/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(j(x,y),y) -> g(f(x,k(y)))
 f(x,h1(y,z)) -> h2(0(),x,h1(y,z))
 g(h2(x,y,h1(z,u))) -> h2(s(x),y,h1(z,u))
 h2(x,j(y,h1(z,u)),h1(z,u)) -> h2(s(x),y,h1(s(z),u))
 i(f(x,h(y))) -> y
 i(h2(s(x),y,h1(x,z))) -> z
 k(h(x)) -> h1(0(),x)
 k(h1(x,y)) -> h1(s(x),y)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [i](x0) = x0 + 2,
   
   [h](x0) = 4x0 + 3,
   
   [s](x0) = x0 + 1,
   
   [h2](x0, x1, x2) = 2x0 + 2x1 + 4x2 + 7,
   
   [0] = 0,
   
   [h1](x0, x1) = 2x0 + 2x1 + 2,
   
   [g](x0) = 2x0 + 1,
   
   [k](x0) = x0 + 2,
   
   [f](x0, x1) = 4x0 + 4x1 + 7,
   
   [j](x0, x1) = 2x0 + x1 + 6
  orientation:
   f(j(x,y),y) = 8x + 8y + 31 >= 8x + 8y + 31 = g(f(x,k(y)))
   
   f(x,h1(y,z)) = 4x + 8y + 8z + 15 >= 2x + 8y + 8z + 15 = h2(0(),x,h1(y,z))
   
   g(h2(x,y,h1(z,u))) = 16u + 4x + 4y + 16z + 31 >= 8u + 2x + 2y + 8z + 17 = h2(s(x),y,h1(z,u))
   
   h2(x,j(y,h1(z,u)),h1(z,u)) = 12u + 2x + 4y + 12z + 31 >= 8u + 2x + 2y + 8z + 25 = h2(s(x),y,h1(s(z),u))
   
   i(f(x,h(y))) = 4x + 16y + 21 >= y = y
   
   i(h2(s(x),y,h1(x,z))) = 10x + 2y + 8z + 19 >= z = z
   
   k(h(x)) = 4x + 5 >= 2x + 2 = h1(0(),x)
   
   k(h1(x,y)) = 2x + 2y + 4 >= 2x + 2y + 4 = h1(s(x),y)
  problem:
   f(j(x,y),y) -> g(f(x,k(y)))
   f(x,h1(y,z)) -> h2(0(),x,h1(y,z))
   k(h1(x,y)) -> h1(s(x),y)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [s](x0) = x0,
    
    [h2](x0, x1, x2) = 4x0 + 2x1 + 2x2,
    
    [0] = 0,
    
    [h1](x0, x1) = 4x0 + 4x1,
    
    [g](x0) = 4x0 + 4,
    
    [k](x0) = 2x0 + 1,
    
    [f](x0, x1) = 2x0 + 2x1,
    
    [j](x0, x1) = 4x0 + 7x1 + 6
   orientation:
    f(j(x,y),y) = 8x + 16y + 12 >= 8x + 16y + 12 = g(f(x,k(y)))
    
    f(x,h1(y,z)) = 2x + 8y + 8z >= 2x + 8y + 8z = h2(0(),x,h1(y,z))
    
    k(h1(x,y)) = 8x + 8y + 1 >= 4x + 4y = h1(s(x),y)
   problem:
    f(j(x,y),y) -> g(f(x,k(y)))
    f(x,h1(y,z)) -> h2(0(),x,h1(y,z))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [h2](x0, x1, x2) = x0 + 2x1 + x2,
     
     [0] = 0,
     
     [h1](x0, x1) = 2x0 + 2x1 + 4,
     
     [g](x0) = x0,
     
     [k](x0) = x0,
     
     [f](x0, x1) = 4x0 + x1,
     
     [j](x0, x1) = 2x0 + 2x1 + 2
    orientation:
     f(j(x,y),y) = 8x + 9y + 8 >= 4x + y = g(f(x,k(y)))
     
     f(x,h1(y,z)) = 4x + 2y + 2z + 4 >= 2x + 2y + 2z + 4 = h2(0(),x,h1(y,z))
    problem:
     f(x,h1(y,z)) -> h2(0(),x,h1(y,z))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                         [1 0 0]     [1 0 0]     [1 0 0]  
      [h2](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]
      [0] = [0]
            [0],
      
                     [1 0 0]     [1 1 0]  
      [h1](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                     [0 0 0]     [0 0 0]  ,
      
                    [1 0 0]     [1 0 0]     [1]
      [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [0]
                    [0 0 0]     [0 0 0]     [0]
     orientation:
                     [1 0 0]    [1 0 0]    [1 1 0]    [1]    [1 0 0]    [1 0 0]    [1 1 0]                     
      f(x,h1(y,z)) = [0 0 0]x + [0 0 0]y + [0 0 0]z + [0] >= [0 0 0]x + [0 0 0]y + [0 0 0]z = h2(0(),x,h1(y,z))
                     [0 0 0]    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0 0 0]                     
     problem:
      
     Qed