/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 X1 X2 Y Z)
(RULES
activate(n__first(X1,X2)) -> first(X1,X2)
activate(n__from(X)) -> from(X)
activate(X) -> X
first(0,X) -> nil
first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
first(X1,X2) -> n__first(X1,X2)
from(X) -> cons(X,n__from(s(X)))
from(X) -> n__from(X)
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVATE(n__first(X1,X2)) -> FIRST(X1,X2)
 ACTIVATE(n__from(X)) -> FROM(X)
 FIRST(s(X),cons(Y,Z)) -> ACTIVATE(Z)
-> Rules:
 activate(n__first(X1,X2)) -> first(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(X) -> X
 first(0,X) -> nil
 first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
 first(X1,X2) -> n__first(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)

Problem 1: 

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

Problem 1: 

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

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 activate(n__first(X1,X2)) -> first(X1,X2)
 activate(n__from(X)) -> from(X)
 activate(X) -> X
 first(0,X) -> nil
 first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
 first(X1,X2) -> n__first(X1,X2)
 from(X) -> cons(X,n__from(s(X)))
 from(X) -> n__from(X)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.