a__f(X) → a__if(mark(X), c, f(true))
a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)
mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)
mark(c) → c
mark(true) → true
mark(false) → false
a__f(X) → f(X)
a__if(X1, X2, X3) → if(X1, X2, X3)
↳ QTRS
↳ DependencyPairsProof
a__f(X) → a__if(mark(X), c, f(true))
a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)
mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)
mark(c) → c
mark(true) → true
mark(false) → false
a__f(X) → f(X)
a__if(X1, X2, X3) → if(X1, X2, X3)
MARK(if(X1, X2, X3)) → A__IF(mark(X1), mark(X2), X3)
MARK(if(X1, X2, X3)) → MARK(X1)
A__IF(false, X, Y) → MARK(Y)
A__F(X) → A__IF(mark(X), c, f(true))
MARK(f(X)) → A__F(mark(X))
A__IF(true, X, Y) → MARK(X)
A__F(X) → MARK(X)
MARK(if(X1, X2, X3)) → MARK(X2)
MARK(f(X)) → MARK(X)
a__f(X) → a__if(mark(X), c, f(true))
a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)
mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)
mark(c) → c
mark(true) → true
mark(false) → false
a__f(X) → f(X)
a__if(X1, X2, X3) → if(X1, X2, X3)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
MARK(if(X1, X2, X3)) → A__IF(mark(X1), mark(X2), X3)
MARK(if(X1, X2, X3)) → MARK(X1)
A__IF(false, X, Y) → MARK(Y)
A__F(X) → A__IF(mark(X), c, f(true))
MARK(f(X)) → A__F(mark(X))
A__IF(true, X, Y) → MARK(X)
A__F(X) → MARK(X)
MARK(if(X1, X2, X3)) → MARK(X2)
MARK(f(X)) → MARK(X)
a__f(X) → a__if(mark(X), c, f(true))
a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)
mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)
mark(c) → c
mark(true) → true
mark(false) → false
a__f(X) → f(X)
a__if(X1, X2, X3) → if(X1, X2, X3)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A__F(X) → MARK(X)
MARK(f(X)) → MARK(X)
Used ordering: Polynomial interpretation [25,35]:
MARK(if(X1, X2, X3)) → A__IF(mark(X1), mark(X2), X3)
MARK(if(X1, X2, X3)) → MARK(X1)
A__IF(false, X, Y) → MARK(Y)
A__F(X) → A__IF(mark(X), c, f(true))
MARK(f(X)) → A__F(mark(X))
A__IF(true, X, Y) → MARK(X)
MARK(if(X1, X2, X3)) → MARK(X2)
The value of delta used in the strict ordering is 1.
POL(A__IF(x1, x2, x3)) = x_2 + x_3
POL(c) = 0
POL(MARK(x1)) = x_1
POL(if(x1, x2, x3)) = x_1 + x_2 + x_3
POL(f(x1)) = 1 + x_1
POL(a__f(x1)) = 1 + x_1
POL(true) = 0
POL(mark(x1)) = x_1
POL(false) = 0
POL(A__F(x1)) = 1 + x_1
POL(a__if(x1, x2, x3)) = x_1 + x_2 + x_3
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)
a__f(X) → a__if(mark(X), c, f(true))
mark(f(X)) → a__f(mark(X))
a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)
mark(c) → c
mark(false) → false
mark(true) → true
a__if(X1, X2, X3) → if(X1, X2, X3)
a__f(X) → f(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
MARK(if(X1, X2, X3)) → A__IF(mark(X1), mark(X2), X3)
A__IF(false, X, Y) → MARK(Y)
MARK(if(X1, X2, X3)) → MARK(X1)
A__F(X) → A__IF(mark(X), c, f(true))
MARK(f(X)) → A__F(mark(X))
A__IF(true, X, Y) → MARK(X)
MARK(if(X1, X2, X3)) → MARK(X2)
a__f(X) → a__if(mark(X), c, f(true))
a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)
mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)
mark(c) → c
mark(true) → true
mark(false) → false
a__f(X) → f(X)
a__if(X1, X2, X3) → if(X1, X2, X3)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A__IF(false, X, Y) → MARK(Y)
Used ordering: Polynomial interpretation [25,35]:
MARK(if(X1, X2, X3)) → A__IF(mark(X1), mark(X2), X3)
MARK(if(X1, X2, X3)) → MARK(X1)
A__F(X) → A__IF(mark(X), c, f(true))
MARK(f(X)) → A__F(mark(X))
A__IF(true, X, Y) → MARK(X)
MARK(if(X1, X2, X3)) → MARK(X2)
The value of delta used in the strict ordering is 1.
POL(A__IF(x1, x2, x3)) = x_1 + (2)x_2 + x_3
POL(c) = 0
POL(MARK(x1)) = x_1
POL(if(x1, x2, x3)) = x_1 + (2)x_2 + (2)x_3
POL(f(x1)) = x_1
POL(a__f(x1)) = x_1
POL(true) = 0
POL(mark(x1)) = x_1
POL(false) = 1
POL(A__F(x1)) = x_1
POL(a__if(x1, x2, x3)) = x_1 + (2)x_2 + (2)x_3
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)
a__f(X) → a__if(mark(X), c, f(true))
mark(f(X)) → a__f(mark(X))
a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)
mark(c) → c
mark(false) → false
mark(true) → true
a__if(X1, X2, X3) → if(X1, X2, X3)
a__f(X) → f(X)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
MARK(if(X1, X2, X3)) → A__IF(mark(X1), mark(X2), X3)
MARK(if(X1, X2, X3)) → MARK(X1)
A__F(X) → A__IF(mark(X), c, f(true))
MARK(f(X)) → A__F(mark(X))
A__IF(true, X, Y) → MARK(X)
MARK(if(X1, X2, X3)) → MARK(X2)
a__f(X) → a__if(mark(X), c, f(true))
a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)
mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)
mark(c) → c
mark(true) → true
mark(false) → false
a__f(X) → f(X)
a__if(X1, X2, X3) → if(X1, X2, X3)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A__F(X) → A__IF(mark(X), c, f(true))
MARK(f(X)) → A__F(mark(X))
Used ordering: Polynomial interpretation [25,35]:
MARK(if(X1, X2, X3)) → A__IF(mark(X1), mark(X2), X3)
MARK(if(X1, X2, X3)) → MARK(X1)
A__IF(true, X, Y) → MARK(X)
MARK(if(X1, X2, X3)) → MARK(X2)
The value of delta used in the strict ordering is 1.
POL(A__IF(x1, x2, x3)) = (2)x_2
POL(c) = 0
POL(MARK(x1)) = x_1
POL(if(x1, x2, x3)) = x_1 + (2)x_2 + x_3
POL(f(x1)) = 4 + x_1
POL(a__f(x1)) = 4 + x_1
POL(true) = 0
POL(mark(x1)) = x_1
POL(A__F(x1)) = 3 + x_1
POL(false) = 0
POL(a__if(x1, x2, x3)) = x_1 + (2)x_2 + x_3
mark(false) → false
mark(true) → true
a__if(X1, X2, X3) → if(X1, X2, X3)
a__f(X) → f(X)
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)
a__f(X) → a__if(mark(X), c, f(true))
mark(f(X)) → a__f(mark(X))
a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)
mark(c) → c
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
MARK(if(X1, X2, X3)) → A__IF(mark(X1), mark(X2), X3)
MARK(if(X1, X2, X3)) → MARK(X1)
A__IF(true, X, Y) → MARK(X)
MARK(if(X1, X2, X3)) → MARK(X2)
a__f(X) → a__if(mark(X), c, f(true))
a__if(true, X, Y) → mark(X)
a__if(false, X, Y) → mark(Y)
mark(f(X)) → a__f(mark(X))
mark(if(X1, X2, X3)) → a__if(mark(X1), mark(X2), X3)
mark(c) → c
mark(true) → true
mark(false) → false
a__f(X) → f(X)
a__if(X1, X2, X3) → if(X1, X2, X3)