/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:
 norm(nil()) -> 0()
 norm(g(x,y)) -> s(norm(x))
 f(x,nil()) -> g(nil(),x)
 f(x,g(y,z)) -> g(f(x,y),z)
 rem(nil(),y) -> nil()
 rem(g(x,y),0()) -> g(x,y)
 rem(g(x,y),s(z)) -> rem(x,z)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [rem](x0, x1) = 4x0 + x1,
   
   [f](x0, x1) = 4x0 + 2x1,
   
   [s](x0) = x0,
   
   [g](x0, x1) = x0 + 4x1,
   
   [0] = 0,
   
   [norm](x0) = 4x0 + 6,
   
   [nil] = 0
  orientation:
   norm(nil()) = 6 >= 0 = 0()
   
   norm(g(x,y)) = 4x + 16y + 6 >= 4x + 6 = s(norm(x))
   
   f(x,nil()) = 4x >= 4x = g(nil(),x)
   
   f(x,g(y,z)) = 4x + 2y + 8z >= 4x + 2y + 4z = g(f(x,y),z)
   
   rem(nil(),y) = y >= 0 = nil()
   
   rem(g(x,y),0()) = 4x + 16y >= x + 4y = g(x,y)
   
   rem(g(x,y),s(z)) = 4x + 16y + z >= 4x + z = rem(x,z)
  problem:
   norm(g(x,y)) -> s(norm(x))
   f(x,nil()) -> g(nil(),x)
   f(x,g(y,z)) -> g(f(x,y),z)
   rem(nil(),y) -> nil()
   rem(g(x,y),0()) -> g(x,y)
   rem(g(x,y),s(z)) -> rem(x,z)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [rem](x0, x1) = 4x0 + x1 + 1,
    
    [f](x0, x1) = 4x0 + x1 + 1,
    
    [s](x0) = x0,
    
    [g](x0, x1) = x0 + 4x1,
    
    [0] = 7,
    
    [norm](x0) = 4x0 + 2,
    
    [nil] = 0
   orientation:
    norm(g(x,y)) = 4x + 16y + 2 >= 4x + 2 = s(norm(x))
    
    f(x,nil()) = 4x + 1 >= 4x = g(nil(),x)
    
    f(x,g(y,z)) = 4x + y + 4z + 1 >= 4x + y + 4z + 1 = g(f(x,y),z)
    
    rem(nil(),y) = y + 1 >= 0 = nil()
    
    rem(g(x,y),0()) = 4x + 16y + 8 >= x + 4y = g(x,y)
    
    rem(g(x,y),s(z)) = 4x + 16y + z + 1 >= 4x + z + 1 = rem(x,z)
   problem:
    norm(g(x,y)) -> s(norm(x))
    f(x,g(y,z)) -> g(f(x,y),z)
    rem(g(x,y),s(z)) -> rem(x,z)
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [rem](x0, x1) = x0 + 4x1 + 2,
     
     [f](x0, x1) = 2x0 + x1,
     
     [s](x0) = x0 + 1,
     
     [g](x0, x1) = x0 + 2x1 + 1,
     
     [norm](x0) = x0 + 7
    orientation:
     norm(g(x,y)) = x + 2y + 8 >= x + 8 = s(norm(x))
     
     f(x,g(y,z)) = 2x + y + 2z + 1 >= 2x + y + 2z + 1 = g(f(x,y),z)
     
     rem(g(x,y),s(z)) = x + 2y + 4z + 7 >= x + 4z + 2 = rem(x,z)
    problem:
     norm(g(x,y)) -> s(norm(x))
     f(x,g(y,z)) -> g(f(x,y),z)
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [f](x0, x1) = 4x0 + x1,
      
      [s](x0) = x0,
      
      [g](x0, x1) = x0 + 4x1 + 2,
      
      [norm](x0) = x0 + 4
     orientation:
      norm(g(x,y)) = x + 4y + 6 >= x + 4 = s(norm(x))
      
      f(x,g(y,z)) = 4x + y + 4z + 2 >= 4x + y + 4z + 2 = g(f(x,y),z)
     problem:
      f(x,g(y,z)) -> g(f(x,y),z)
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [f](x0, x1) = x0 + 4x1 + 3,
       
       [g](x0, x1) = x0 + x1 + 1
      orientation:
       f(x,g(y,z)) = x + 4y + 4z + 7 >= x + 4y + z + 4 = g(f(x,y),z)
      problem:
       
      Qed