#12461 ⟨a, b | aabb=ab, baaa=a⟩

Properties

Sum of relation sides is 11
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:aabb=ab,baaa=a ab - -
aa=a
ba=a
abb=ab

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

3 total

Σ	#	Presentation	Mapping
11	12463	⟨a, b \| aabb=ab, baba=a⟩	φ(a) = a, φ(b) = b
11	19688	⟨a, b \| aba=a, baabb=ab⟩	φ(a) = a, φ(b) = b
11	20203	⟨a, b \| aba=a, aabb=bab⟩	φ(a) = a, φ(b) = b

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

9 total

Σ	#	Presentation	Mapping
11	19474	⟨a, b \| aab=a, bbaaa=ba⟩	φ(a) = a, φ(b) = b
11	19478	⟨a, b \| aab=a, bbaab=ba⟩	φ(a) = a, φ(b) = b
11	19482	⟨a, b \| aab=a, bbaba=ba⟩	φ(a) = a, φ(b) = b
11	19998	⟨a, b \| aab=a, baab=bba⟩	φ(a) = a, φ(b) = b
11	20006	⟨a, b \| aab=a, baba=bba⟩	φ(a) = a, φ(b) = b
11	20014	⟨a, b \| aab=a, babb=bba⟩	φ(a) = a, φ(b) = b
11	20020	⟨a, b \| aab=a, bbaa=baa⟩	φ(a) = a, φ(b) = b
11	20021	⟨a, b \| aab=a, bbaa=bab⟩	φ(a) = a, φ(b) = b
11	20029	⟨a, b \| aab=a, bbab=bab⟩	φ(a) = a, φ(b) = b