/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 N X XS)
(RULES
activate(n__from(X)) -> from(activate(X))
activate(n__s(X)) -> s(activate(X))
activate(X) -> X
after(s(N),cons(X,XS)) -> after(N,activate(XS))
after(0,XS) -> XS
from(X) -> cons(X,n__from(n__s(X)))
from(X) -> n__from(X)
s(X) -> n__s(X)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVATE(n__from(X)) -> ACTIVATE(X)
 ACTIVATE(n__from(X)) -> FROM(activate(X))
 ACTIVATE(n__s(X)) -> ACTIVATE(X)
 ACTIVATE(n__s(X)) -> S(activate(X))
 AFTER(s(N),cons(X,XS)) -> ACTIVATE(XS)
 AFTER(s(N),cons(X,XS)) -> AFTER(N,activate(XS))
-> Rules:
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(X) -> X
 after(s(N),cons(X,XS)) -> after(N,activate(XS))
 after(0,XS) -> XS
 from(X) -> cons(X,n__from(n__s(X)))
 from(X) -> n__from(X)
 s(X) -> n__s(X)

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__from(X)) -> ACTIVATE(X)
 ACTIVATE(n__from(X)) -> FROM(activate(X))
 ACTIVATE(n__s(X)) -> ACTIVATE(X)
 ACTIVATE(n__s(X)) -> S(activate(X))
 AFTER(s(N),cons(X,XS)) -> ACTIVATE(XS)
 AFTER(s(N),cons(X,XS)) -> AFTER(N,activate(XS))
-> Rules:
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(X) -> X
 after(s(N),cons(X,XS)) -> after(N,activate(XS))
 after(0,XS) -> XS
 from(X) -> cons(X,n__from(n__s(X)))
 from(X) -> n__from(X)
 s(X) -> n__s(X)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__from(X)) -> ACTIVATE(X)
 ACTIVATE(n__s(X)) -> ACTIVATE(X)
->->-> Rules:
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(X) -> X
 after(s(N),cons(X,XS)) -> after(N,activate(XS))
 after(0,XS) -> XS
 from(X) -> cons(X,n__from(n__s(X)))
 from(X) -> n__from(X)
 s(X) -> n__s(X)
->->Cycle:
->->-> Pairs:
 AFTER(s(N),cons(X,XS)) -> AFTER(N,activate(XS))
->->-> Rules:
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(X) -> X
 after(s(N),cons(X,XS)) -> after(N,activate(XS))
 after(0,XS) -> XS
 from(X) -> cons(X,n__from(n__s(X)))
 from(X) -> n__from(X)
 s(X) -> n__s(X)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 ACTIVATE(n__from(X)) -> ACTIVATE(X)
 ACTIVATE(n__s(X)) -> ACTIVATE(X)
-> Rules:
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(X) -> X
 after(s(N),cons(X,XS)) -> after(N,activate(XS))
 after(0,XS) -> XS
 from(X) -> cons(X,n__from(n__s(X)))
 from(X) -> n__from(X)
 s(X) -> n__s(X)
->Projection:
 pi(ACTIVATE) = 1

Problem 1.1: 

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

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 AFTER(s(N),cons(X,XS)) -> AFTER(N,activate(XS))
-> Rules:
 activate(n__from(X)) -> from(activate(X))
 activate(n__s(X)) -> s(activate(X))
 activate(X) -> X
 after(s(N),cons(X,XS)) -> after(N,activate(XS))
 after(0,XS) -> XS
 from(X) -> cons(X,n__from(n__s(X)))
 from(X) -> n__from(X)
 s(X) -> n__s(X)
->Projection:
 pi(AFTER) = 1

Problem 1.2: 

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

The problem is finite.