/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR N X X1 X2 XS Y)
(RULES
activate(n__fib1(X1,X2)) -> fib1(X1,X2)
activate(X) -> X
add(0,X) -> X
add(s(X),Y) -> s(add(X,Y))
fib(N) -> sel(N,fib1(s(0),s(0)))
fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
fib1(X1,X2) -> n__fib1(X1,X2)
sel(0,cons(X,XS)) -> X
sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 ACTIVATE(n__fib1(X1,X2)) -> FIB1(X1,X2)
 ADD(s(X),Y) -> ADD(X,Y)
 FIB(N) -> FIB1(s(0),s(0))
 FIB(N) -> SEL(N,fib1(s(0),s(0)))
 FIB1(X,Y) -> ADD(X,Y)
 SEL(s(N),cons(X,XS)) -> ACTIVATE(XS)
 SEL(s(N),cons(X,XS)) -> SEL(N,activate(XS))
-> Rules:
 activate(n__fib1(X1,X2)) -> fib1(X1,X2)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(add(X,Y))
 fib(N) -> sel(N,fib1(s(0),s(0)))
 fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
 fib1(X1,X2) -> n__fib1(X1,X2)
 sel(0,cons(X,XS)) -> X
 sel(s(N),cons(X,XS)) -> sel(N,activate(XS))

Problem 1: 

SCC Processor:
-> Pairs:
 ACTIVATE(n__fib1(X1,X2)) -> FIB1(X1,X2)
 ADD(s(X),Y) -> ADD(X,Y)
 FIB(N) -> FIB1(s(0),s(0))
 FIB(N) -> SEL(N,fib1(s(0),s(0)))
 FIB1(X,Y) -> ADD(X,Y)
 SEL(s(N),cons(X,XS)) -> ACTIVATE(XS)
 SEL(s(N),cons(X,XS)) -> SEL(N,activate(XS))
-> Rules:
 activate(n__fib1(X1,X2)) -> fib1(X1,X2)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(add(X,Y))
 fib(N) -> sel(N,fib1(s(0),s(0)))
 fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
 fib1(X1,X2) -> n__fib1(X1,X2)
 sel(0,cons(X,XS)) -> X
 sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 ADD(s(X),Y) -> ADD(X,Y)
->->-> Rules:
 activate(n__fib1(X1,X2)) -> fib1(X1,X2)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(add(X,Y))
 fib(N) -> sel(N,fib1(s(0),s(0)))
 fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
 fib1(X1,X2) -> n__fib1(X1,X2)
 sel(0,cons(X,XS)) -> X
 sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
->->Cycle:
->->-> Pairs:
 SEL(s(N),cons(X,XS)) -> SEL(N,activate(XS))
->->-> Rules:
 activate(n__fib1(X1,X2)) -> fib1(X1,X2)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(add(X,Y))
 fib(N) -> sel(N,fib1(s(0),s(0)))
 fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
 fib1(X1,X2) -> n__fib1(X1,X2)
 sel(0,cons(X,XS)) -> X
 sel(s(N),cons(X,XS)) -> sel(N,activate(XS))


The problem is decomposed in 2 subproblems.

Problem 1.1: 

Subterm Processor:
-> Pairs:
 ADD(s(X),Y) -> ADD(X,Y)
-> Rules:
 activate(n__fib1(X1,X2)) -> fib1(X1,X2)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(add(X,Y))
 fib(N) -> sel(N,fib1(s(0),s(0)))
 fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
 fib1(X1,X2) -> n__fib1(X1,X2)
 sel(0,cons(X,XS)) -> X
 sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
->Projection:
 pi(ADD) = 1

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 activate(n__fib1(X1,X2)) -> fib1(X1,X2)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(add(X,Y))
 fib(N) -> sel(N,fib1(s(0),s(0)))
 fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
 fib1(X1,X2) -> n__fib1(X1,X2)
 sel(0,cons(X,XS)) -> X
 sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

Subterm Processor:
-> Pairs:
 SEL(s(N),cons(X,XS)) -> SEL(N,activate(XS))
-> Rules:
 activate(n__fib1(X1,X2)) -> fib1(X1,X2)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(add(X,Y))
 fib(N) -> sel(N,fib1(s(0),s(0)))
 fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
 fib1(X1,X2) -> n__fib1(X1,X2)
 sel(0,cons(X,XS)) -> X
 sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
->Projection:
 pi(SEL) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 activate(n__fib1(X1,X2)) -> fib1(X1,X2)
 activate(X) -> X
 add(0,X) -> X
 add(s(X),Y) -> s(add(X,Y))
 fib(N) -> sel(N,fib1(s(0),s(0)))
 fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
 fib1(X1,X2) -> n__fib1(X1,X2)
 sel(0,cons(X,XS)) -> X
 sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.