#5383 ⟨a, b | aab=ab, bab=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:
- a² ⋅ a = a² and a ⋅ a = a², however a² ≠ 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=ab,bab=aa a/b - -
aaa=aa
ab=baa
bbaa=aa

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

4 total

Σ	#	Presentation	Mapping
10	5418	⟨a, b \| aba=ab, bab=aa⟩	φ(a) = a, φ(b) = b
11	16181	⟨a, b \| aab=ab, baab=aa⟩	φ(a) = a, φ(b) = b
11	16409	⟨a, b \| aba=ab, baab=aa⟩	φ(a) = a, φ(b) = b
11	16413	⟨a, b \| aba=ab, baba=aa⟩	φ(a) = a, φ(b) = b

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

6 total

Σ	#	Presentation	Mapping
10	5402	⟨a, b \| aab=ba, bba=aa⟩	φ(a) = a, φ(b) = b
11	16229	⟨a, b \| aab=ba, abab=aa⟩	φ(a) = a, φ(b) = b
11	16245	⟨a, b \| aab=ba, baab=aa⟩	φ(a) = a, φ(b) = b
11	16249	⟨a, b \| aab=ba, baba=aa⟩	φ(a) = a, φ(b) = b
11	16282	⟨a, b \| aab=bb, aaba=ab⟩	φ(a) = b, φ(b) = a
11	16445	⟨a, b \| aba=bb, aaba=ab⟩	φ(a) = b, φ(b) = a