#5390 ⟨a, b | aab=ba, aba=aa⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element b has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ a² = a² and a ⋅ a = a², however a² ≠ a
Not right cancellative, because right multiplication by a is not injective:
- b ⋅ a = a² and a ⋅ a = a², however b ≠ 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:aab=ba,aba=aa ab - -
ba=aa
aaa=aa
aab=aa

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

5 total

Σ	#	Presentation	Mapping
11	16213	⟨a, b \| aab=ba, aaab=aa⟩	φ(a) = a, φ(b) = b
11	16217	⟨a, b \| aab=ba, aaba=aa⟩	φ(a) = a, φ(b) = b
11	16225	⟨a, b \| aab=ba, abaa=aa⟩	φ(a) = a, φ(b) = b
11	16241	⟨a, b \| aab=ba, baaa=aa⟩	φ(a) = a, φ(b) = b
11	16354	⟨a, b \| aba=aa, abab=ba⟩	φ(a) = a, φ(b) = b