/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

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

Proof:
 DP Processor:
  DPs:
   fib#(N) -> fib1#(s(0()),s(0()))
   fib#(N) -> sel#(N,fib1(s(0()),s(0())))
   fib1#(X,Y) -> add#(X,Y)
   add#(s(X),Y) -> add#(X,Y)
   sel#(s(N),cons(X,XS)) -> activate#(XS)
   sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
   activate#(n__fib1(X1,X2)) -> fib1#(X1,X2)
  TRS:
   fib(N) -> sel(N,fib1(s(0()),s(0())))
   fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
   add(0(),X) -> X
   add(s(X),Y) -> s(add(X,Y))
   sel(0(),cons(X,XS)) -> X
   sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
   fib1(X1,X2) -> n__fib1(X1,X2)
   activate(n__fib1(X1,X2)) -> fib1(X1,X2)
   activate(X) -> X
  TDG Processor:
   DPs:
    fib#(N) -> fib1#(s(0()),s(0()))
    fib#(N) -> sel#(N,fib1(s(0()),s(0())))
    fib1#(X,Y) -> add#(X,Y)
    add#(s(X),Y) -> add#(X,Y)
    sel#(s(N),cons(X,XS)) -> activate#(XS)
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
    activate#(n__fib1(X1,X2)) -> fib1#(X1,X2)
   TRS:
    fib(N) -> sel(N,fib1(s(0()),s(0())))
    fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
    add(0(),X) -> X
    add(s(X),Y) -> s(add(X,Y))
    sel(0(),cons(X,XS)) -> X
    sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
    fib1(X1,X2) -> n__fib1(X1,X2)
    activate(n__fib1(X1,X2)) -> fib1(X1,X2)
    activate(X) -> X
   graph:
    activate#(n__fib1(X1,X2)) -> fib1#(X1,X2) -> fib1#(X,Y) -> add#(X,Y)
    add#(s(X),Y) -> add#(X,Y) -> add#(s(X),Y) -> add#(X,Y)
    sel#(s(N),cons(X,XS)) -> activate#(XS) ->
    activate#(n__fib1(X1,X2)) -> fib1#(X1,X2)
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS)) ->
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS)) ->
    sel#(s(N),cons(X,XS)) -> activate#(XS)
    fib1#(X,Y) -> add#(X,Y) -> add#(s(X),Y) -> add#(X,Y)
    fib#(N) -> sel#(N,fib1(s(0()),s(0()))) ->
    sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
    fib#(N) -> sel#(N,fib1(s(0()),s(0()))) ->
    sel#(s(N),cons(X,XS)) -> activate#(XS)
    fib#(N) -> fib1#(s(0()),s(0())) -> fib1#(X,Y) -> add#(X,Y)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 9/49
    DPs:
     sel#(s(N),cons(X,XS)) -> sel#(N,activate(XS))
    TRS:
     fib(N) -> sel(N,fib1(s(0()),s(0())))
     fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
     add(0(),X) -> X
     add(s(X),Y) -> s(add(X,Y))
     sel(0(),cons(X,XS)) -> X
     sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
     fib1(X1,X2) -> n__fib1(X1,X2)
     activate(n__fib1(X1,X2)) -> fib1(X1,X2)
     activate(X) -> X
    Subterm Criterion Processor:
     simple projection:
      pi(sel#) = 0
     problem:
      DPs:
       
      TRS:
       fib(N) -> sel(N,fib1(s(0()),s(0())))
       fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
       add(0(),X) -> X
       add(s(X),Y) -> s(add(X,Y))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
       fib1(X1,X2) -> n__fib1(X1,X2)
       activate(n__fib1(X1,X2)) -> fib1(X1,X2)
       activate(X) -> X
     Qed
    
    DPs:
     add#(s(X),Y) -> add#(X,Y)
    TRS:
     fib(N) -> sel(N,fib1(s(0()),s(0())))
     fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
     add(0(),X) -> X
     add(s(X),Y) -> s(add(X,Y))
     sel(0(),cons(X,XS)) -> X
     sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
     fib1(X1,X2) -> n__fib1(X1,X2)
     activate(n__fib1(X1,X2)) -> fib1(X1,X2)
     activate(X) -> X
    Subterm Criterion Processor:
     simple projection:
      pi(add#) = 0
     problem:
      DPs:
       
      TRS:
       fib(N) -> sel(N,fib1(s(0()),s(0())))
       fib1(X,Y) -> cons(X,n__fib1(Y,add(X,Y)))
       add(0(),X) -> X
       add(s(X),Y) -> s(add(X,Y))
       sel(0(),cons(X,XS)) -> X
       sel(s(N),cons(X,XS)) -> sel(N,activate(XS))
       fib1(X1,X2) -> n__fib1(X1,X2)
       activate(n__fib1(X1,X2)) -> fib1(X1,X2)
       activate(X) -> X
     Qed