#3020 ⟨a, b | aa=a, abba=ab⟩

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,abba=ab ab - -
aa=a
aba=ab
abb=ab

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

10 total

Σ	#	Presentation	Mapping
10	8863	⟨a, b \| aa=a, aabba=ab⟩	φ(a) = a, φ(b) = b
10	8875	⟨a, b \| aa=a, ababa=ab⟩	φ(a) = a, φ(b) = b
10	9151	⟨a, b \| aa=a, abba=aab⟩	φ(a) = a, φ(b) = b
11	24612	⟨a, b \| aa=a, aaabba=ab⟩	φ(a) = a, φ(b) = b
11	24624	⟨a, b \| aa=a, aababa=ab⟩	φ(a) = a, φ(b) = b
11	24632	⟨a, b \| aa=a, aabbaa=ab⟩	φ(a) = a, φ(b) = b
11	24651	⟨a, b \| aa=a, abaaba=ab⟩	φ(a) = a, φ(b) = b
11	25161	⟨a, b \| aa=a, aabba=aab⟩	φ(a) = a, φ(b) = b
11	25185	⟨a, b \| aa=a, ababa=aab⟩	φ(a) = a, φ(b) = b
11	25675	⟨a, b \| aa=a, abba=aaab⟩	φ(a) = a, φ(b) = b

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

4 total

Σ	#	Presentation	Mapping
10	8864	⟨a, b \| aa=a, aabba=ba⟩	φ(a) = a, φ(b) = b
11	24613	⟨a, b \| aa=a, aaabba=ba⟩	φ(a) = a, φ(b) = b
11	24625	⟨a, b \| aa=a, aababa=ba⟩	φ(a) = a, φ(b) = b
11	25164	⟨a, b \| aa=a, aabba=baa⟩	φ(a) = a, φ(b) = b