/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 v_NonEmpty:S X:S Y:S Z:S)
(RULES
activate(n__from(X:S)) -> from(activate(X:S))
activate(n__s(X:S)) -> s(activate(X:S))
activate(X:S) -> X:S
from(X:S) -> cons(X:S,n__from(n__s(X:S)))
from(X:S) -> n__from(X:S)
s(X:S) -> n__s(X:S)
sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
sel(0,cons(X:S,Y:S)) -> X:S
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__from(X:S)) -> FROM(activate(X:S))
 ACTIVATE(n__s(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__s(X:S)) -> S(activate(X:S))
 SEL(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 SEL(s(X:S),cons(Y:S,Z:S)) -> SEL(X:S,activate(Z:S))
-> Rules:
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 s(X:S) -> n__s(X:S)
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
 sel(0,cons(X:S,Y:S)) -> X:S

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__from(X:S)) -> FROM(activate(X:S))
 ACTIVATE(n__s(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__s(X:S)) -> S(activate(X:S))
 SEL(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
 SEL(s(X:S),cons(Y:S,Z:S)) -> SEL(X:S,activate(Z:S))
-> Rules:
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 s(X:S) -> n__s(X:S)
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
 sel(0,cons(X:S,Y:S)) -> X:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__s(X:S)) -> ACTIVATE(X:S)
->->-> Rules:
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 s(X:S) -> n__s(X:S)
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
 sel(0,cons(X:S,Y:S)) -> X:S
->->Cycle:
->->-> Pairs:
 SEL(s(X:S),cons(Y:S,Z:S)) -> SEL(X:S,activate(Z:S))
->->-> Rules:
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 s(X:S) -> n__s(X:S)
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
 sel(0,cons(X:S,Y:S)) -> X:S


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 ACTIVATE(n__from(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__s(X:S)) -> ACTIVATE(X:S)
-> Rules:
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 s(X:S) -> n__s(X:S)
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
 sel(0,cons(X:S,Y:S)) -> X:S
->Projection:
 pi(ACTIVATE) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 s(X:S) -> n__s(X:S)
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
 sel(0,cons(X:S,Y:S)) -> X:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 SEL(s(X:S),cons(Y:S,Z:S)) -> SEL(X:S,activate(Z:S))
-> Rules:
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 s(X:S) -> n__s(X:S)
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
 sel(0,cons(X:S,Y:S)) -> X:S
->Projection:
 pi(SEL) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 activate(n__from(X:S)) -> from(activate(X:S))
 activate(n__s(X:S)) -> s(activate(X:S))
 activate(X:S) -> X:S
 from(X:S) -> cons(X:S,n__from(n__s(X:S)))
 from(X:S) -> n__from(X:S)
 s(X:S) -> n__s(X:S)
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
 sel(0,cons(X:S,Y:S)) -> X:S
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.