#3128 ⟨a, b | ab=a, bbba=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,bbba=aa ab - -
ab=a
aaa=aa
bbba=aa

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

9 total

Σ	#	Presentation	Mapping
10	9100	⟨a, b \| ab=a, bbbab=aa⟩	φ(a) = a, φ(b) = b
10	9369	⟨a, b \| ab=a, bbba=aab⟩	φ(a) = a, φ(b) = b
10	9370	⟨a, b \| ab=a, bbba=aba⟩	φ(a) = a, φ(b) = b
11	25096	⟨a, b \| ab=a, bbbabb=aa⟩	φ(a) = a, φ(b) = b
11	25637	⟨a, b \| ab=a, bbbab=aab⟩	φ(a) = a, φ(b) = b
11	25638	⟨a, b \| ab=a, bbbab=aba⟩	φ(a) = a, φ(b) = b
11	25886	⟨a, b \| ab=a, bbba=aabb⟩	φ(a) = a, φ(b) = b
11	25888	⟨a, b \| ab=a, bbba=abab⟩	φ(a) = a, φ(b) = b
11	25889	⟨a, b \| ab=a, bbba=abba⟩	φ(a) = a, φ(b) = b