#1596 ⟨a, b | aaa=ab, bba=a⟩

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 = a³ and a ⋅ a² = a³, however b ≠ a²
Not right cancellative, because right multiplication by a is not injective:
- b² ⋅ a = a and 1 ⋅ a = a, however b² ≠ 1

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:aaa=ab,bba=a a/b - -
aaaaaa=aa
ab=aaa
bba=a

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

6 total

Σ	#	Presentation	Mapping
11	19534	⟨a, b \| aab=b, aabbb=ba⟩	φ(a) = b, φ(b) = a
11	19582	⟨a, b \| aab=b, baabb=ba⟩	φ(a) = b, φ(b) = a
11	19590	⟨a, b \| aab=b, babab=ba⟩	φ(a) = b, φ(b) = a
11	19606	⟨a, b \| aab=b, bbaab=ba⟩	φ(a) = b, φ(b) = a
11	20071	⟨a, b \| aab=b, aaba=bbb⟩	φ(a) = b, φ(b) = a
11	20106	⟨a, b \| aab=b, abbb=aba⟩	φ(a) = b, φ(b) = a