/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:
 g(c(x,s(y))) -> g(c(s(x),y))
 f(c(s(x),y)) -> f(c(x,s(y)))
 f(f(x)) -> f(d(f(x)))
 f(x) -> x

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [d](x0) = x0,
   
   [c](x0, x1) = x0 + 2x1,
   
   [f](x0) = 2x0 + 4,
   
   [s](x0) = x0,
   
   [g](x0) = 2x0
  orientation:
   g(c(x,s(y))) = 2x + 4y >= 2x + 4y = g(c(s(x),y))
   
   f(c(s(x),y)) = 2x + 4y + 4 >= 2x + 4y + 4 = f(c(x,s(y)))
   
   f(f(x)) = 4x + 12 >= 4x + 12 = f(d(f(x)))
   
   f(x) = 2x + 4 >= x = x
  problem:
   g(c(x,s(y))) -> g(c(s(x),y))
   f(c(s(x),y)) -> f(c(x,s(y)))
   f(f(x)) -> f(d(f(x)))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]  
    [d](x0) = [0 0 0]x0
              [0 0 1]  ,
    
                  [1 0 0]     [1 0 0]  
    [c](x0, x1) = [0 0 0]x0 + [0 0 1]x1
                  [0 1 0]     [0 0 0]  ,
    
              [1 0 1]     [0]
    [f](x0) = [0 0 1]x0 + [0]
              [0 0 0]     [1],
    
              [1 0 0]     [0]
    [s](x0) = [0 1 1]x0 + [0]
              [0 0 1]     [1],
    
              [1 1 0]  
    [g](x0) = [0 0 0]x0
              [0 0 0]  
   orientation:
                   [1 0 0]    [1 0 1]    [1]    [1 0 0]    [1 0 1]                
    g(c(x,s(y))) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y = g(c(s(x),y))
                   [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                
    
                   [1 1 1]    [1 0 0]    [0]    [1 1 0]    [1 0 0]    [0]               
    f(c(s(x),y)) = [0 1 1]x + [0 0 0]y + [0] >= [0 1 0]x + [0 0 0]y + [0] = f(c(x,s(y)))
                   [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [1]               
    
              [1 0 1]    [1]    [1 0 1]    [1]             
    f(f(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = f(d(f(x)))
              [0 0 0]    [1]    [0 0 0]    [1]             
   problem:
    f(c(s(x),y)) -> f(c(x,s(y)))
    f(f(x)) -> f(d(f(x)))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 0 0]     [0]
     [d](x0) = [0 0 0]x0 + [1]
               [0 0 0]     [0],
     
                   [1 1 0]     [1 0 0]     [0]
     [c](x0, x1) = [0 1 0]x0 + [0 0 0]x1 + [0]
                   [0 0 0]     [0 0 0]     [1],
     
               [1 0 0]     [0]
     [f](x0) = [1 0 0]x0 + [0]
               [0 0 0]     [1],
     
               [1 0 0]     [0]
     [s](x0) = [0 1 0]x0 + [1]
               [0 0 0]     [0]
    orientation:
                    [1 1 0]    [1 0 0]    [1]    [1 1 0]    [1 0 0]    [0]               
     f(c(s(x),y)) = [1 1 0]x + [1 0 0]y + [1] >= [1 1 0]x + [1 0 0]y + [0] = f(c(x,s(y)))
                    [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [1]               
     
               [1 0 0]    [0]    [1 0 0]    [0]             
     f(f(x)) = [1 0 0]x + [0] >= [1 0 0]x + [0] = f(d(f(x)))
               [0 0 0]    [1]    [0 0 0]    [1]             
    problem:
     f(f(x)) -> f(d(f(x)))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                [1 0 0]  
      [d](x0) = [0 0 0]x0
                [0 0 0]  ,
      
                [1 0 1]     [0]
      [f](x0) = [0 0 0]x0 + [0]
                [0 0 0]     [1]
     orientation:
                [1 0 1]    [1]    [1 0 1]    [0]             
      f(f(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = f(d(f(x)))
                [0 0 0]    [1]    [0 0 0]    [1]             
     problem:
      
     Qed