#20722 ⟨a, b | ab=aa, aaaaa=ba⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ b = a² and a ⋅ a = a², however b ≠ a
Not right cancellative, because right multiplication by a is not injective:
- a⁵ ⋅ a = a³ and a² ⋅ a = a³, however a⁵ ≠ a²

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=aa,aaaaa=ba a/b - -
aaaaaa=aaa
ba=aaaaa
ab=aa

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

15 total

Σ	#	Presentation	Mapping
11	20726	⟨a, b \| ab=aa, aaaab=ba⟩	φ(a) = a, φ(b) = b
11	20730	⟨a, b \| ab=aa, aaaba=ba⟩	φ(a) = a, φ(b) = b
11	20734	⟨a, b \| ab=aa, aaabb=ba⟩	φ(a) = a, φ(b) = b
11	20738	⟨a, b \| ab=aa, aabaa=ba⟩	φ(a) = a, φ(b) = b
11	20742	⟨a, b \| ab=aa, aabab=ba⟩	φ(a) = a, φ(b) = b
11	20746	⟨a, b \| ab=aa, aabba=ba⟩	φ(a) = a, φ(b) = b
11	20750	⟨a, b \| ab=aa, aabbb=ba⟩	φ(a) = a, φ(b) = b
11	20754	⟨a, b \| ab=aa, abaaa=ba⟩	φ(a) = a, φ(b) = b
11	20758	⟨a, b \| ab=aa, abaab=ba⟩	φ(a) = a, φ(b) = b
11	20762	⟨a, b \| ab=aa, ababa=ba⟩	φ(a) = a, φ(b) = b
11	20766	⟨a, b \| ab=aa, ababb=ba⟩	φ(a) = a, φ(b) = b
11	20770	⟨a, b \| ab=aa, abbaa=ba⟩	φ(a) = a, φ(b) = b
11	20774	⟨a, b \| ab=aa, abbab=ba⟩	φ(a) = a, φ(b) = b
11	20778	⟨a, b \| ab=aa, abbba=ba⟩	φ(a) = a, φ(b) = b
11	20782	⟨a, b \| ab=aa, abbbb=ba⟩	φ(a) = a, φ(b) = b