#5294 ⟨a, b | aaa=aa, aab=aa⟩

Properties

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

#	Rule	Proof
1.	a³ ⇒ a²	[1]
2.	a²b ⇒ a²	[2]

# ab:aaa=aa,aab=aa ab - -
aaa=aa
aab=aa

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

4 total

Σ	#	Presentation	Mapping
11	15948	⟨a, b \| aaa=aa, aaab=aa⟩	φ(a) = a, φ(b) = b
11	16085	⟨a, b \| aab=aa, aaab=aa⟩	φ(a) = a, φ(b) = b
11	16089	⟨a, b \| aab=aa, aaba=aa⟩	φ(a) = a, φ(b) = b
11	16473	⟨a, b \| aaa=aa, aab=aaa⟩	φ(a) = a, φ(b) = b