#1636 ⟨a, b | aab=ba, abb=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 ⋅ b² = a and a ⋅ 1 = a, however b² ≠ 1
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:aab=ba,abb=a reversed:a/b - -
aaaaa=aa
ba=aab
abb=a

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

1 total

Σ	#	Presentation	Mapping
9	1681	⟨a, b \| aba=bb, baa=b⟩	φ(a) = b, φ(b) = a

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

6 total

Σ	#	Presentation	Mapping
11	19515	⟨a, b \| aab=b, aaaba=bb⟩	φ(a) = b, φ(b) = a
11	19518	⟨a, b \| aab=b, aaabb=ba⟩	φ(a) = b, φ(b) = a
11	19542	⟨a, b \| aab=b, abaab=ba⟩	φ(a) = b, φ(b) = a
11	20067	⟨a, b \| aab=b, aaba=abb⟩	φ(a) = b, φ(b) = a
11	20074	⟨a, b \| aab=b, aabb=aba⟩	φ(a) = b, φ(b) = a
11	20122	⟨a, b \| aab=b, baab=aba⟩	φ(a) = b, φ(b) = a