#19531 ⟨a, b | aab=b, aabba=bb⟩

Properties

Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element a has infinite order
Not left cancellative, because left multiplication by b is not injective:
- b ⋅ ba = b² and b ⋅ b = b², however ba ≠ b
Not right cancellative, because right multiplication by b is not injective:
- a² ⋅ b = b and 1 ⋅ b = b, however a² ≠ 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.	a²b ⇒ b	[1]
2.	b²a ⇒ b²	[2]

# ab:aab=b,aabba=bb ab - -
aab=b
bba=bb

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

4 total

Σ	#	Presentation	Mapping
11	19579	⟨a, b \| aab=b, baaba=bb⟩	φ(a) = a, φ(b) = b
11	20078	⟨a, b \| aab=b, aabb=bba⟩	φ(a) = a, φ(b) = b
11	20099	⟨a, b \| aab=b, abba=abb⟩	φ(a) = a, φ(b) = b
11	20126	⟨a, b \| aab=b, baab=bba⟩	φ(a) = a, φ(b) = b