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

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