/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:
 f(0()) -> s(0())
 f(s(0())) -> s(s(0()))
 f(s(0())) -> *(s(s(0())),f(0()))
 f(+(x,s(0()))) -> +(s(s(0())),f(x))
 f(+(x,y)) -> *(f(x),f(y))

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