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


--------------------------------------------------------------------------------


YES

Problem:
 fib(0()) -> 0()
 fib(s(0())) -> s(0())
 fib(s(s(x))) -> +(fib(s(x)),fib(x))
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))

Proof:
 DP Processor:
  DPs:
   fib#(s(s(x))) -> fib#(x)
   fib#(s(s(x))) -> fib#(s(x))
   fib#(s(s(x))) -> +#(fib(s(x)),fib(x))
   +#(x,s(y)) -> +#(x,y)
  TRS:
   fib(0()) -> 0()
   fib(s(0())) -> s(0())
   fib(s(s(x))) -> +(fib(s(x)),fib(x))
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
  TDG Processor:
   DPs:
    fib#(s(s(x))) -> fib#(x)
    fib#(s(s(x))) -> fib#(s(x))
    fib#(s(s(x))) -> +#(fib(s(x)),fib(x))
    +#(x,s(y)) -> +#(x,y)
   TRS:
    fib(0()) -> 0()
    fib(s(0())) -> s(0())
    fib(s(s(x))) -> +(fib(s(x)),fib(x))
    +(x,0()) -> x
    +(x,s(y)) -> s(+(x,y))
   graph:
    +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
    fib#(s(s(x))) -> +#(fib(s(x)),fib(x)) -> +#(x,s(y)) -> +#(x,y)
    fib#(s(s(x))) -> fib#(s(x)) -> fib#(s(s(x))) -> +#(fib(s(x)),fib(x))
    fib#(s(s(x))) -> fib#(s(x)) -> fib#(s(s(x))) -> fib#(s(x))
    fib#(s(s(x))) -> fib#(s(x)) -> fib#(s(s(x))) -> fib#(x)
    fib#(s(s(x))) -> fib#(x) -> fib#(s(s(x))) -> +#(fib(s(x)),fib(x))
    fib#(s(s(x))) -> fib#(x) -> fib#(s(s(x))) -> fib#(s(x))
    fib#(s(s(x))) -> fib#(x) -> fib#(s(s(x))) -> fib#(x)
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 8/16
    DPs:
     fib#(s(s(x))) -> fib#(s(x))
     fib#(s(s(x))) -> fib#(x)
    TRS:
     fib(0()) -> 0()
     fib(s(0())) -> s(0())
     fib(s(s(x))) -> +(fib(s(x)),fib(x))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(fib#) = 0
     problem:
      DPs:
       
      TRS:
       fib(0()) -> 0()
       fib(s(0())) -> s(0())
       fib(s(s(x))) -> +(fib(s(x)),fib(x))
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
     Qed
    
    DPs:
     +#(x,s(y)) -> +#(x,y)
    TRS:
     fib(0()) -> 0()
     fib(s(0())) -> s(0())
     fib(s(s(x))) -> +(fib(s(x)),fib(x))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
    Subterm Criterion Processor:
     simple projection:
      pi(+#) = 1
     problem:
      DPs:
       
      TRS:
       fib(0()) -> 0()
       fib(s(0())) -> s(0())
       fib(s(s(x))) -> +(fib(s(x)),fib(x))
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
     Qed