#5384 ⟨a, b | aab=ab, bab=ab⟩

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 = ab and a ⋅ b = ab, however ab ≠ b
Not right cancellative, because right multiplication by b is not injective:
- a² ⋅ b = ab and a ⋅ b = ab, 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.	a²b ⇒ ab	[1]
2.	bab ⇒ ab	[2]

# ab:aab=ab,bab=ab ab - -
aab=ab
bab=ab

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

2 total

Σ	#	Presentation	Mapping
11	16182	⟨a, b \| aab=ab, baab=ab⟩	φ(a) = a, φ(b) = b
11	16504	⟨a, b \| aab=ab, bab=aab⟩	φ(a) = a, φ(b) = b