#20988 ⟨a, b | ab=aa, baaa=baa⟩

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:
- ba² ⋅ a = ba² and ba ⋅ a = ba², however ba² ≠ ba

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,baaa=baa ab - -
ab=aa
baaa=baa
aaaaa=aaaa

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

7 total

Σ	#	Presentation	Mapping
11	20989	⟨a, b \| ab=aa, baaa=bab⟩	φ(a) = a, φ(b) = b
11	20996	⟨a, b \| ab=aa, baab=baa⟩	φ(a) = a, φ(b) = b
11	20997	⟨a, b \| ab=aa, baab=bab⟩	φ(a) = a, φ(b) = b
11	21004	⟨a, b \| ab=aa, baba=baa⟩	φ(a) = a, φ(b) = b
11	21005	⟨a, b \| ab=aa, baba=bab⟩	φ(a) = a, φ(b) = b
11	21012	⟨a, b \| ab=aa, babb=baa⟩	φ(a) = a, φ(b) = b
11	21013	⟨a, b \| ab=aa, babb=bab⟩	φ(a) = a, φ(b) = b