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

Problem 1: 

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

Problem 1: 

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


The problem is decomposed in 3 subproblems.

Problem 1.1: 

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

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

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

Problem 1.2: 

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

The problem is finite.

Problem 1.3: 

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

Problem 1.3: 

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

The problem is finite.