#20816 ⟨a, b | ab=aa, bbaaa=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:
- a⁴ ⋅ a = a² and a ⋅ a = a², however a⁴ ≠ 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=aa,bbaaa=aa ab - -
ab=aa
bbaa=aaaa
aaaaa=aa

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

7 total

Σ	#	Presentation	Mapping
11	20817	⟨a, b \| ab=aa, bbaaa=ab⟩	φ(a) = a, φ(b) = b
11	20820	⟨a, b \| ab=aa, bbaab=aa⟩	φ(a) = a, φ(b) = b
11	20821	⟨a, b \| ab=aa, bbaab=ab⟩	φ(a) = a, φ(b) = b
11	20824	⟨a, b \| ab=aa, bbaba=aa⟩	φ(a) = a, φ(b) = b
11	20825	⟨a, b \| ab=aa, bbaba=ab⟩	φ(a) = a, φ(b) = b
11	20828	⟨a, b \| ab=aa, bbabb=aa⟩	φ(a) = a, φ(b) = b
11	20829	⟨a, b \| ab=aa, bbabb=ab⟩	φ(a) = a, φ(b) = b