#9256 ⟨a, b | ab=a, aaaa=aaa⟩

Properties

Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element b 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:
- a³ ⋅ a = a³ and a² ⋅ a = a³, however a³ ≠ 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.	a⁴ ⇒ a³	[2]

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

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

7 total

Σ	#	Presentation	Mapping
11	25412	⟨a, b \| ab=a, aaaab=aaa⟩	φ(a) = a, φ(b) = b
11	25420	⟨a, b \| ab=a, aaaba=aaa⟩	φ(a) = a, φ(b) = b
11	25436	⟨a, b \| ab=a, aabaa=aaa⟩	φ(a) = a, φ(b) = b
11	25468	⟨a, b \| ab=a, abaaa=aaa⟩	φ(a) = a, φ(b) = b
11	25792	⟨a, b \| ab=a, aaab=aaaa⟩	φ(a) = a, φ(b) = b
11	25793	⟨a, b \| ab=a, aaba=aaaa⟩	φ(a) = a, φ(b) = b
11	25798	⟨a, b \| ab=a, abaa=aaaa⟩	φ(a) = a, φ(b) = b