#9050 ⟨a, b | ab=a, baaaa=ba⟩

Properties

Sum of relation sides is 10
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:
- a⁴ ⋅ a = a² and a ⋅ a = a², however a⁴ ≠ 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,baaaa=ba ab - -
ab=a
aaaaa=aa
baaaa=ba

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

5 total

Σ	#	Presentation	Mapping
11	24994	⟨a, b \| ab=a, baaaab=ba⟩	φ(a) = a, φ(b) = b
11	24998	⟨a, b \| ab=a, baaaba=ba⟩	φ(a) = a, φ(b) = b
11	25006	⟨a, b \| ab=a, baabaa=ba⟩	φ(a) = a, φ(b) = b
11	25022	⟨a, b \| ab=a, babaaa=ba⟩	φ(a) = a, φ(b) = b
11	25537	⟨a, b \| ab=a, baaaa=bab⟩	φ(a) = a, φ(b) = b