	φ(a) = a, φ(b) = b
11	25566	⟨a, b \| ab=a, babaa=aba⟩	φ(a) = a, φ(b) = b
11	25823	⟨a, b \| ab=a, baaa=aabb⟩	φ(a) = a, φ(b) = b
11	25825	⟨a, b \| ab=a, baaa=abab⟩	φ(a) = a, φ(b) = b
11	25826	⟨a, b \| ab=a, baaa=abba⟩	φ(a) = a, φ(b) = b