/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(c(a(),z,x)) -> b(a(),z)
 b(x,b(z,y)) -> f(b(f(f(z)),c(x,z,y)))
 b(y,z) -> z

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [b](x0, x1) = 6x0 + 3x1 + 4,
   
   [f](x0) = x0,
   
   [c](x0, x1, x2) = 2x0 + 4x1 + 2x2 + 4,
   
   [a] = 0
  orientation:
   f(c(a(),z,x)) = 2x + 4z + 4 >= 3z + 4 = b(a(),z)
   
   b(x,b(z,y)) = 6x + 9y + 18z + 16 >= 6x + 6y + 18z + 16 = f(b(f(f(z)),c(x,z,y)))
   
   b(y,z) = 6y + 3z + 4 >= z = z
  problem:
   f(c(a(),z,x)) -> b(a(),z)
   b(x,b(z,y)) -> f(b(f(f(z)),c(x,z,y)))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  [1 0 0]     [1 1 0]     [0]
    [b](x0, x1) = [1 1 0]x0 + [1 1 0]x1 + [1]
                  [0 0 0]     [0 1 0]     [0],
    
              [1 0 0]     [0]
    [f](x0) = [1 0 0]x0 + [1]
              [0 0 1]     [0],
    
                      [1 0 0]     [1 1 0]     [1 0 0]  
    [c](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2
                      [0 0 0]     [1 1 0]     [0 0 0]  ,
    
          [0]
    [a] = [0]
          [0]
   orientation:
                    [1 0 0]    [1 1 0]    [0]    [1 1 0]    [0]           
    f(c(a(),z,x)) = [1 0 0]x + [1 1 0]z + [1] >= [1 1 0]z + [1] = b(a(),z)
                    [0 0 0]    [1 1 0]    [0]    [0 1 0]    [0]           
    
                  [1 0 0]    [2 2 0]    [2 1 0]    [1]    [1 0 0]    [1 0 0]    [2 1 0]    [0]                         
    b(x,b(z,y)) = [1 1 0]x + [2 2 0]y + [2 1 0]z + [2] >= [1 0 0]x + [1 0 0]y + [2 1 0]z + [1] = f(b(f(f(z)),c(x,z,y)))
                  [0 0 0]    [1 1 0]    [1 1 0]    [1]    [0 0 0]    [0 0 0]    [0 0 0]    [0]                         
   problem:
    f(c(a(),z,x)) -> b(a(),z)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                   [1 0 0]     [1 0 0]  
     [b](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                   [0 0 0]     [0 0 0]  ,
     
               [1 0 0]     [1]
     [f](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [0],
     
                       [1 0 0]     [1 0 0]     [1 0 0]  
     [c](x0, x1, x2) = [0 0 0]x0 + [0 0 0]x1 + [0 0 0]x2
                       [0 0 0]     [0 0 0]     [0 0 0]  ,
     
           [0]
     [a] = [0]
           [0]
    orientation:
                     [1 0 0]    [1 0 0]    [1]    [1 0 0]            
     f(c(a(),z,x)) = [0 0 0]x + [0 0 0]z + [0] >= [0 0 0]z = b(a(),z)
                     [0 0 0]    [0 0 0]    [0]    [0 0 0]            
    problem:
     
    Qed