/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 X:S X1:S X2:S Y:S Z:S)
(RULES
activate(n__first(X1:S,X2:S)) -> first(X1:S,X2:S)
activate(n__from(X:S)) -> from(X:S)
activate(X:S) -> X:S
first(0,Z:S) -> nil
first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__first(X:S,activate(Z:S)))
first(X1:S,X2:S) -> n__first(X1:S,X2:S)
from(X:S) -> cons(X:S,n__from(s(X:S)))
from(X:S) -> n__from(X:S)
sel(0,cons(X:S,Z: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__first(X1:S,X2:S)) -> FIRST(X1:S,X2:S)
 ACTIVATE(n__from(X:S)) -> FROM(X:S)
 FIRST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z: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__first(X1:S,X2:S)) -> first(X1:S,X2:S)
 activate(n__from(X:S)) -> from(X:S)
 activate(X:S) -> X:S
 first(0,Z:S) -> nil
 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__first(X:S,activate(Z:S)))
 first(X1:S,X2:S) -> n__first(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 sel(0,cons(X:S,Z: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__first(X1:S,X2:S)) -> FIRST(X1:S,X2:S)
 ACTIVATE(n__from(X:S)) -> FROM(X:S)
 FIRST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z: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__first(X1:S,X2:S)) -> first(X1:S,X2:S)
 activate(n__from(X:S)) -> from(X:S)
 activate(X:S) -> X:S
 first(0,Z:S) -> nil
 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__first(X:S,activate(Z:S)))
 first(X1:S,X2:S) -> n__first(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 sel(0,cons(X:S,Z:S)) -> X:S
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ACTIVATE(n__first(X1:S,X2:S)) -> FIRST(X1:S,X2:S)
 FIRST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
->->-> Rules:
 activate(n__first(X1:S,X2:S)) -> first(X1:S,X2:S)
 activate(n__from(X:S)) -> from(X:S)
 activate(X:S) -> X:S
 first(0,Z:S) -> nil
 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__first(X:S,activate(Z:S)))
 first(X1:S,X2:S) -> n__first(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 sel(0,cons(X:S,Z: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__first(X1:S,X2:S)) -> first(X1:S,X2:S)
 activate(n__from(X:S)) -> from(X:S)
 activate(X:S) -> X:S
 first(0,Z:S) -> nil
 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__first(X:S,activate(Z:S)))
 first(X1:S,X2:S) -> n__first(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 sel(0,cons(X:S,Z:S)) -> X:S
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 ACTIVATE(n__first(X1:S,X2:S)) -> FIRST(X1:S,X2:S)
 FIRST(s(X:S),cons(Y:S,Z:S)) -> ACTIVATE(Z:S)
-> Rules:
 activate(n__first(X1:S,X2:S)) -> first(X1:S,X2:S)
 activate(n__from(X:S)) -> from(X:S)
 activate(X:S) -> X:S
 first(0,Z:S) -> nil
 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__first(X:S,activate(Z:S)))
 first(X1:S,X2:S) -> n__first(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 sel(0,cons(X:S,Z:S)) -> X:S
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
->Projection:
 pi(ACTIVATE) = 1
 pi(FIRST) = 2

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 activate(n__first(X1:S,X2:S)) -> first(X1:S,X2:S)
 activate(n__from(X:S)) -> from(X:S)
 activate(X:S) -> X:S
 first(0,Z:S) -> nil
 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__first(X:S,activate(Z:S)))
 first(X1:S,X2:S) -> n__first(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 sel(0,cons(X:S,Z: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:
 SEL(s(X:S),cons(Y:S,Z:S)) -> SEL(X:S,activate(Z:S))
-> Rules:
 activate(n__first(X1:S,X2:S)) -> first(X1:S,X2:S)
 activate(n__from(X:S)) -> from(X:S)
 activate(X:S) -> X:S
 first(0,Z:S) -> nil
 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__first(X:S,activate(Z:S)))
 first(X1:S,X2:S) -> n__first(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 sel(0,cons(X:S,Z:S)) -> X:S
 sel(s(X:S),cons(Y:S,Z:S)) -> sel(X:S,activate(Z:S))
->Projection:
 pi(SEL) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 activate(n__first(X1:S,X2:S)) -> first(X1:S,X2:S)
 activate(n__from(X:S)) -> from(X:S)
 activate(X:S) -> X:S
 first(0,Z:S) -> nil
 first(s(X:S),cons(Y:S,Z:S)) -> cons(Y:S,n__first(X:S,activate(Z:S)))
 first(X1:S,X2:S) -> n__first(X1:S,X2:S)
 from(X:S) -> cons(X:S,n__from(s(X:S)))
 from(X:S) -> n__from(X:S)
 sel(0,cons(X:S,Z: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.