/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:
 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:
   [c](x0, x1, x2) = 2x0 + 2x1 + x2 + 2,
   
   [b](x0, x1) = 4x0 + 2x1 + 2,
   
   [a] = 0,
   
   [f](x0) = x0
  orientation:
   f(c(a(),z,x)) = x + 2z + 2 >= 2z + 2 = b(a(),z)
   
   b(x,b(z,y)) = 4x + 4y + 8z + 6 >= 4x + 2y + 8z + 6 = f(b(f(f(z)),c(x,z,y)))
   
   b(y,z) = 4y + 2z + 2 >= 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 1]     [1 1 0]     [1]
    [c](x0, x1, x2) = [0 0 0]x0 + [0 1 1]x1 + [0 1 1]x2 + [0]
                      [0 0 0]     [0 0 0]     [0 0 0]     [0],
    
                  [1 0 1]     [1 1 1]     [0]
    [b](x0, x1) = [1 1 0]x0 + [0 1 1]x1 + [0]
                  [1 1 1]     [1 1 1]     [1],
    
          [0]
    [a] = [0]
          [0],
    
              [1 0 0]  
    [f](x0) = [0 1 0]x0
              [1 0 0]  
   orientation:
                    [1 1 0]    [1 1 1]    [1]    [1 1 1]    [0]           
    f(c(a(),z,x)) = [0 1 1]x + [0 1 1]z + [0] >= [0 1 1]z + [0] = b(a(),z)
                    [1 1 0]    [1 1 1]    [1]    [1 1 1]    [1]           
    
                  [1 0 1]    [2 3 3]    [3 2 2]    [1]    [1 0 0]    [1 2 1]    [3 2 2]    [1]                         
    b(x,b(z,y)) = [1 1 0]x + [1 2 2]y + [2 2 1]z + [1] >= [0 0 0]x + [0 1 1]y + [1 2 1]z + [0] = f(b(f(f(z)),c(x,z,y)))
                  [1 1 1]    [2 3 3]    [3 2 2]    [2]    [1 0 0]    [1 2 1]    [3 2 2]    [1]                         
   problem:
    b(x,b(z,y)) -> f(b(f(f(z)),c(x,z,y)))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [c](x0, x1, x2) = x0 + x1 + 2x2 + 2,
     
     [b](x0, x1) = 2x0 + 2x1 + 6,
     
     [f](x0) = x0 + 1
    orientation:
     b(x,b(z,y)) = 2x + 4y + 4z + 18 >= 2x + 4y + 4z + 15 = f(b(f(f(z)),c(x,z,y)))
    problem:
     
    Qed