/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /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=3
  
  interpretation:
             [1 1 0]  
   [s](x0) = [0 0 0]x0
             [0 0 1]  ,
   
                [1 0 1]     [0]
   [norm](x0) = [0 0 0]x0 + [1]
                [0 0 1]     [0],
   
                      [1 0 0]     [1]
   [g](x0, x1) = x0 + [0 0 0]x1 + [0]
                      [0 0 0]     [0],
   
                 [1 1 1]     [1 1 0]     [0]
   [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                 [1 0 0]     [0 1 0]     [0],
   
           [0]
   [nil] = [1]
           [1],
   
                   [1 0 1]     [1 0 0]  
   [rem](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                   [0 0 1]     [0 0 1]  ,
   
         [0]
   [0] = [0]
         [1]
  orientation:
                 [1]    [0]      
   norm(nil()) = [1] >= [0] = 0()
                 [1]    [1]      
   
                  [1 0 1]    [1 0 0]    [1]    [1 0 1]    [1]             
   norm(g(x,y)) = [0 0 0]x + [0 0 0]y + [1] >= [0 0 0]x + [0] = s(norm(x))
                  [0 0 1]    [0 0 0]    [0]    [0 0 1]    [0]             
   
                [1 1 1]    [1]    [1 0 0]    [1]             
   f(x,nil()) = [0 0 0]x + [1] >= [0 0 0]x + [1] = g(nil(),x)
                [1 0 0]    [1]    [0 0 0]    [1]             
   
                 [1 1 1]    [1 1 0]    [1 0 0]    [1]    [1 1 1]    [1 1 0]    [1 0 0]    [1]              
   f(x,g(y,z)) = [0 0 0]x + [0 0 0]y + [0 0 0]z + [1] >= [0 0 0]x + [0 0 0]y + [0 0 0]z + [1] = g(f(x,y),z)
                 [1 0 0]    [0 1 0]    [0 0 0]    [0]    [1 0 0]    [0 1 0]    [0 0 0]    [0]              
   
                  [1 0 0]    [1]    [0]        
   rem(nil(),y) = [0 0 0]y + [1] >= [1] = nil()
                  [0 0 1]    [1]    [1]        
   
                     [1 0 1]    [1 0 0]    [1]        [1 0 0]    [1]         
   rem(g(x,y),0()) = [0 1 0]x + [0 0 0]y + [0] >= x + [0 0 0]y + [0] = g(x,y)
                     [0 0 1]    [0 0 0]    [1]        [0 0 0]    [0]         
   
                      [1 0 1]    [1 0 0]    [1 1 0]    [1]    [1 0 1]    [1 0 0]            
   rem(g(x,y),s(z)) = [0 1 0]x + [0 0 0]y + [0 0 0]z + [0] >= [0 1 0]x + [0 0 0]z = rem(x,z)
                      [0 0 1]    [0 0 0]    [0 0 1]    [0]    [0 0 1]    [0 0 1]            
  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(g(x,y),0()) -> g(x,y)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [s](x0) = x0 + 2,
    
    [norm](x0) = 2x0 + 2,
    
    [g](x0, x1) = x0 + 6x1 + 6,
    
    [f](x0, x1) = 6x0 + 2x1 + 6,
    
    [nil] = 0,
    
    [rem](x0, x1) = x0 + 2x1,
    
    [0] = 4
   orientation:
    norm(g(x,y)) = 2x + 12y + 14 >= 2x + 4 = s(norm(x))
    
    f(x,nil()) = 6x + 6 >= 6x + 6 = g(nil(),x)
    
    f(x,g(y,z)) = 6x + 2y + 12z + 18 >= 6x + 2y + 6z + 12 = g(f(x,y),z)
    
    rem(g(x,y),0()) = x + 6y + 14 >= x + 6y + 6 = g(x,y)
   problem:
    f(x,nil()) -> g(nil(),x)
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                   [1 0 0]     [1 0 0]  
     [g](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],
     
             [0]
     [nil] = [0]
             [0]
    orientation:
                  [1 0 0]    [1]    [1 0 0]              
     f(x,nil()) = [0 0 0]x + [0] >= [0 0 0]x = g(nil(),x)
                  [0 0 0]    [0]    [0 0 0]              
    problem:
     
    Qed