#9320 ⟨a, b | ab=a, baaa=aaa⟩

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 ⋅ b = a and a ⋅ 1 = a, however b ≠ 1
Not right cancellative, because right multiplication by a is not injective:
- ba² ⋅ a = a³ and a² ⋅ a = a³, however ba² ≠ a²

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.	ab ⇒ a	[1]
2.	ba³ ⇒ a³	[2]

# ab:ab=a,baaa=aaa ab - -
ab=a
baaa=aaa

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

6 total

Σ	#	Presentation	Mapping
11	25540	⟨a, b \| ab=a, baaab=aaa⟩	φ(a) = a, φ(b) = b
11	25548	⟨a, b \| ab=a, baaba=aaa⟩	φ(a) = a, φ(b) = b
11	25564	⟨a, b \| ab=a, babaa=aaa⟩	φ(a) = a, φ(b) = b
11	25821	⟨a, b \| ab=a, baaa=aaab⟩	φ(a) = a, φ(b) = b
11	25822	⟨a, b \| ab=a, baaa=aaba⟩	φ(a) = a, φ(b) = b
11	25824	⟨a, b \| ab=a, baaa=abaa⟩	φ(a) = a, φ(b) = b