/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(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:
   [h1](x0, x1) = x0 + x1,
   
   [h](x0) = x0 + 3,
   
   [f](x0, x1) = x0 + x1 + 2,
   
   [g](x0) = 4x0,
   
   [0] = 0,
   
   [j](x0, x1) = 4x0 + 3x1 + 6,
   
   [s](x0) = x0,
   
   [i](x0) = x0 + 1,
   
   [h2](x0, x1, x2) = x0 + x1 + x2 + 2,
   
   [k](x0) = x0
  orientation:
   f(j(x,y),y) = 4x + 4y + 8 >= 4x + 4y + 8 = g(f(x,k(y)))
   
   f(x,h1(y,z)) = x + y + z + 2 >= x + y + z + 2 = h2(0(),x,h1(y,z))
   
   g(h2(x,y,h1(z,u))) = 4u + 4x + 4y + 4z + 8 >= u + x + y + z + 2 = h2(s(x),y,h1(z,u))
   
   h2(x,j(y,h1(z,u)),h1(z,u)) = 4u + x + 4y + 4z + 8 >= u + x + y + z + 2 = h2(s(x),y,h1(s(z),u))
   
   i(f(x,h(y))) = x + y + 6 >= y = y
   
   i(h2(s(x),y,h1(x,z))) = 2x + y + z + 3 >= z = z
   
   k(h(x)) = x + 3 >= x = h1(0(),x)
   
   k(h1(x,y)) = x + y >= x + y = 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:
    [h1](x0, x1) = x0 + x1,
    
    [f](x0, x1) = 4x0 + 4x1 + 2,
    
    [g](x0) = 2x0 + 6,
    
    [0] = 0,
    
    [j](x0, x1) = 2x0 + x1 + 4,
    
    [s](x0) = x0,
    
    [h2](x0, x1, x2) = x0 + 4x1 + 4x2 + 2,
    
    [k](x0) = x0 + 1
   orientation:
    f(j(x,y),y) = 8x + 8y + 18 >= 8x + 8y + 18 = g(f(x,k(y)))
    
    f(x,h1(y,z)) = 4x + 4y + 4z + 2 >= 4x + 4y + 4z + 2 = h2(0(),x,h1(y,z))
    
    k(h1(x,y)) = x + y + 1 >= x + y = 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:
     [h1](x0, x1) = x0 + x1 + 4,
     
     [f](x0, x1) = x0 + x1 + 3,
     
     [g](x0) = x0,
     
     [0] = 0,
     
     [j](x0, x1) = x0 + x1 + 1,
     
     [h2](x0, x1, x2) = x0 + x1 + x2 + 2,
     
     [k](x0) = 2x0 + 1
    orientation:
     f(j(x,y),y) = x + 2y + 4 >= x + 2y + 4 = g(f(x,k(y)))
     
     f(x,h1(y,z)) = x + y + z + 7 >= x + y + z + 6 = h2(0(),x,h1(y,z))
    problem:
     f(j(x,y),y) -> g(f(x,k(y)))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [f](x0, x1) = x0 + x1 + 3,
      
      [g](x0) = x0 + 1,
      
      [j](x0, x1) = x0 + x1 + 6,
      
      [k](x0) = 2x0 + 4
     orientation:
      f(j(x,y),y) = x + 2y + 9 >= x + 2y + 8 = g(f(x,k(y)))
     problem:
      
     Qed