/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()) -> true()
 f(1()) -> false()
 f(s(x)) -> f(x)
 if(true(),x,y) -> x
 if(false(),x,y) -> y
 g(s(x),s(y)) -> if(f(x),s(x),s(y))
 g(x,c(y)) -> g(x,g(s(c(y)),y))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
             [1 0]     [0]
   [c](x0) = [2 1]x0 + [2],
   
                 [2 0]     [1 2]     [1]
   [g](x0, x1) = [0 0]x0 + [0 0]x1 + [0],
   
                      [1 0]     [1 0]       
   [if](x0, x1, x2) = [0 0]x0 + [0 2]x1 + x2,
   
             [2 0]     [1]
   [s](x0) = [0 0]x0 + [0],
   
             [0]
   [false] = [0],
   
         [0]
   [1] = [0],
   
            [0]
   [true] = [0],
   
             [2 0]  
   [f](x0) = [0 0]x0,
   
         [1]
   [0] = [0]
  orientation:
            [2]    [0]         
   f(0()) = [0] >= [0] = true()
   
            [0]    [0]          
   f(1()) = [0] >= [0] = false()
   
             [4 0]    [2]    [2 0]        
   f(s(x)) = [0 0]x + [0] >= [0 0]x = f(x)
   
                    [1 0]              
   if(true(),x,y) = [0 2]x + y >= x = x
   
                     [1 0]              
   if(false(),x,y) = [0 2]x + y >= y = y
   
                  [4 0]    [2 0]    [4]    [4 0]    [2 0]    [2]                     
   g(s(x),s(y)) = [0 0]x + [0 0]y + [0] >= [0 0]x + [0 0]y + [0] = if(f(x),s(x),s(y))
   
               [2 0]    [5 2]    [5]    [2 0]    [5 2]    [4]                    
   g(x,c(y)) = [0 0]x + [0 0]y + [0] >= [0 0]x + [0 0]y + [0] = g(x,g(s(c(y)),y))
  problem:
   f(1()) -> false()
   if(true(),x,y) -> x
   if(false(),x,y) -> y
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                       [1 0 0]            
    [if](x0, x1, x2) = [0 0 0]x0 + x1 + x2
                       [0 0 0]            ,
    
              [0]
    [false] = [0]
              [0],
    
          [0]
    [1] = [0]
          [1],
    
             [0]
    [true] = [0]
             [0],
    
              [1 0 1]  
    [f](x0) = [0 0 0]x0
              [0 0 0]  
   orientation:
             [1]    [0]          
    f(1()) = [0] >= [0] = false()
             [0]    [0]          
    
                                   
    if(true(),x,y) = x + y >= x = x
                                   
    
                                    
    if(false(),x,y) = x + y >= y = y
                                    
   problem:
    if(true(),x,y) -> x
    if(false(),x,y) -> y
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                        [1 1 0]            
     [if](x0, x1, x2) = [0 0 0]x0 + x1 + x2
                        [0 0 0]            ,
     
               [0]
     [false] = [1]
               [0],
     
              [1]
     [true] = [0]
              [0]
    orientation:
                              [1]         
     if(true(),x,y) = x + y + [0] >= x = x
                              [0]         
     
                               [1]         
     if(false(),x,y) = x + y + [0] >= y = y
                               [0]         
    problem:
     
    Qed