#3017 ⟨a, b | aa=a, abab=ba⟩

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 ⋅ a = a and a ⋅ 1 = a, however a ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- a ⋅ a = a and 1 ⋅ a = a, however a ≠ 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:aa=a,abab=ba ab - -
aa=a
aba=ba
bab=ba
bba=ba

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

9 total

Σ	#	Presentation	Mapping
10	8860	⟨a, b \| aa=a, aabab=ba⟩	φ(a) = a, φ(b) = b
10	8872	⟨a, b \| aa=a, abaab=ba⟩	φ(a) = a, φ(b) = b
10	9146	⟨a, b \| aa=a, abab=baa⟩	φ(a) = a, φ(b) = b
11	24609	⟨a, b \| aa=a, aaabab=ba⟩	φ(a) = a, φ(b) = b
11	24621	⟨a, b \| aa=a, aabaab=ba⟩	φ(a) = a, φ(b) = b
11	24648	⟨a, b \| aa=a, abaaab=ba⟩	φ(a) = a, φ(b) = b
11	25156	⟨a, b \| aa=a, aabab=baa⟩	φ(a) = a, φ(b) = b
11	25180	⟨a, b \| aa=a, abaab=baa⟩	φ(a) = a, φ(b) = b
11	25688	⟨a, b \| aa=a, baaa=abab⟩	φ(a) = a, φ(b) = b