#2090 ⟨a, b | aba=a, aabb=a⟩

Properties

Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ba = a and a ⋅ 1 = a, however ba ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- ab ⋅ a = a and 1 ⋅ a = a, however ab ≠ 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

#	Rule	Proof
1.	aba ⇒ a	[1]
2.	a²b² ⇒ a	[2]

# ab:aba=a,aabb=a ab - -
aba=a
aabb=a

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

4 total

Σ	#	Presentation	Mapping
11	19108	⟨a, b \| aba=a, aababb=a⟩	φ(a) = a, φ(b) = b
11	19122	⟨a, b \| aba=a, abaabb=a⟩	φ(a) = a, φ(b) = b
11	19689	⟨a, b \| aba=a, baabb=ba⟩	φ(a) = a, φ(b) = b
11	20200	⟨a, b \| aba=a, aabb=aba⟩	φ(a) = a, φ(b) = b

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

1 total

Σ	#	Presentation	Mapping
11	12344	⟨a, b \| aaba=aa, bbaa=a⟩	φ(a) = a, φ(b) = b