#2591 ⟨a, b | aaa=1, babb=ba⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element aba has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ b² = b and b ⋅ 1 = b, however b² ≠ 1
Not right cancellative, because right multiplication by b is not injective:
- b² ⋅ b = b and 1 ⋅ b = b, however b² ≠ 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:aaa=1,babb=ba ab - -
aaa=1
bbb=b
babb=ba
baabb=baa

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

2 total

Σ	#	Presentation	Mapping
11	22796	⟨a, b \| aaa=1, ababb=aba⟩	φ(a) = a, φ(b) = b
11	22834	⟨a, b \| aaa=1, baabb=baa⟩	φ(a) = a, φ(b) = b

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

3 total

Σ	#	Presentation	Mapping
10	7505	⟨a, b \| aaa=1, aabbab=b⟩	φ(a) = a, φ(b) = b
10	7523	⟨a, b \| aaa=1, abbaab=b⟩	φ(a) = a, φ(b) = b
11	22803	⟨a, b \| aaa=1, abbab=aab⟩	φ(a) = a, φ(b) = b