/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 v_NonEmpty:S N:S X:S X1:S X2:S XS:S)
(RULES
2nd(cons(X:S,XS:S)) -> head(activate(XS:S))
activate(n__from(X:S)) -> from(X:S)
activate(n__take(X1:S,X2:S)) -> take(X1:S,X2:S)
activate(X:S) -> X:S
from(X:S) -> cons(X:S,n__from(s(X:S)))
from(X:S) -> n__from(X:S)
head(cons(X:S,XS:S)) -> X:S
sel(0,cons(X:S,XS:S)) -> X:S
sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,activate(XS:S))
take(0,XS:S) -> nil
take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,n__take(N:S,activate(XS:S)))
take(X1:S,X2:S) -> n__take(X1:S,X2:S)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 2ND(cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 2ND(cons(X:S,XS:S)) -> HEAD(activate(XS:S))
 ACTIVATE(n__from(X:S)) -> FROM(X:S)
 ACTIVATE(n__take(X1:S,X2:S)) -> TAKE(X1:S,X2:S)
 SEL(s(N:S),cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 SEL(s(N:S),cons(X:S,XS:S)) -> SEL(N:S,activate(XS:S))
 TAKE(s(N:S),cons(X:S,XS:S)) -> ACTIVATE(XS:S)
-> Rules:
 2nd(cons(X:S,XS:S)) -> head(activate(XS:S))
 activate(n__from(X:S)) -> from(X:S)
 activate(n__take(X1:S,X2:S)) -> take(X1:S,X2:S)
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 head(cons(X:S,XS:S)) -> X:S
 sel(0,cons(X:S,XS:S)) -> X:S
 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,activate(XS:S))
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,n__take(N:S,activate(XS:S)))
 take(X1:S,X2:S) -> n__take(X1:S,X2:S)

Problem 1: 

SCC Processor:
-> Pairs:
 2ND(cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 2ND(cons(X:S,XS:S)) -> HEAD(activate(XS:S))
 ACTIVATE(n__from(X:S)) -> FROM(X:S)
 ACTIVATE(n__take(X1:S,X2:S)) -> TAKE(X1:S,X2:S)
 SEL(s(N:S),cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 SEL(s(N:S),cons(X:S,XS:S)) -> SEL(N:S,activate(XS:S))
 TAKE(s(N:S),cons(X:S,XS:S)) -> ACTIVATE(XS:S)
-> Rules:
 2nd(cons(X:S,XS:S)) -> head(activate(XS:S))
 activate(n__from(X:S)) -> from(X:S)
 activate(n__take(X1:S,X2:S)) -> take(X1:S,X2:S)
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 head(cons(X:S,XS:S)) -> X:S
 sel(0,cons(X:S,XS:S)) -> X:S
 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,activate(XS:S))
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,n__take(N:S,activate(XS:S)))
 take(X1:S,X2:S) -> n__take(X1:S,X2:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__take(X1:S,X2:S)) -> TAKE(X1:S,X2:S)
 TAKE(s(N:S),cons(X:S,XS:S)) -> ACTIVATE(XS:S)
->->-> Rules:
 2nd(cons(X:S,XS:S)) -> head(activate(XS:S))
 activate(n__from(X:S)) -> from(X:S)
 activate(n__take(X1:S,X2:S)) -> take(X1:S,X2:S)
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 head(cons(X:S,XS:S)) -> X:S
 sel(0,cons(X:S,XS:S)) -> X:S
 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,activate(XS:S))
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,n__take(N:S,activate(XS:S)))
 take(X1:S,X2:S) -> n__take(X1:S,X2:S)
->->Cycle:
->->-> Pairs:
 SEL(s(N:S),cons(X:S,XS:S)) -> SEL(N:S,activate(XS:S))
->->-> Rules:
 2nd(cons(X:S,XS:S)) -> head(activate(XS:S))
 activate(n__from(X:S)) -> from(X:S)
 activate(n__take(X1:S,X2:S)) -> take(X1:S,X2:S)
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 head(cons(X:S,XS:S)) -> X:S
 sel(0,cons(X:S,XS:S)) -> X:S
 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,activate(XS:S))
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,n__take(N:S,activate(XS:S)))
 take(X1:S,X2:S) -> n__take(X1:S,X2:S)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 ACTIVATE(n__take(X1:S,X2:S)) -> TAKE(X1:S,X2:S)
 TAKE(s(N:S),cons(X:S,XS:S)) -> ACTIVATE(XS:S)
-> Rules:
 2nd(cons(X:S,XS:S)) -> head(activate(XS:S))
 activate(n__from(X:S)) -> from(X:S)
 activate(n__take(X1:S,X2:S)) -> take(X1:S,X2:S)
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 head(cons(X:S,XS:S)) -> X:S
 sel(0,cons(X:S,XS:S)) -> X:S
 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,activate(XS:S))
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,n__take(N:S,activate(XS:S)))
 take(X1:S,X2:S) -> n__take(X1:S,X2:S)
->Projection:
 pi(ACTIVATE) = 1
 pi(TAKE) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 2nd(cons(X:S,XS:S)) -> head(activate(XS:S))
 activate(n__from(X:S)) -> from(X:S)
 activate(n__take(X1:S,X2:S)) -> take(X1:S,X2:S)
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 head(cons(X:S,XS:S)) -> X:S
 sel(0,cons(X:S,XS:S)) -> X:S
 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,activate(XS:S))
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,n__take(N:S,activate(XS:S)))
 take(X1:S,X2:S) -> n__take(X1:S,X2:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 SEL(s(N:S),cons(X:S,XS:S)) -> SEL(N:S,activate(XS:S))
-> Rules:
 2nd(cons(X:S,XS:S)) -> head(activate(XS:S))
 activate(n__from(X:S)) -> from(X:S)
 activate(n__take(X1:S,X2:S)) -> take(X1:S,X2:S)
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 head(cons(X:S,XS:S)) -> X:S
 sel(0,cons(X:S,XS:S)) -> X:S
 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,activate(XS:S))
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,n__take(N:S,activate(XS:S)))
 take(X1:S,X2:S) -> n__take(X1:S,X2:S)
->Projection:
 pi(SEL) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 2nd(cons(X:S,XS:S)) -> head(activate(XS:S))
 activate(n__from(X:S)) -> from(X:S)
 activate(n__take(X1:S,X2:S)) -> take(X1:S,X2:S)
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 head(cons(X:S,XS:S)) -> X:S
 sel(0,cons(X:S,XS:S)) -> X:S
 sel(s(N:S),cons(X:S,XS:S)) -> sel(N:S,activate(XS:S))
 take(0,XS:S) -> nil
 take(s(N:S),cons(X:S,XS:S)) -> cons(X:S,n__take(N:S,activate(XS:S)))
 take(X1:S,X2:S) -> n__take(X1:S,X2:S)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.