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


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YES

Problem:
 strict:
  f(0()) -> s(0())
  f(s(0())) -> s(0())
  f(s(s(x))) -> f(f(s(x)))
 weak:
  rand(x) -> x
  rand(x) -> rand(s(x))

Proof:
 Arctic Interpretation Processor:
  dimension: 2
  interpretation:
                [1 1]  
   [rand](x0) = [7 7]x0,
   
             [0  -&]  
   [s](x0) = [0  0 ]x0,
   
             [0  0 ]  
   [f](x0) = [-& 0 ]x0,
   
         [4]
   [0] = [4]
  orientation:
            [4]    [4]         
   f(0()) = [4] >= [4] = s(0())
   
               [4]    [4]         
   f(s(0())) = [4] >= [4] = s(0())
   
                [0 0]     [0 0]              
   f(s(s(x))) = [0 0]x >= [0 0]x = f(f(s(x)))
   
             [1 1]          
   rand(x) = [7 7]x >= x = x
   
             [1 1]     [1 1]              
   rand(x) = [7 7]x >= [7 7]x = rand(s(x))
  problem:
   strict:
    f(0()) -> s(0())
    f(s(0())) -> s(0())
    f(s(s(x))) -> f(f(s(x)))
   weak:
    rand(x) -> rand(s(x))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
                 [1 0]  
    [rand](x0) = [0 2]x0,
    
              [1 0]  
    [s](x0) = [0 0]x0,
    
              [1 2]  
    [f](x0) = [0 0]x0,
    
          [0]
    [0] = [1]
   orientation:
             [2]    [0]         
    f(0()) = [0] >= [0] = s(0())
    
                [0]    [0]         
    f(s(0())) = [0] >= [0] = s(0())
    
                 [1 0]     [1 0]              
    f(s(s(x))) = [0 0]x >= [0 0]x = f(f(s(x)))
    
              [1 0]     [1 0]              
    rand(x) = [0 2]x >= [0 0]x = rand(s(x))
   problem:
    strict:
     f(s(0())) -> s(0())
     f(s(s(x))) -> f(f(s(x)))
    weak:
     rand(x) -> rand(s(x))
   Arctic Interpretation Processor:
    dimension: 2
    interpretation:
                  [0  -&]  
     [rand](x0) = [-& -&]x0,
     
               [0  -&]  
     [s](x0) = [6  2 ]x0,
     
               [1  1 ]  
     [f](x0) = [-& 0 ]x0,
     
           [0]
     [0] = [6]
    orientation:
                 [9]    [0]         
     f(s(0())) = [8] >= [8] = s(0())
     
                  [9 5]     [8 4]              
     f(s(s(x))) = [8 4]x >= [6 2]x = f(f(s(x)))
     
               [0  -&]     [0  -&]              
     rand(x) = [-& -&]x >= [-& -&]x = rand(s(x))
    problem:
     strict:
      f(s(0())) -> s(0())
     weak:
      rand(x) -> rand(s(x))
    Arctic Interpretation Processor:
     dimension: 4
     interpretation:
                   [1  0  0  0 ]  
                   [0  -& 0  0 ]  
      [rand](x0) = [2  1  2  2 ]x0
                   [0  -& -& -&]  ,
      
                [0  -& -& -&]  
                [1  -& 0  -&]  
      [s](x0) = [0  -& -& -&]x0
                [-& -& 0  0 ]  ,
      
                [1  -& 1  2 ]  
                [2  -& -& -&]  
      [f](x0) = [-& 0  1  -&]x0
                [1  1  1  -&]  ,
      
            [1 ]
            [0 ]
      [0] = [-&]
            [1 ]
     orientation:
                  [3]    [1]         
                  [3]    [2]         
      f(s(0())) = [2] >= [1] = s(0())
                  [3]    [1]         
      
                [1  0  0  0 ]     [1  -& 0  0 ]              
                [0  -& 0  0 ]     [0  -& 0  0 ]              
      rand(x) = [2  1  2  2 ]x >= [2  -& 2  2 ]x = rand(s(x))
                [0  -& -& -&]     [0  -& -& -&]              
     problem:
      strict:
       
      weak:
       rand(x) -> rand(s(x))
     Qed