#20786 ⟨a, b | ab=aa, baaaa=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:
- ba³ ⋅ a = ba and b ⋅ a = ba, however ba³ ≠ b

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,baaaa=ba ab - -
ab=aa
baaaa=ba
aaaaaa=aaa

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

7 total

Σ	#	Presentation	Mapping
11	20790	⟨a, b \| ab=aa, baaab=ba⟩	φ(a) = a, φ(b) = b
11	20794	⟨a, b \| ab=aa, baaba=ba⟩	φ(a) = a, φ(b) = b
11	20798	⟨a, b \| ab=aa, baabb=ba⟩	φ(a) = a, φ(b) = b
11	20802	⟨a, b \| ab=aa, babaa=ba⟩	φ(a) = a, φ(b) = b
11	20806	⟨a, b \| ab=aa, babab=ba⟩	φ(a) = a, φ(b) = b
11	20810	⟨a, b \| ab=aa, babba=ba⟩	φ(a) = a, φ(b) = b
11	20814	⟨a, b \| ab=aa, babbb=ba⟩	φ(a) = a, φ(b) = b