/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR N X XS Y YS ZS)
(RULES
U11(tt,N,X,XS) -> U12(splitAt(activate(N),activate(XS)),activate(X))
U12(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
activate(n__natsFrom(X)) -> natsFrom(X)
activate(X) -> X
afterNth(N,XS) -> snd(splitAt(N,XS))
and(tt,X) -> activate(X)
fst(pair(X,Y)) -> X
head(cons(N,XS)) -> N
natsFrom(N) -> cons(N,n__natsFrom(s(N)))
natsFrom(X) -> n__natsFrom(X)
sel(N,XS) -> head(afterNth(N,XS))
snd(pair(X,Y)) -> Y
splitAt(0,XS) -> pair(nil,XS)
splitAt(s(N),cons(X,XS)) -> U11(tt,N,X,activate(XS))
tail(cons(N,XS)) -> activate(XS)
take(N,XS) -> fst(splitAt(N,XS))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 U11#(tt,N,X,XS) -> U12#(splitAt(activate(N),activate(XS)),activate(X))
 U11#(tt,N,X,XS) -> ACTIVATE(N)
 U11#(tt,N,X,XS) -> ACTIVATE(X)
 U11#(tt,N,X,XS) -> ACTIVATE(XS)
 U11#(tt,N,X,XS) -> SPLITAT(activate(N),activate(XS))
 U12#(pair(YS,ZS),X) -> ACTIVATE(X)
 ACTIVATE(n__natsFrom(X)) -> NATSFROM(X)
 AFTERNTH(N,XS) -> SND(splitAt(N,XS))
 AFTERNTH(N,XS) -> SPLITAT(N,XS)
 AND(tt,X) -> ACTIVATE(X)
 SEL(N,XS) -> AFTERNTH(N,XS)
 SEL(N,XS) -> HEAD(afterNth(N,XS))
 SPLITAT(s(N),cons(X,XS)) -> U11#(tt,N,X,activate(XS))
 SPLITAT(s(N),cons(X,XS)) -> ACTIVATE(XS)
 TAIL(cons(N,XS)) -> ACTIVATE(XS)
 TAKE(N,XS) -> FST(splitAt(N,XS))
 TAKE(N,XS) -> SPLITAT(N,XS)
-> Rules:
 U11(tt,N,X,XS) -> U12(splitAt(activate(N),activate(XS)),activate(X))
 U12(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
 activate(n__natsFrom(X)) -> natsFrom(X)
 activate(X) -> X
 afterNth(N,XS) -> snd(splitAt(N,XS))
 and(tt,X) -> activate(X)
 fst(pair(X,Y)) -> X
 head(cons(N,XS)) -> N
 natsFrom(N) -> cons(N,n__natsFrom(s(N)))
 natsFrom(X) -> n__natsFrom(X)
 sel(N,XS) -> head(afterNth(N,XS))
 snd(pair(X,Y)) -> Y
 splitAt(0,XS) -> pair(nil,XS)
 splitAt(s(N),cons(X,XS)) -> U11(tt,N,X,activate(XS))
 tail(cons(N,XS)) -> activate(XS)
 take(N,XS) -> fst(splitAt(N,XS))

Problem 1: 

SCC Processor:
-> Pairs:
 U11#(tt,N,X,XS) -> U12#(splitAt(activate(N),activate(XS)),activate(X))
 U11#(tt,N,X,XS) -> ACTIVATE(N)
 U11#(tt,N,X,XS) -> ACTIVATE(X)
 U11#(tt,N,X,XS) -> ACTIVATE(XS)
 U11#(tt,N,X,XS) -> SPLITAT(activate(N),activate(XS))
 U12#(pair(YS,ZS),X) -> ACTIVATE(X)
 ACTIVATE(n__natsFrom(X)) -> NATSFROM(X)
 AFTERNTH(N,XS) -> SND(splitAt(N,XS))
 AFTERNTH(N,XS) -> SPLITAT(N,XS)
 AND(tt,X) -> ACTIVATE(X)
 SEL(N,XS) -> AFTERNTH(N,XS)
 SEL(N,XS) -> HEAD(afterNth(N,XS))
 SPLITAT(s(N),cons(X,XS)) -> U11#(tt,N,X,activate(XS))
 SPLITAT(s(N),cons(X,XS)) -> ACTIVATE(XS)
 TAIL(cons(N,XS)) -> ACTIVATE(XS)
 TAKE(N,XS) -> FST(splitAt(N,XS))
 TAKE(N,XS) -> SPLITAT(N,XS)
-> Rules:
 U11(tt,N,X,XS) -> U12(splitAt(activate(N),activate(XS)),activate(X))
 U12(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
 activate(n__natsFrom(X)) -> natsFrom(X)
 activate(X) -> X
 afterNth(N,XS) -> snd(splitAt(N,XS))
 and(tt,X) -> activate(X)
 fst(pair(X,Y)) -> X
 head(cons(N,XS)) -> N
 natsFrom(N) -> cons(N,n__natsFrom(s(N)))
 natsFrom(X) -> n__natsFrom(X)
 sel(N,XS) -> head(afterNth(N,XS))
 snd(pair(X,Y)) -> Y
 splitAt(0,XS) -> pair(nil,XS)
 splitAt(s(N),cons(X,XS)) -> U11(tt,N,X,activate(XS))
 tail(cons(N,XS)) -> activate(XS)
 take(N,XS) -> fst(splitAt(N,XS))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 U11#(tt,N,X,XS) -> SPLITAT(activate(N),activate(XS))
 SPLITAT(s(N),cons(X,XS)) -> U11#(tt,N,X,activate(XS))
->->-> Rules:
 U11(tt,N,X,XS) -> U12(splitAt(activate(N),activate(XS)),activate(X))
 U12(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
 activate(n__natsFrom(X)) -> natsFrom(X)
 activate(X) -> X
 afterNth(N,XS) -> snd(splitAt(N,XS))
 and(tt,X) -> activate(X)
 fst(pair(X,Y)) -> X
 head(cons(N,XS)) -> N
 natsFrom(N) -> cons(N,n__natsFrom(s(N)))
 natsFrom(X) -> n__natsFrom(X)
 sel(N,XS) -> head(afterNth(N,XS))
 snd(pair(X,Y)) -> Y
 splitAt(0,XS) -> pair(nil,XS)
 splitAt(s(N),cons(X,XS)) -> U11(tt,N,X,activate(XS))
 tail(cons(N,XS)) -> activate(XS)
 take(N,XS) -> fst(splitAt(N,XS))

Problem 1: 

Reduction Pair Processor:
-> Pairs:
 U11#(tt,N,X,XS) -> SPLITAT(activate(N),activate(XS))
 SPLITAT(s(N),cons(X,XS)) -> U11#(tt,N,X,activate(XS))
-> Rules:
 U11(tt,N,X,XS) -> U12(splitAt(activate(N),activate(XS)),activate(X))
 U12(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
 activate(n__natsFrom(X)) -> natsFrom(X)
 activate(X) -> X
 afterNth(N,XS) -> snd(splitAt(N,XS))
 and(tt,X) -> activate(X)
 fst(pair(X,Y)) -> X
 head(cons(N,XS)) -> N
 natsFrom(N) -> cons(N,n__natsFrom(s(N)))
 natsFrom(X) -> n__natsFrom(X)
 sel(N,XS) -> head(afterNth(N,XS))
 snd(pair(X,Y)) -> Y
 splitAt(0,XS) -> pair(nil,XS)
 splitAt(s(N),cons(X,XS)) -> U11(tt,N,X,activate(XS))
 tail(cons(N,XS)) -> activate(XS)
 take(N,XS) -> fst(splitAt(N,XS))
-> Usable rules:
 activate(n__natsFrom(X)) -> natsFrom(X)
 activate(X) -> X
 natsFrom(N) -> cons(N,n__natsFrom(s(N)))
 natsFrom(X) -> n__natsFrom(X)
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[activate](X) = X + 1
[natsFrom](X) = 2
[cons](X1,X2) = X2 + 1
[n__natsFrom](X) = 1
[s](X) = 2.X + 2
[tt] = 2
[U11#](X1,X2,X3,X4) = 2.X1 + 2.X2 + X4
[SPLITAT](X1,X2) = 2.X1 + X2

Problem 1: 

SCC Processor:
-> Pairs:
 SPLITAT(s(N),cons(X,XS)) -> U11#(tt,N,X,activate(XS))
-> Rules:
 U11(tt,N,X,XS) -> U12(splitAt(activate(N),activate(XS)),activate(X))
 U12(pair(YS,ZS),X) -> pair(cons(activate(X),YS),ZS)
 activate(n__natsFrom(X)) -> natsFrom(X)
 activate(X) -> X
 afterNth(N,XS) -> snd(splitAt(N,XS))
 and(tt,X) -> activate(X)
 fst(pair(X,Y)) -> X
 head(cons(N,XS)) -> N
 natsFrom(N) -> cons(N,n__natsFrom(s(N)))
 natsFrom(X) -> n__natsFrom(X)
 sel(N,XS) -> head(afterNth(N,XS))
 snd(pair(X,Y)) -> Y
 splitAt(0,XS) -> pair(nil,XS)
 splitAt(s(N),cons(X,XS)) -> U11(tt,N,X,activate(XS))
 tail(cons(N,XS)) -> activate(XS)
 take(N,XS) -> fst(splitAt(N,XS))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.