/export/starexec/sandbox/solver/bin/starexec_run_ttt2 /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES

Problem:
 half(0()) -> 0()
 half(s(s(x))) -> s(half(x))
 log(s(0())) -> 0()
 log(s(s(x))) -> s(log(s(half(x))))

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