/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__f(X:S)) -> f(activate(X:S))
activate(n__g(X:S)) -> g(activate(X:S))
activate(X:S) -> X:S
f(X:S) -> cons(X:S,n__f(n__g(X:S)))
f(X:S) -> n__f(X:S)
g(0) -> s(0)
g(s(X:S)) -> s(s(g(X:S)))
g(X:S) -> n__g(X:S)
sel(0,cons(X:S,Y:S)) -> X:S
sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVATE(n__f(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__f(X:S)) -> F(activate(X:S))
 ACTIVATE(n__g(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__g(X:S)) -> G(activate(X:S))
 G(s(X:S)) -> G(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__f(X:S)) -> f(activate(X:S))
 activate(n__g(X:S)) -> g(activate(X:S))
 activate(X:S) -> X:S
 f(X:S) -> cons(X:S,n__f(n__g(X:S)))
 f(X:S) -> n__f(X:S)
 g(0) -> s(0)
 g(s(X:S)) -> s(s(g(X:S)))
 g(X:S) -> n__g(X:S)
 sel(0,cons(X:S,Y:S)) -> X:S
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__f(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__f(X:S)) -> F(activate(X:S))
 ACTIVATE(n__g(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__g(X:S)) -> G(activate(X:S))
 G(s(X:S)) -> G(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__f(X:S)) -> f(activate(X:S))
 activate(n__g(X:S)) -> g(activate(X:S))
 activate(X:S) -> X:S
 f(X:S) -> cons(X:S,n__f(n__g(X:S)))
 f(X:S) -> n__f(X:S)
 g(0) -> s(0)
 g(s(X:S)) -> s(s(g(X:S)))
 g(X:S) -> n__g(X:S)
 sel(0,cons(X:S,Y:S)) -> X:S
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 G(s(X:S)) -> G(X:S)
->->-> Rules:
 activate(n__f(X:S)) -> f(activate(X:S))
 activate(n__g(X:S)) -> g(activate(X:S))
 activate(X:S) -> X:S
 f(X:S) -> cons(X:S,n__f(n__g(X:S)))
 f(X:S) -> n__f(X:S)
 g(0) -> s(0)
 g(s(X:S)) -> s(s(g(X:S)))
 g(X:S) -> n__g(X:S)
 sel(0,cons(X:S,Y:S)) -> X:S
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__f(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__g(X:S)) -> ACTIVATE(X:S)
->->-> Rules:
 activate(n__f(X:S)) -> f(activate(X:S))
 activate(n__g(X:S)) -> g(activate(X:S))
 activate(X:S) -> X:S
 f(X:S) -> cons(X:S,n__f(n__g(X:S)))
 f(X:S) -> n__f(X:S)
 g(0) -> s(0)
 g(s(X:S)) -> s(s(g(X:S)))
 g(X:S) -> n__g(X:S)
 sel(0,cons(X:S,Y:S)) -> X:S
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
->->Cycle:
->->-> Pairs:
 SEL(s(X:S),cons(Y:S,Z:S)) -> SEL(X:S,activate(Z:S))
->->-> Rules:
 activate(n__f(X:S)) -> f(activate(X:S))
 activate(n__g(X:S)) -> g(activate(X:S))
 activate(X:S) -> X:S
 f(X:S) -> cons(X:S,n__f(n__g(X:S)))
 f(X:S) -> n__f(X:S)
 g(0) -> s(0)
 g(s(X:S)) -> s(s(g(X:S)))
 g(X:S) -> n__g(X:S)
 sel(0,cons(X:S,Y:S)) -> X:S
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))


The problem is decomposed in 3 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 G(s(X:S)) -> G(X:S)
-> Rules:
 activate(n__f(X:S)) -> f(activate(X:S))
 activate(n__g(X:S)) -> g(activate(X:S))
 activate(X:S) -> X:S
 f(X:S) -> cons(X:S,n__f(n__g(X:S)))
 f(X:S) -> n__f(X:S)
 g(0) -> s(0)
 g(s(X:S)) -> s(s(g(X:S)))
 g(X:S) -> n__g(X:S)
 sel(0,cons(X:S,Y:S)) -> X:S
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
->Projection:
 pi(G) = 1

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 ACTIVATE(n__f(X:S)) -> ACTIVATE(X:S)
 ACTIVATE(n__g(X:S)) -> ACTIVATE(X:S)
-> Rules:
 activate(n__f(X:S)) -> f(activate(X:S))
 activate(n__g(X:S)) -> g(activate(X:S))
 activate(X:S) -> X:S
 f(X:S) -> cons(X:S,n__f(n__g(X:S)))
 f(X:S) -> n__f(X:S)
 g(0) -> s(0)
 g(s(X:S)) -> s(s(g(X:S)))
 g(X:S) -> n__g(X:S)
 sel(0,cons(X:S,Y:S)) -> X:S
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
->Projection:
 pi(ACTIVATE) = 1

Problem 1.2: 

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

The problem is finite.

Problem 1.3: 

Subterm Processor:
-> Pairs:
 SEL(s(X:S),cons(Y:S,Z:S)) -> SEL(X:S,activate(Z:S))
-> Rules:
 activate(n__f(X:S)) -> f(activate(X:S))
 activate(n__g(X:S)) -> g(activate(X:S))
 activate(X:S) -> X:S
 f(X:S) -> cons(X:S,n__f(n__g(X:S)))
 f(X:S) -> n__f(X:S)
 g(0) -> s(0)
 g(s(X:S)) -> s(s(g(X:S)))
 g(X:S) -> n__g(X:S)
 sel(0,cons(X:S,Y:S)) -> X:S
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
->Projection:
 pi(SEL) = 1

Problem 1.3: 

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

The problem is finite.