#20784 ⟨a, b | ab=aa, baaaa=aa⟩

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:
- ba ⋅ a = a³ and a² ⋅ a = a³, however ba ≠ 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,baaaa=aa ab - -
ab=aa
baa=aaa
aaaaa=aa

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

15 total

Σ	#	Presentation	Mapping
11	20785	⟨a, b \| ab=aa, baaaa=ab⟩	φ(a) = a, φ(b) = b
11	20788	⟨a, b \| ab=aa, baaab=aa⟩	φ(a) = a, φ(b) = b
11	20789	⟨a, b \| ab=aa, baaab=ab⟩	φ(a) = a, φ(b) = b
11	20792	⟨a, b \| ab=aa, baaba=aa⟩	φ(a) = a, φ(b) = b
11	20793	⟨a, b \| ab=aa, baaba=ab⟩	φ(a) = a, φ(b) = b
11	20796	⟨a, b \| ab=aa, baabb=aa⟩	φ(a) = a, φ(b) = b
11	20797	⟨a, b \| ab=aa, baabb=ab⟩	φ(a) = a, φ(b) = b
11	20800	⟨a, b \| ab=aa, babaa=aa⟩	φ(a) = a, φ(b) = b
11	20801	⟨a, b \| ab=aa, babaa=ab⟩	φ(a) = a, φ(b) = b
11	20804	⟨a, b \| ab=aa, babab=aa⟩	φ(a) = a, φ(b) = b
11	20805	⟨a, b \| ab=aa, babab=ab⟩	φ(a) = a, φ(b) = b
11	20808	⟨a, b \| ab=aa, babba=aa⟩	φ(a) = a, φ(b) = b
11	20809	⟨a, b \| ab=aa, babba=ab⟩	φ(a) = a, φ(b) = b
11	20812	⟨a, b \| ab=aa, babbb=aa⟩	φ(a) = a, φ(b) = b
11	20813	⟨a, b \| ab=aa, babbb=ab⟩	φ(a) = a, φ(b) = b