#3191 ⟨a, b | ab=a, bba=baa⟩

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,bba=baa ab - -
ab=a
aaa=aa
bba=baa

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

9 total

Σ	#	Presentation	Mapping
10	9334	⟨a, b \| ab=a, baab=bba⟩	φ(a) = a, φ(b) = b
10	9342	⟨a, b \| ab=a, baba=bba⟩	φ(a) = a, φ(b) = b
10	9364	⟨a, b \| ab=a, bbab=baa⟩	φ(a) = a, φ(b) = b
11	25562	⟨a, b \| ab=a, baabb=bba⟩	φ(a) = a, φ(b) = b
11	25578	⟨a, b \| ab=a, babab=bba⟩	φ(a) = a, φ(b) = b
11	25586	⟨a, b \| ab=a, babba=bba⟩	φ(a) = a, φ(b) = b
11	25624	⟨a, b \| ab=a, bbabb=baa⟩	φ(a) = a, φ(b) = b
11	25879	⟨a, b \| ab=a, bbab=baab⟩	φ(a) = a, φ(b) = b
11	25880	⟨a, b \| ab=a, bbab=baba⟩	φ(a) = a, φ(b) = b