/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:
 sqr(0()) -> 0()
 sqr(s(x)) -> +(sqr(x),s(double(x)))
 double(0()) -> 0()
 double(s(x)) -> s(s(double(x)))
 +(x,0()) -> x
 +(x,s(y)) -> s(+(x,y))
 sqr(s(x)) -> s(+(sqr(x),double(x)))

Proof:
 DP Processor:
  DPs:
   sqr#(s(x)) -> double#(x)
   sqr#(s(x)) -> sqr#(x)
   sqr#(s(x)) -> +#(sqr(x),s(double(x)))
   double#(s(x)) -> double#(x)
   +#(x,s(y)) -> +#(x,y)
   sqr#(s(x)) -> +#(sqr(x),double(x))
  TRS:
   sqr(0()) -> 0()
   sqr(s(x)) -> +(sqr(x),s(double(x)))
   double(0()) -> 0()
   double(s(x)) -> s(s(double(x)))
   +(x,0()) -> x
   +(x,s(y)) -> s(+(x,y))
   sqr(s(x)) -> s(+(sqr(x),double(x)))
  TDG Processor:
   DPs:
    sqr#(s(x)) -> double#(x)
    sqr#(s(x)) -> sqr#(x)
    sqr#(s(x)) -> +#(sqr(x),s(double(x)))
    double#(s(x)) -> double#(x)
    +#(x,s(y)) -> +#(x,y)
    sqr#(s(x)) -> +#(sqr(x),double(x))
   TRS:
    sqr(0()) -> 0()
    sqr(s(x)) -> +(sqr(x),s(double(x)))
    double(0()) -> 0()
    double(s(x)) -> s(s(double(x)))
    +(x,0()) -> x
    +(x,s(y)) -> s(+(x,y))
    sqr(s(x)) -> s(+(sqr(x),double(x)))
   graph:
    +#(x,s(y)) -> +#(x,y) -> +#(x,s(y)) -> +#(x,y)
    double#(s(x)) -> double#(x) -> double#(s(x)) -> double#(x)
    sqr#(s(x)) -> +#(sqr(x),double(x)) ->
    +#(x,s(y)) -> +#(x,y)
    sqr#(s(x)) -> +#(sqr(x),s(double(x))) -> +#(x,s(y)) -> +#(x,y)
    sqr#(s(x)) -> double#(x) -> double#(s(x)) -> double#(x)
    sqr#(s(x)) -> sqr#(x) -> sqr#(s(x)) -> +#(sqr(x),double(x))
    sqr#(s(x)) -> sqr#(x) -> sqr#(s(x)) -> +#(sqr(x),s(double(x)))
    sqr#(s(x)) -> sqr#(x) -> sqr#(s(x)) -> sqr#(x)
    sqr#(s(x)) -> sqr#(x) -> sqr#(s(x)) -> double#(x)
   SCC Processor:
    #sccs: 3
    #rules: 3
    #arcs: 9/36
    DPs:
     sqr#(s(x)) -> sqr#(x)
    TRS:
     sqr(0()) -> 0()
     sqr(s(x)) -> +(sqr(x),s(double(x)))
     double(0()) -> 0()
     double(s(x)) -> s(s(double(x)))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     sqr(s(x)) -> s(+(sqr(x),double(x)))
    Subterm Criterion Processor:
     simple projection:
      pi(sqr#) = 0
     problem:
      DPs:
       
      TRS:
       sqr(0()) -> 0()
       sqr(s(x)) -> +(sqr(x),s(double(x)))
       double(0()) -> 0()
       double(s(x)) -> s(s(double(x)))
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       sqr(s(x)) -> s(+(sqr(x),double(x)))
     Qed
    
    DPs:
     double#(s(x)) -> double#(x)
    TRS:
     sqr(0()) -> 0()
     sqr(s(x)) -> +(sqr(x),s(double(x)))
     double(0()) -> 0()
     double(s(x)) -> s(s(double(x)))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     sqr(s(x)) -> s(+(sqr(x),double(x)))
    Subterm Criterion Processor:
     simple projection:
      pi(double#) = 0
     problem:
      DPs:
       
      TRS:
       sqr(0()) -> 0()
       sqr(s(x)) -> +(sqr(x),s(double(x)))
       double(0()) -> 0()
       double(s(x)) -> s(s(double(x)))
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       sqr(s(x)) -> s(+(sqr(x),double(x)))
     Qed
    
    DPs:
     +#(x,s(y)) -> +#(x,y)
    TRS:
     sqr(0()) -> 0()
     sqr(s(x)) -> +(sqr(x),s(double(x)))
     double(0()) -> 0()
     double(s(x)) -> s(s(double(x)))
     +(x,0()) -> x
     +(x,s(y)) -> s(+(x,y))
     sqr(s(x)) -> s(+(sqr(x),double(x)))
    Subterm Criterion Processor:
     simple projection:
      pi(+#) = 1
     problem:
      DPs:
       
      TRS:
       sqr(0()) -> 0()
       sqr(s(x)) -> +(sqr(x),s(double(x)))
       double(0()) -> 0()
       double(s(x)) -> s(s(double(x)))
       +(x,0()) -> x
       +(x,s(y)) -> s(+(x,y))
       sqr(s(x)) -> s(+(sqr(x),double(x)))
     Qed