a__f(a, b, X) → a__f(X, X, mark(X))
a__c → a
a__c → b
mark(f(X1, X2, X3)) → a__f(X1, X2, mark(X3))
mark(c) → a__c
mark(a) → a
mark(b) → b
a__f(X1, X2, X3) → f(X1, X2, X3)
a__c → c
↳ QTRS
↳ DependencyPairsProof
a__f(a, b, X) → a__f(X, X, mark(X))
a__c → a
a__c → b
mark(f(X1, X2, X3)) → a__f(X1, X2, mark(X3))
mark(c) → a__c
mark(a) → a
mark(b) → b
a__f(X1, X2, X3) → f(X1, X2, X3)
a__c → c
MARK(f(X1, X2, X3)) → MARK(X3)
A__F(a, b, X) → A__F(X, X, mark(X))
MARK(f(X1, X2, X3)) → A__F(X1, X2, mark(X3))
A__F(a, b, X) → MARK(X)
MARK(c) → A__C
a__f(a, b, X) → a__f(X, X, mark(X))
a__c → a
a__c → b
mark(f(X1, X2, X3)) → a__f(X1, X2, mark(X3))
mark(c) → a__c
mark(a) → a
mark(b) → b
a__f(X1, X2, X3) → f(X1, X2, X3)
a__c → c
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
MARK(f(X1, X2, X3)) → MARK(X3)
A__F(a, b, X) → A__F(X, X, mark(X))
MARK(f(X1, X2, X3)) → A__F(X1, X2, mark(X3))
A__F(a, b, X) → MARK(X)
MARK(c) → A__C
a__f(a, b, X) → a__f(X, X, mark(X))
a__c → a
a__c → b
mark(f(X1, X2, X3)) → a__f(X1, X2, mark(X3))
mark(c) → a__c
mark(a) → a
mark(b) → b
a__f(X1, X2, X3) → f(X1, X2, X3)
a__c → c
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
MARK(f(X1, X2, X3)) → MARK(X3)
A__F(a, b, X) → A__F(X, X, mark(X))
MARK(f(X1, X2, X3)) → A__F(X1, X2, mark(X3))
A__F(a, b, X) → MARK(X)
a__f(a, b, X) → a__f(X, X, mark(X))
a__c → a
a__c → b
mark(f(X1, X2, X3)) → a__f(X1, X2, mark(X3))
mark(c) → a__c
mark(a) → a
mark(b) → b
a__f(X1, X2, X3) → f(X1, X2, X3)
a__c → c
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
MARK(f(X1, X2, X3)) → MARK(X3)
MARK(f(X1, X2, X3)) → A__F(X1, X2, mark(X3))
Used ordering: Polynomial interpretation [25,35]:
A__F(a, b, X) → A__F(X, X, mark(X))
A__F(a, b, X) → MARK(X)
The value of delta used in the strict ordering is 3.
POL(c) = 0
POL(MARK(x1)) = 2 + (3)x_1
POL(a) = 0
POL(a__c) = 0
POL(f(x1, x2, x3)) = 1 + (2)x_3
POL(a__f(x1, x2, x3)) = 1 + (2)x_3
POL(mark(x1)) = x_1
POL(b) = 0
POL(A__F(x1, x2, x3)) = 2 + (4)x_3
a__f(a, b, X) → a__f(X, X, mark(X))
a__c → a
a__c → b
mark(f(X1, X2, X3)) → a__f(X1, X2, mark(X3))
mark(c) → a__c
mark(a) → a
mark(b) → b
a__f(X1, X2, X3) → f(X1, X2, X3)
a__c → c
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
A__F(a, b, X) → A__F(X, X, mark(X))
A__F(a, b, X) → MARK(X)
a__f(a, b, X) → a__f(X, X, mark(X))
a__c → a
a__c → b
mark(f(X1, X2, X3)) → a__f(X1, X2, mark(X3))
mark(c) → a__c
mark(a) → a
mark(b) → b
a__f(X1, X2, X3) → f(X1, X2, X3)
a__c → c
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
A__F(a, b, X) → A__F(X, X, mark(X))
a__f(a, b, X) → a__f(X, X, mark(X))
a__c → a
a__c → b
mark(f(X1, X2, X3)) → a__f(X1, X2, mark(X3))
mark(c) → a__c
mark(a) → a
mark(b) → b
a__f(X1, X2, X3) → f(X1, X2, X3)
a__c → c