f(X) → if(X, c, n__f(n__true))
if(true, X, Y) → X
if(false, X, Y) → activate(Y)
f(X) → n__f(X)
true → n__true
activate(n__f(X)) → f(activate(X))
activate(n__true) → true
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
f(X) → if(X, c, n__f(n__true))
if(true, X, Y) → X
if(false, X, Y) → activate(Y)
f(X) → n__f(X)
true → n__true
activate(n__f(X)) → f(activate(X))
activate(n__true) → true
activate(X) → X
ACTIVATE(n__true) → TRUE
ACTIVATE(n__f(X)) → F(activate(X))
ACTIVATE(n__f(X)) → ACTIVATE(X)
IF(false, X, Y) → ACTIVATE(Y)
F(X) → IF(X, c, n__f(n__true))
f(X) → if(X, c, n__f(n__true))
if(true, X, Y) → X
if(false, X, Y) → activate(Y)
f(X) → n__f(X)
true → n__true
activate(n__f(X)) → f(activate(X))
activate(n__true) → true
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
ACTIVATE(n__true) → TRUE
ACTIVATE(n__f(X)) → F(activate(X))
ACTIVATE(n__f(X)) → ACTIVATE(X)
IF(false, X, Y) → ACTIVATE(Y)
F(X) → IF(X, c, n__f(n__true))
f(X) → if(X, c, n__f(n__true))
if(true, X, Y) → X
if(false, X, Y) → activate(Y)
f(X) → n__f(X)
true → n__true
activate(n__f(X)) → f(activate(X))
activate(n__true) → true
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
ACTIVATE(n__f(X)) → F(activate(X))
ACTIVATE(n__f(X)) → ACTIVATE(X)
IF(false, X, Y) → ACTIVATE(Y)
F(X) → IF(X, c, n__f(n__true))
f(X) → if(X, c, n__f(n__true))
if(true, X, Y) → X
if(false, X, Y) → activate(Y)
f(X) → n__f(X)
true → n__true
activate(n__f(X)) → f(activate(X))
activate(n__true) → true
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVATE(n__f(X)) → F(activate(X))
IF(false, X, Y) → ACTIVATE(Y)
Used ordering: Polynomial interpretation [25,35]:
ACTIVATE(n__f(X)) → ACTIVATE(X)
F(X) → IF(X, c, n__f(n__true))
The value of delta used in the strict ordering is 1.
POL(c) = 0
POL(if(x1, x2, x3)) = x_1 + x_2 + (4)x_3
POL(f(x1)) = (4)x_1
POL(n__true) = 0
POL(n__f(x1)) = (4)x_1
POL(true) = 0
POL(false) = 2
POL(activate(x1)) = x_1
POL(IF(x1, x2, x3)) = 1 + (2)x_1 + (4)x_2 + (4)x_3
POL(ACTIVATE(x1)) = 4 + (2)x_1
POL(F(x1)) = 1 + (4)x_1
if(true, X, Y) → X
f(X) → if(X, c, n__f(n__true))
if(false, X, Y) → activate(Y)
activate(n__f(X)) → f(activate(X))
f(X) → n__f(X)
true → n__true
activate(n__true) → true
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
ACTIVATE(n__f(X)) → ACTIVATE(X)
F(X) → IF(X, c, n__f(n__true))
f(X) → if(X, c, n__f(n__true))
if(true, X, Y) → X
if(false, X, Y) → activate(Y)
f(X) → n__f(X)
true → n__true
activate(n__f(X)) → f(activate(X))
activate(n__true) → true
activate(X) → X
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
ACTIVATE(n__f(X)) → ACTIVATE(X)
f(X) → if(X, c, n__f(n__true))
if(true, X, Y) → X
if(false, X, Y) → activate(Y)
f(X) → n__f(X)
true → n__true
activate(n__f(X)) → f(activate(X))
activate(n__true) → true
activate(X) → X
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ACTIVATE(n__f(X)) → ACTIVATE(X)
The value of delta used in the strict ordering is 4.
POL(n__f(x1)) = 1 + (4)x_1
POL(ACTIVATE(x1)) = (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
f(X) → if(X, c, n__f(n__true))
if(true, X, Y) → X
if(false, X, Y) → activate(Y)
f(X) → n__f(X)
true → n__true
activate(n__f(X)) → f(activate(X))
activate(n__true) → true
activate(X) → X