/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 XS: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
after(s(N:S),cons(X:S,XS:S)) -> after(N:S,activate(XS:S))
after(0,XS:S) -> XS: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)
)

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))
 AFTER(s(N:S),cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 AFTER(s(N:S),cons(X:S,XS:S)) -> AFTER(N:S,activate(XS: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
 after(s(N:S),cons(X:S,XS:S)) -> after(N:S,activate(XS:S))
 after(0,XS:S) -> XS: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)

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))
 AFTER(s(N:S),cons(X:S,XS:S)) -> ACTIVATE(XS:S)
 AFTER(s(N:S),cons(X:S,XS:S)) -> AFTER(N:S,activate(XS: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
 after(s(N:S),cons(X:S,XS:S)) -> after(N:S,activate(XS:S))
 after(0,XS:S) -> XS: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)
->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
 after(s(N:S),cons(X:S,XS:S)) -> after(N:S,activate(XS:S))
 after(0,XS:S) -> XS: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)
->->Cycle:
->->-> Pairs:
 AFTER(s(N:S),cons(X:S,XS:S)) -> AFTER(N:S,activate(XS: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
 after(s(N:S),cons(X:S,XS:S)) -> after(N:S,activate(XS:S))
 after(0,XS:S) -> XS: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)


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
 after(s(N:S),cons(X:S,XS:S)) -> after(N:S,activate(XS:S))
 after(0,XS:S) -> XS: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)
->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
 after(s(N:S),cons(X:S,XS:S)) -> after(N:S,activate(XS:S))
 after(0,XS:S) -> XS: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)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 AFTER(s(N:S),cons(X:S,XS:S)) -> AFTER(N:S,activate(XS: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
 after(s(N:S),cons(X:S,XS:S)) -> after(N:S,activate(XS:S))
 after(0,XS:S) -> XS: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)
->Projection:
 pi(AFTER) = 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
 after(s(N:S),cons(X:S,XS:S)) -> after(N:S,activate(XS:S))
 after(0,XS:S) -> XS: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)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.