#9144 ⟨a, b | aa=a, abab=aba⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element ab² 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

#	Rule	Proof
1.	a² ⇒ a	[1]
2.	(ab)² ⇒ aba	[2]

# ab:aa=a,abab=aba ab - -
aa=a
abab=aba

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

4 total

Σ	#	Presentation	Mapping
11	25154	⟨a, b \| aa=a, aabab=aba⟩	φ(a) = a, φ(b) = b
11	25178	⟨a, b \| aa=a, abaab=aba⟩	φ(a) = a, φ(b) = b
11	25671	⟨a, b \| aa=a, abab=aaba⟩	φ(a) = a, φ(b) = b
11	25673	⟨a, b \| aa=a, abab=abaa⟩	φ(a) = a, φ(b) = b