/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:
 p(s(x)) -> x
 fac(0()) -> s(0())
 fac(s(x)) -> times(s(x),fac(p(s(x))))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                     [1 0 0]     [1 0 0]     [0]
   [times](x0, x1) = [0 0 1]x0 + [0 0 1]x1 + [0]
                     [0 0 0]     [0 0 0]     [1],
   
               [1 1 0]     [0]
   [fac](x0) = [1 1 1]x0 + [1]
               [0 0 1]     [1],
   
         [0]
   [0] = [0]
         [0],
   
             [1 0 0]     [1]
   [p](x0) = [0 0 1]x0 + [0]
             [1 1 0]     [0],
   
             [1 0 1]     [0]
   [s](x0) = [1 1 1]x0 + [1]
             [0 1 0]     [0]
  orientation:
             [1 0 1]    [1]         
   p(s(x)) = [0 1 0]x + [0] >= x = x
             [2 1 2]    [1]         
   
              [0]    [0]         
   fac(0()) = [1] >= [1] = s(0())
              [1]    [0]         
   
               [2 1 2]    [1]    [2 1 2]    [1]                           
   fac(s(x)) = [2 2 2]x + [2] >= [2 2 2]x + [2] = times(s(x),fac(p(s(x))))
               [0 1 0]    [1]    [0 0 0]    [1]                           
  problem:
   fac(0()) -> s(0())
   fac(s(x)) -> times(s(x),fac(p(s(x))))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                      [1 0 0]     [1 0 0]     [0]
    [times](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                      [0 0 0]     [1 0 0]     [0],
    
                [1 1 1]     [0]
    [fac](x0) = [1 1 0]x0 + [1]
                [1 0 1]     [0],
    
          [0]
    [0] = [0]
          [0],
    
              [1 0 0]  
    [p](x0) = [0 0 0]x0
              [0 0 0]  ,
    
              [1 0 1]     [0]
    [s](x0) = [1 1 0]x0 + [1]
              [0 0 1]     [0]
   orientation:
               [0]    [0]         
    fac(0()) = [1] >= [1] = s(0())
               [0]    [0]         
    
                [2 1 2]    [1]    [2 0 2]    [0]                           
    fac(s(x)) = [2 1 1]x + [2] >= [0 0 0]x + [1] = times(s(x),fac(p(s(x))))
                [1 0 2]    [0]    [1 0 1]    [0]                           
   problem:
    fac(0()) -> s(0())
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                 [1 0 0]     [1]
     [fac](x0) = [0 1 0]x0 + [0]
                 [0 1 0]     [0],
     
           [0]
     [0] = [1]
           [0],
     
               [1 0 0]     [0]
     [s](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [1]
    orientation:
                [1]    [0]         
     fac(0()) = [1] >= [0] = s(0())
                [1]    [1]         
    problem:
     
    Qed