/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:
 minus(x,0()) -> x
 minus(s(x),s(y)) -> minus(x,y)
 double(0()) -> 0()
 double(s(x)) -> s(s(double(x)))
 plus(0(),y) -> y
 plus(s(x),y) -> s(plus(x,y))
 plus(s(x),y) -> plus(x,s(y))
 plus(s(x),y) -> s(plus(minus(x,y),double(y)))

Proof:
 DP Processor:
  DPs:
   minus#(s(x),s(y)) -> minus#(x,y)
   double#(s(x)) -> double#(x)
   plus#(s(x),y) -> plus#(x,y)
   plus#(s(x),y) -> plus#(x,s(y))
   plus#(s(x),y) -> double#(y)
   plus#(s(x),y) -> minus#(x,y)
   plus#(s(x),y) -> plus#(minus(x,y),double(y))
  TRS:
   minus(x,0()) -> x
   minus(s(x),s(y)) -> minus(x,y)
   double(0()) -> 0()
   double(s(x)) -> s(s(double(x)))
   plus(0(),y) -> y
   plus(s(x),y) -> s(plus(x,y))
   plus(s(x),y) -> plus(x,s(y))
   plus(s(x),y) -> s(plus(minus(x,y),double(y)))
  TDG Processor:
   DPs:
    minus#(s(x),s(y)) -> minus#(x,y)
    double#(s(x)) -> double#(x)
    plus#(s(x),y) -> plus#(x,y)
    plus#(s(x),y) -> plus#(x,s(y))
    plus#(s(x),y) -> double#(y)
    plus#(s(x),y) -> minus#(x,y)
    plus#(s(x),y) -> plus#(minus(x,y),double(y))
   TRS:
    minus(x,0()) -> x
    minus(s(x),s(y)) -> minus(x,y)
    double(0()) -> 0()
    double(s(x)) -> s(s(double(x)))
    plus(0(),y) -> y
    plus(s(x),y) -> s(plus(x,y))
    plus(s(x),y) -> plus(x,s(y))
    plus(s(x),y) -> s(plus(minus(x,y),double(y)))
   graph:
    plus#(s(x),y) -> plus#(minus(x,y),double(y)) ->
    plus#(s(x),y) -> plus#(minus(x,y),double(y))
    plus#(s(x),y) -> plus#(minus(x,y),double(y)) ->
    plus#(s(x),y) -> minus#(x,y)
    plus#(s(x),y) -> plus#(minus(x,y),double(y)) ->
    plus#(s(x),y) -> double#(y)
    plus#(s(x),y) -> plus#(minus(x,y),double(y)) ->
    plus#(s(x),y) -> plus#(x,s(y))
    plus#(s(x),y) -> plus#(minus(x,y),double(y)) ->
    plus#(s(x),y) -> plus#(x,y)
    plus#(s(x),y) -> plus#(x,s(y)) ->
    plus#(s(x),y) -> plus#(minus(x,y),double(y))
    plus#(s(x),y) -> plus#(x,s(y)) -> plus#(s(x),y) -> minus#(x,y)
    plus#(s(x),y) -> plus#(x,s(y)) -> plus#(s(x),y) -> double#(y)
    plus#(s(x),y) -> plus#(x,s(y)) -> plus#(s(x),y) -> plus#(x,s(y))
    plus#(s(x),y) -> plus#(x,s(y)) -> plus#(s(x),y) -> plus#(x,y)
    plus#(s(x),y) -> plus#(x,y) ->
    plus#(s(x),y) -> plus#(minus(x,y),double(y))
    plus#(s(x),y) -> plus#(x,y) -> plus#(s(x),y) -> minus#(x,y)
    plus#(s(x),y) -> plus#(x,y) -> plus#(s(x),y) -> double#(y)
    plus#(s(x),y) -> plus#(x,y) -> plus#(s(x),y) -> plus#(x,s(y))
    plus#(s(x),y) -> plus#(x,y) -> plus#(s(x),y) -> plus#(x,y)
    plus#(s(x),y) -> double#(y) -> double#(s(x)) -> double#(x)
    plus#(s(x),y) -> minus#(x,y) -> minus#(s(x),s(y)) -> minus#(x,y)
    double#(s(x)) -> double#(x) -> double#(s(x)) -> double#(x)
    minus#(s(x),s(y)) -> minus#(x,y) -> minus#(s(x),s(y)) -> minus#(x,y)
   SCC Processor:
    #sccs: 3
    #rules: 5
    #arcs: 19/49
    DPs:
     plus#(s(x),y) -> plus#(minus(x,y),double(y))
     plus#(s(x),y) -> plus#(x,y)
     plus#(s(x),y) -> plus#(x,s(y))
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     double(0()) -> 0()
     double(s(x)) -> s(s(double(x)))
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     plus(s(x),y) -> plus(x,s(y))
     plus(s(x),y) -> s(plus(minus(x,y),double(y)))
    Subterm Criterion Processor:
     simple projection:
      pi(minus) = [0,0]
      pi(s) = [0,0,0]
      pi(plus#) = 0
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       double(0()) -> 0()
       double(s(x)) -> s(s(double(x)))
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       plus(s(x),y) -> plus(x,s(y))
       plus(s(x),y) -> s(plus(minus(x,y),double(y)))
     Qed
    
    DPs:
     minus#(s(x),s(y)) -> minus#(x,y)
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     double(0()) -> 0()
     double(s(x)) -> s(s(double(x)))
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     plus(s(x),y) -> plus(x,s(y))
     plus(s(x),y) -> s(plus(minus(x,y),double(y)))
    Subterm Criterion Processor:
     simple projection:
      pi(minus#) = 0
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       double(0()) -> 0()
       double(s(x)) -> s(s(double(x)))
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       plus(s(x),y) -> plus(x,s(y))
       plus(s(x),y) -> s(plus(minus(x,y),double(y)))
     Qed
    
    DPs:
     double#(s(x)) -> double#(x)
    TRS:
     minus(x,0()) -> x
     minus(s(x),s(y)) -> minus(x,y)
     double(0()) -> 0()
     double(s(x)) -> s(s(double(x)))
     plus(0(),y) -> y
     plus(s(x),y) -> s(plus(x,y))
     plus(s(x),y) -> plus(x,s(y))
     plus(s(x),y) -> s(plus(minus(x,y),double(y)))
    Subterm Criterion Processor:
     simple projection:
      pi(double#) = 0
     problem:
      DPs:
       
      TRS:
       minus(x,0()) -> x
       minus(s(x),s(y)) -> minus(x,y)
       double(0()) -> 0()
       double(s(x)) -> s(s(double(x)))
       plus(0(),y) -> y
       plus(s(x),y) -> s(plus(x,y))
       plus(s(x),y) -> plus(x,s(y))
       plus(s(x),y) -> s(plus(minus(x,y),double(y)))
     Qed