#5353 ⟨a, b | aab=aa, aba=aa⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by a is not injective:
- a ⋅ ab = a² and a ⋅ a = a², however ab ≠ a
Not right cancellative, because right multiplication by a is not injective:
- ab ⋅ a = a² and a ⋅ a = a², however ab ≠ 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.	a²b ⇒ a²	[1]
2.	aba ⇒ a²	[2]

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

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

2 total

Σ	#	Presentation	Mapping
11	16352	⟨a, b \| aba=aa, abab=aa⟩	φ(a) = a, φ(b) = b
11	16490	⟨a, b \| aab=aa, aba=aab⟩	φ(a) = a, φ(b) = b