/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem 1: 

(VAR I P X X1 X2 Y Z)
(RULES
a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
a____(nil,X) -> mark(X)
a____(X,nil) -> mark(X)
a____(X1,X2) -> __(X1,X2)
a__and(tt,X) -> mark(X)
a__and(X1,X2) -> and(X1,X2)
a__isNePal(__(I,__(P,I))) -> tt
a__isNePal(X) -> isNePal(X)
mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
mark(and(X1,X2)) -> a__and(mark(X1),X2)
mark(isNePal(X)) -> a__isNePal(mark(X))
mark(nil) -> nil
mark(tt) -> tt
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 A____(__(X,Y),Z) -> A____(mark(X),a____(mark(Y),mark(Z)))
 A____(__(X,Y),Z) -> A____(mark(Y),mark(Z))
 A____(__(X,Y),Z) -> MARK(X)
 A____(__(X,Y),Z) -> MARK(Y)
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> A__ISNEPAL(mark(X))
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

SCC Processor:
-> Pairs:
 A____(__(X,Y),Z) -> A____(mark(X),a____(mark(Y),mark(Z)))
 A____(__(X,Y),Z) -> A____(mark(Y),mark(Z))
 A____(__(X,Y),Z) -> MARK(X)
 A____(__(X,Y),Z) -> MARK(Y)
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> A__ISNEPAL(mark(X))
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A____(__(X,Y),Z) -> A____(mark(X),a____(mark(Y),mark(Z)))
 A____(__(X,Y),Z) -> A____(mark(Y),mark(Z))
 A____(__(X,Y),Z) -> MARK(X)
 A____(__(X,Y),Z) -> MARK(Y)
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
->->-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A____(__(X,Y),Z) -> A____(mark(X),a____(mark(Y),mark(Z)))
 A____(__(X,Y),Z) -> A____(mark(Y),mark(Z))
 A____(__(X,Y),Z) -> MARK(X)
 A____(__(X,Y),Z) -> MARK(Y)
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
-> Usable rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a____](X1,X2) = 2.X1 + X2 + 2
[a__and](X1,X2) = 2.X1 + 2.X2 + 2
[a__isNePal](X) = X + 1
[mark](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[and](X1,X2) = 2.X1 + 2.X2 + 2
[isNePal](X) = X + 1
[nil] = 2
[tt] = 2
[A____](X1,X2) = 2.X1 + X2
[A__AND](X1,X2) = 2.X1 + 2.X2
[MARK](X) = X

Problem 1: 

SCC Processor:
-> Pairs:
 A____(__(X,Y),Z) -> A____(mark(Y),mark(Z))
 A____(__(X,Y),Z) -> MARK(X)
 A____(__(X,Y),Z) -> MARK(Y)
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A____(__(X,Y),Z) -> A____(mark(Y),mark(Z))
 A____(__(X,Y),Z) -> MARK(X)
 A____(__(X,Y),Z) -> MARK(Y)
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
->->-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A____(__(X,Y),Z) -> A____(mark(Y),mark(Z))
 A____(__(X,Y),Z) -> MARK(X)
 A____(__(X,Y),Z) -> MARK(Y)
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
-> Usable rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a____](X1,X2) = 2.X1 + X2 + 2
[a__and](X1,X2) = 2.X1 + 2.X2 + 2
[a__isNePal](X) = X + 1
[mark](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[and](X1,X2) = 2.X1 + 2.X2 + 2
[isNePal](X) = X + 1
[nil] = 0
[tt] = 1
[A____](X1,X2) = 2.X1 + 2.X2 + 2
[A__AND](X1,X2) = 2.X2 + 2
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A____(__(X,Y),Z) -> MARK(X)
 A____(__(X,Y),Z) -> MARK(Y)
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A____(__(X,Y),Z) -> MARK(X)
 A____(__(X,Y),Z) -> MARK(Y)
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
->->-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A____(__(X,Y),Z) -> MARK(X)
 A____(__(X,Y),Z) -> MARK(Y)
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
-> Usable rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a____](X1,X2) = 2.X1 + X2 + 2
[a__and](X1,X2) = 2.X1 + 2.X2 + 2
[a__isNePal](X) = 2.X + 1
[mark](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[and](X1,X2) = 2.X1 + 2.X2 + 2
[isNePal](X) = 2.X + 1
[nil] = 0
[tt] = 1
[A____](X1,X2) = 2.X1 + X2 + 2
[A__AND](X1,X2) = 2.X1 + 2.X2
[MARK](X) = X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A____(__(X,Y),Z) -> MARK(Y)
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A____(__(X,Y),Z) -> MARK(Y)
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
->->-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A____(__(X,Y),Z) -> MARK(Y)
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
-> Usable rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a____](X1,X2) = 2.X1 + X2 + 1
[a__and](X1,X2) = X1 + 2.X2 + 2
[a__isNePal](X) = X + 2
[mark](X) = X
[__](X1,X2) = 2.X1 + X2 + 1
[and](X1,X2) = X1 + 2.X2 + 2
[isNePal](X) = X + 2
[nil] = 0
[tt] = 2
[A____](X1,X2) = 2.X1 + 2.X2 + 2
[A__AND](X1,X2) = X1 + 2.X2 + 2
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
->->-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A____(__(X,Y),Z) -> MARK(Z)
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
-> Usable rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a____](X1,X2) = 2.X1 + X2 + 2
[a__and](X1,X2) = X1 + 2.X2 + 2
[a__isNePal](X) = X
[mark](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[and](X1,X2) = X1 + 2.X2 + 2
[isNePal](X) = X
[nil] = 2
[tt] = 2
[A____](X1,X2) = 2.X1 + 2.X2
[A__AND](X1,X2) = X1 + 2.X2 + 1
[MARK](X) = 2.X

Problem 1: 

SCC Processor:
-> Pairs:
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
->->-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A____(nil,X) -> MARK(X)
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
-> Usable rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a____](X1,X2) = 2.X1 + X2 + 2
[a__and](X1,X2) = 2.X1 + 2.X2 + 2
[a__isNePal](X) = 2.X + 1
[mark](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[and](X1,X2) = 2.X1 + 2.X2 + 2
[isNePal](X) = 2.X + 1
[nil] = 2
[tt] = 0
[A____](X1,X2) = 2.X1 + 2.X2 + 2
[A__AND](X1,X2) = X1 + 2.X2 + 1
[MARK](X) = 2.X + 1

Problem 1: 

SCC Processor:
-> Pairs:
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
->->-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 A____(X,nil) -> MARK(X)
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
-> Usable rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[a____](X1,X2) = 2.X1 + X2 + 2
[a__and](X1,X2) = X1 + 2.X2 + 2
[a__isNePal](X) = 2.X + 1
[mark](X) = X
[__](X1,X2) = 2.X1 + X2 + 2
[and](X1,X2) = X1 + 2.X2 + 2
[isNePal](X) = 2.X + 1
[nil] = 1
[tt] = 2
[A____](X1,X2) = 2.X1 + 2.X2 + 2
[A__AND](X1,X2) = 2.X2 + 2
[MARK](X) = 2.X + 2

Problem 1: 

SCC Processor:
-> Pairs:
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> A____(mark(X1),mark(X2))
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
->->-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt

Problem 1: 

Subterm Processor:
-> Pairs:
 A__AND(tt,X) -> MARK(X)
 MARK(__(X1,X2)) -> MARK(X1)
 MARK(__(X1,X2)) -> MARK(X2)
 MARK(and(X1,X2)) -> A__AND(mark(X1),X2)
 MARK(and(X1,X2)) -> MARK(X1)
 MARK(isNePal(X)) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Projection:
 pi(A__AND) = 2
 pi(MARK) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 A__AND(tt,X) -> MARK(X)
-> Rules:
 a____(__(X,Y),Z) -> a____(mark(X),a____(mark(Y),mark(Z)))
 a____(nil,X) -> mark(X)
 a____(X,nil) -> mark(X)
 a____(X1,X2) -> __(X1,X2)
 a__and(tt,X) -> mark(X)
 a__and(X1,X2) -> and(X1,X2)
 a__isNePal(__(I,__(P,I))) -> tt
 a__isNePal(X) -> isNePal(X)
 mark(__(X1,X2)) -> a____(mark(X1),mark(X2))
 mark(and(X1,X2)) -> a__and(mark(X1),X2)
 mark(isNePal(X)) -> a__isNePal(mark(X))
 mark(nil) -> nil
 mark(tt) -> tt
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.