YES

Problem:
 active(filter(cons(X,Y),0(),M)) -> mark(cons(0(),filter(Y,M,M)))
 active(filter(cons(X,Y),s(N),M)) -> mark(cons(X,filter(Y,N,M)))
 active(sieve(cons(0(),Y))) -> mark(cons(0(),sieve(Y)))
 active(sieve(cons(s(N),Y))) -> mark(cons(s(N),sieve(filter(Y,N,N))))
 active(nats(N)) -> mark(cons(N,nats(s(N))))
 active(zprimes()) -> mark(sieve(nats(s(s(0())))))
 active(filter(X1,X2,X3)) -> filter(active(X1),X2,X3)
 active(filter(X1,X2,X3)) -> filter(X1,active(X2),X3)
 active(filter(X1,X2,X3)) -> filter(X1,X2,active(X3))
 active(cons(X1,X2)) -> cons(active(X1),X2)
 active(s(X)) -> s(active(X))
 active(sieve(X)) -> sieve(active(X))
 active(nats(X)) -> nats(active(X))
 filter(mark(X1),X2,X3) -> mark(filter(X1,X2,X3))
 filter(X1,mark(X2),X3) -> mark(filter(X1,X2,X3))
 filter(X1,X2,mark(X3)) -> mark(filter(X1,X2,X3))
 cons(mark(X1),X2) -> mark(cons(X1,X2))
 s(mark(X)) -> mark(s(X))
 sieve(mark(X)) -> mark(sieve(X))
 nats(mark(X)) -> mark(nats(X))
 proper(filter(X1,X2,X3)) -> filter(proper(X1),proper(X2),proper(X3))
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(0()) -> ok(0())
 proper(s(X)) -> s(proper(X))
 proper(sieve(X)) -> sieve(proper(X))
 proper(nats(X)) -> nats(proper(X))
 proper(zprimes()) -> ok(zprimes())
 filter(ok(X1),ok(X2),ok(X3)) -> ok(filter(X1,X2,X3))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 s(ok(X)) -> ok(s(X))
 sieve(ok(X)) -> ok(sieve(X))
 nats(ok(X)) -> ok(nats(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Matrix Interpretation Processor: dim=2
  
  interpretation:
                     [0]
   [mark](x0) = x0 + [1],
   
               [0]
   [zprimes] = [3],
   
         [0]
   [0] = [0],
   
                  [2 0]  
   [active](x0) = [0 1]x0,
   
               
   [s](x0) = x0,
   
              [2 0]  
   [ok](x0) = [0 1]x0,
   
                    [2 0]     [1 0]  
   [cons](x0, x1) = [0 1]x0 + [0 0]x1,
   
                [2 0]     [0]
   [nats](x0) = [0 1]x0 + [1],
   
               [2 2]     [0]
   [top](x0) = [0 1]x0 + [2],
   
                    
   [proper](x0) = x0,
   
                      [0]
   [sieve](x0) = x0 + [1],
   
                          [1 0]               [0]
   [filter](x0, x1, x2) = [0 2]x0 + x1 + x2 + [2]
  orientation:
                                     [2 0]    [4 0]    [2 0]    [0]    [2 0]    [1 0]    [0]                                
   active(filter(cons(X,Y),0(),M)) = [0 1]M + [0 2]X + [0 0]Y + [2] >= [0 0]M + [0 0]Y + [1] = mark(cons(0(),filter(Y,M,M)))
   
                                      [2 0]    [2 0]    [4 0]    [2 0]    [0]    [1 0]    [1 0]    [2 0]    [1 0]    [0]                              
   active(filter(cons(X,Y),s(N),M)) = [0 1]M + [0 1]N + [0 2]X + [0 0]Y + [2] >= [0 0]M + [0 0]N + [0 1]X + [0 0]Y + [1] = mark(cons(X,filter(Y,N,M)))
   
                                [2 0]    [0]    [1 0]    [0]                           
   active(sieve(cons(0(),Y))) = [0 0]Y + [1] >= [0 0]Y + [1] = mark(cons(0(),sieve(Y)))
   
                                 [4 0]    [2 0]    [0]    [4 0]    [1 0]    [0]                                        
   active(sieve(cons(s(N),Y))) = [0 1]N + [0 0]Y + [1] >= [0 1]N + [0 0]Y + [1] = mark(cons(s(N),sieve(filter(Y,N,N))))
   
                     [4 0]    [0]    [4 0]    [0]                           
   active(nats(N)) = [0 1]N + [1] >= [0 1]N + [1] = mark(cons(N,nats(s(N))))
   
                       [0]    [0]                               
   active(zprimes()) = [3] >= [3] = mark(sieve(nats(s(s(0())))))
   
                              [2 0]     [2 0]     [2 0]     [0]    [2 0]               [0]                           
   active(filter(X1,X2,X3)) = [0 2]X1 + [0 1]X2 + [0 1]X3 + [2] >= [0 2]X1 + X2 + X3 + [2] = filter(active(X1),X2,X3)
   
                              [2 0]     [2 0]     [2 0]     [0]    [1 0]     [2 0]          [0]                           
   active(filter(X1,X2,X3)) = [0 2]X1 + [0 1]X2 + [0 1]X3 + [2] >= [0 2]X1 + [0 1]X2 + X3 + [2] = filter(X1,active(X2),X3)
   
                              [2 0]     [2 0]     [2 0]     [0]    [1 0]          [2 0]     [0]                           
   active(filter(X1,X2,X3)) = [0 2]X1 + [0 1]X2 + [0 1]X3 + [2] >= [0 2]X1 + X2 + [0 1]X3 + [2] = filter(X1,X2,active(X3))
   
                         [4 0]     [2 0]      [4 0]     [1 0]                        
   active(cons(X1,X2)) = [0 1]X1 + [0 0]X2 >= [0 1]X1 + [0 0]X2 = cons(active(X1),X2)
   
                  [2 0]     [2 0]                
   active(s(X)) = [0 1]X >= [0 1]X = s(active(X))
   
                      [2 0]    [0]    [2 0]    [0]                   
   active(sieve(X)) = [0 1]X + [1] >= [0 1]X + [1] = sieve(active(X))
   
                     [4 0]    [0]    [4 0]    [0]                  
   active(nats(X)) = [0 1]X + [1] >= [0 1]X + [1] = nats(active(X))
   
                            [1 0]               [0]    [1 0]               [0]                         
   filter(mark(X1),X2,X3) = [0 2]X1 + X2 + X3 + [4] >= [0 2]X1 + X2 + X3 + [3] = mark(filter(X1,X2,X3))
   
                            [1 0]               [0]    [1 0]               [0]                         
   filter(X1,mark(X2),X3) = [0 2]X1 + X2 + X3 + [3] >= [0 2]X1 + X2 + X3 + [3] = mark(filter(X1,X2,X3))
   
                            [1 0]               [0]    [1 0]               [0]                         
   filter(X1,X2,mark(X3)) = [0 2]X1 + X2 + X3 + [3] >= [0 2]X1 + X2 + X3 + [3] = mark(filter(X1,X2,X3))
   
                       [2 0]     [1 0]     [0]    [2 0]     [1 0]     [0]                    
   cons(mark(X1),X2) = [0 1]X1 + [0 0]X2 + [1] >= [0 1]X1 + [0 0]X2 + [1] = mark(cons(X1,X2))
   
                    [0]        [0]             
   s(mark(X)) = X + [1] >= X + [1] = mark(s(X))
   
                        [0]        [0]                 
   sieve(mark(X)) = X + [2] >= X + [2] = mark(sieve(X))
   
                   [2 0]    [0]    [2 0]    [0]                
   nats(mark(X)) = [0 1]X + [2] >= [0 1]X + [2] = mark(nats(X))
   
                              [1 0]               [0]    [1 0]               [0]                                           
   proper(filter(X1,X2,X3)) = [0 2]X1 + X2 + X3 + [2] >= [0 2]X1 + X2 + X3 + [2] = filter(proper(X1),proper(X2),proper(X3))
   
                         [2 0]     [1 0]      [2 0]     [1 0]                                
   proper(cons(X1,X2)) = [0 1]X1 + [0 0]X2 >= [0 1]X1 + [0 0]X2 = cons(proper(X1),proper(X2))
   
                 [0]    [0]          
   proper(0()) = [0] >= [0] = ok(0())
   
                                       
   proper(s(X)) = X >= X = s(proper(X))
   
                          [0]        [0]                   
   proper(sieve(X)) = X + [1] >= X + [1] = sieve(proper(X))
   
                     [2 0]    [0]    [2 0]    [0]                  
   proper(nats(X)) = [0 1]X + [1] >= [0 1]X + [1] = nats(proper(X))
   
                       [0]    [0]                
   proper(zprimes()) = [3] >= [3] = ok(zprimes())
   
                                  [2 0]     [2 0]     [2 0]     [0]    [2 0]     [2 0]     [2 0]     [0]                       
   filter(ok(X1),ok(X2),ok(X3)) = [0 2]X1 + [0 1]X2 + [0 1]X3 + [2] >= [0 2]X1 + [0 1]X2 + [0 1]X3 + [2] = ok(filter(X1,X2,X3))
   
                         [4 0]     [2 0]      [4 0]     [2 0]                    
   cons(ok(X1),ok(X2)) = [0 1]X1 + [0 0]X2 >= [0 1]X1 + [0 0]X2 = ok(cons(X1,X2))
   
              [2 0]     [2 0]            
   s(ok(X)) = [0 1]X >= [0 1]X = ok(s(X))
   
                  [2 0]    [0]    [2 0]    [0]               
   sieve(ok(X)) = [0 1]X + [1] >= [0 1]X + [1] = ok(sieve(X))
   
                 [4 0]    [0]    [4 0]    [0]              
   nats(ok(X)) = [0 1]X + [1] >= [0 1]X + [1] = ok(nats(X))
   
                  [2 2]    [2]    [2 2]    [0]                 
   top(mark(X)) = [0 1]X + [3] >= [0 1]X + [2] = top(proper(X))
   
                [4 2]    [0]    [4 2]    [0]                 
   top(ok(X)) = [0 1]X + [2] >= [0 1]X + [2] = top(active(X))
  problem:
   active(filter(cons(X,Y),0(),M)) -> mark(cons(0(),filter(Y,M,M)))
   active(filter(cons(X,Y),s(N),M)) -> mark(cons(X,filter(Y,N,M)))
   active(sieve(cons(0(),Y))) -> mark(cons(0(),sieve(Y)))
   active(sieve(cons(s(N),Y))) -> mark(cons(s(N),sieve(filter(Y,N,N))))
   active(nats(N)) -> mark(cons(N,nats(s(N))))
   active(zprimes()) -> mark(sieve(nats(s(s(0())))))
   active(filter(X1,X2,X3)) -> filter(active(X1),X2,X3)
   active(filter(X1,X2,X3)) -> filter(X1,active(X2),X3)
   active(filter(X1,X2,X3)) -> filter(X1,X2,active(X3))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(s(X)) -> s(active(X))
   active(sieve(X)) -> sieve(active(X))
   active(nats(X)) -> nats(active(X))
   filter(mark(X1),X2,X3) -> mark(filter(X1,X2,X3))
   filter(X1,mark(X2),X3) -> mark(filter(X1,X2,X3))
   filter(X1,X2,mark(X3)) -> mark(filter(X1,X2,X3))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   s(mark(X)) -> mark(s(X))
   sieve(mark(X)) -> mark(sieve(X))
   nats(mark(X)) -> mark(nats(X))
   proper(filter(X1,X2,X3)) -> filter(proper(X1),proper(X2),proper(X3))
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(0()) -> ok(0())
   proper(s(X)) -> s(proper(X))
   proper(sieve(X)) -> sieve(proper(X))
   proper(nats(X)) -> nats(proper(X))
   proper(zprimes()) -> ok(zprimes())
   filter(ok(X1),ok(X2),ok(X3)) -> ok(filter(X1,X2,X3))
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   s(ok(X)) -> ok(s(X))
   sieve(ok(X)) -> ok(sieve(X))
   nats(ok(X)) -> ok(nats(X))
   top(ok(X)) -> top(active(X))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [mark](x0) = x0,
    
    [zprimes] = 3,
    
    [0] = 0,
    
    [active](x0) = 2x0,
    
    [s](x0) = x0,
    
    [ok](x0) = 3x0,
    
    [cons](x0, x1) = 2x0 + x1,
    
    [nats](x0) = 4x0,
    
    [top](x0) = x0,
    
    [proper](x0) = 4x0,
    
    [sieve](x0) = 4x0,
    
    [filter](x0, x1, x2) = 2x0 + x1 + x2
   orientation:
    active(filter(cons(X,Y),0(),M)) = 2M + 8X + 4Y >= 2M + 2Y = mark(cons(0(),filter(Y,M,M)))
    
    active(filter(cons(X,Y),s(N),M)) = 2M + 2N + 8X + 4Y >= M + N + 2X + 2Y = mark(cons(X,filter(Y,N,M)))
    
    active(sieve(cons(0(),Y))) = 8Y >= 4Y = mark(cons(0(),sieve(Y)))
    
    active(sieve(cons(s(N),Y))) = 16N + 8Y >= 10N + 8Y = mark(cons(s(N),sieve(filter(Y,N,N))))
    
    active(nats(N)) = 8N >= 6N = mark(cons(N,nats(s(N))))
    
    active(zprimes()) = 6 >= 0 = mark(sieve(nats(s(s(0())))))
    
    active(filter(X1,X2,X3)) = 4X1 + 2X2 + 2X3 >= 4X1 + X2 + X3 = filter(active(X1),X2,X3)
    
    active(filter(X1,X2,X3)) = 4X1 + 2X2 + 2X3 >= 2X1 + 2X2 + X3 = filter(X1,active(X2),X3)
    
    active(filter(X1,X2,X3)) = 4X1 + 2X2 + 2X3 >= 2X1 + X2 + 2X3 = filter(X1,X2,active(X3))
    
    active(cons(X1,X2)) = 4X1 + 2X2 >= 4X1 + X2 = cons(active(X1),X2)
    
    active(s(X)) = 2X >= 2X = s(active(X))
    
    active(sieve(X)) = 8X >= 8X = sieve(active(X))
    
    active(nats(X)) = 8X >= 8X = nats(active(X))
    
    filter(mark(X1),X2,X3) = 2X1 + X2 + X3 >= 2X1 + X2 + X3 = mark(filter(X1,X2,X3))
    
    filter(X1,mark(X2),X3) = 2X1 + X2 + X3 >= 2X1 + X2 + X3 = mark(filter(X1,X2,X3))
    
    filter(X1,X2,mark(X3)) = 2X1 + X2 + X3 >= 2X1 + X2 + X3 = mark(filter(X1,X2,X3))
    
    cons(mark(X1),X2) = 2X1 + X2 >= 2X1 + X2 = mark(cons(X1,X2))
    
    s(mark(X)) = X >= X = mark(s(X))
    
    sieve(mark(X)) = 4X >= 4X = mark(sieve(X))
    
    nats(mark(X)) = 4X >= 4X = mark(nats(X))
    
    proper(filter(X1,X2,X3)) = 8X1 + 4X2 + 4X3 >= 8X1 + 4X2 + 4X3 = filter(proper(X1),proper(X2),proper(X3))
    
    proper(cons(X1,X2)) = 8X1 + 4X2 >= 8X1 + 4X2 = cons(proper(X1),proper(X2))
    
    proper(0()) = 0 >= 0 = ok(0())
    
    proper(s(X)) = 4X >= 4X = s(proper(X))
    
    proper(sieve(X)) = 16X >= 16X = sieve(proper(X))
    
    proper(nats(X)) = 16X >= 16X = nats(proper(X))
    
    proper(zprimes()) = 12 >= 9 = ok(zprimes())
    
    filter(ok(X1),ok(X2),ok(X3)) = 6X1 + 3X2 + 3X3 >= 6X1 + 3X2 + 3X3 = ok(filter(X1,X2,X3))
    
    cons(ok(X1),ok(X2)) = 6X1 + 3X2 >= 6X1 + 3X2 = ok(cons(X1,X2))
    
    s(ok(X)) = 3X >= 3X = ok(s(X))
    
    sieve(ok(X)) = 12X >= 12X = ok(sieve(X))
    
    nats(ok(X)) = 12X >= 12X = ok(nats(X))
    
    top(ok(X)) = 3X >= 2X = top(active(X))
   problem:
    active(filter(cons(X,Y),0(),M)) -> mark(cons(0(),filter(Y,M,M)))
    active(filter(cons(X,Y),s(N),M)) -> mark(cons(X,filter(Y,N,M)))
    active(sieve(cons(0(),Y))) -> mark(cons(0(),sieve(Y)))
    active(sieve(cons(s(N),Y))) -> mark(cons(s(N),sieve(filter(Y,N,N))))
    active(nats(N)) -> mark(cons(N,nats(s(N))))
    active(filter(X1,X2,X3)) -> filter(active(X1),X2,X3)
    active(filter(X1,X2,X3)) -> filter(X1,active(X2),X3)
    active(filter(X1,X2,X3)) -> filter(X1,X2,active(X3))
    active(cons(X1,X2)) -> cons(active(X1),X2)
    active(s(X)) -> s(active(X))
    active(sieve(X)) -> sieve(active(X))
    active(nats(X)) -> nats(active(X))
    filter(mark(X1),X2,X3) -> mark(filter(X1,X2,X3))
    filter(X1,mark(X2),X3) -> mark(filter(X1,X2,X3))
    filter(X1,X2,mark(X3)) -> mark(filter(X1,X2,X3))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    s(mark(X)) -> mark(s(X))
    sieve(mark(X)) -> mark(sieve(X))
    nats(mark(X)) -> mark(nats(X))
    proper(filter(X1,X2,X3)) -> filter(proper(X1),proper(X2),proper(X3))
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(0()) -> ok(0())
    proper(s(X)) -> s(proper(X))
    proper(sieve(X)) -> sieve(proper(X))
    proper(nats(X)) -> nats(proper(X))
    filter(ok(X1),ok(X2),ok(X3)) -> ok(filter(X1,X2,X3))
    cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    s(ok(X)) -> ok(s(X))
    sieve(ok(X)) -> ok(sieve(X))
    nats(ok(X)) -> ok(nats(X))
    top(ok(X)) -> top(active(X))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [mark](x0) = x0 + 4,
     
     [0] = 0,
     
     [active](x0) = 4x0 + 2,
     
     [s](x0) = x0,
     
     [ok](x0) = 4x0 + 3,
     
     [cons](x0, x1) = 4x0 + x1 + 2,
     
     [nats](x0) = 4x0 + 2,
     
     [top](x0) = 2x0 + 4,
     
     [proper](x0) = 7x0 + 3,
     
     [sieve](x0) = x0,
     
     [filter](x0, x1, x2) = x0 + 2x1 + x2 + 3
    orientation:
     active(filter(cons(X,Y),0(),M)) = 4M + 16X + 4Y + 22 >= 3M + Y + 9 = mark(cons(0(),filter(Y,M,M)))
     
     active(filter(cons(X,Y),s(N),M)) = 4M + 8N + 16X + 4Y + 22 >= M + 2N + 4X + Y + 9 = mark(cons(X,filter(Y,N,M)))
     
     active(sieve(cons(0(),Y))) = 4Y + 10 >= Y + 6 = mark(cons(0(),sieve(Y)))
     
     active(sieve(cons(s(N),Y))) = 16N + 4Y + 10 >= 7N + Y + 9 = mark(cons(s(N),sieve(filter(Y,N,N))))
     
     active(nats(N)) = 16N + 10 >= 8N + 8 = mark(cons(N,nats(s(N))))
     
     active(filter(X1,X2,X3)) = 4X1 + 8X2 + 4X3 + 14 >= 4X1 + 2X2 + X3 + 5 = filter(active(X1),X2,X3)
     
     active(filter(X1,X2,X3)) = 4X1 + 8X2 + 4X3 + 14 >= X1 + 8X2 + X3 + 7 = filter(X1,active(X2),X3)
     
     active(filter(X1,X2,X3)) = 4X1 + 8X2 + 4X3 + 14 >= X1 + 2X2 + 4X3 + 5 = filter(X1,X2,active(X3))
     
     active(cons(X1,X2)) = 16X1 + 4X2 + 10 >= 16X1 + X2 + 10 = cons(active(X1),X2)
     
     active(s(X)) = 4X + 2 >= 4X + 2 = s(active(X))
     
     active(sieve(X)) = 4X + 2 >= 4X + 2 = sieve(active(X))
     
     active(nats(X)) = 16X + 10 >= 16X + 10 = nats(active(X))
     
     filter(mark(X1),X2,X3) = X1 + 2X2 + X3 + 7 >= X1 + 2X2 + X3 + 7 = mark(filter(X1,X2,X3))
     
     filter(X1,mark(X2),X3) = X1 + 2X2 + X3 + 11 >= X1 + 2X2 + X3 + 7 = mark(filter(X1,X2,X3))
     
     filter(X1,X2,mark(X3)) = X1 + 2X2 + X3 + 7 >= X1 + 2X2 + X3 + 7 = mark(filter(X1,X2,X3))
     
     cons(mark(X1),X2) = 4X1 + X2 + 18 >= 4X1 + X2 + 6 = mark(cons(X1,X2))
     
     s(mark(X)) = X + 4 >= X + 4 = mark(s(X))
     
     sieve(mark(X)) = X + 4 >= X + 4 = mark(sieve(X))
     
     nats(mark(X)) = 4X + 18 >= 4X + 6 = mark(nats(X))
     
     proper(filter(X1,X2,X3)) = 7X1 + 14X2 + 7X3 + 24 >= 7X1 + 14X2 + 7X3 + 15 = filter(proper(X1),proper(X2),proper(X3))
     
     proper(cons(X1,X2)) = 28X1 + 7X2 + 17 >= 28X1 + 7X2 + 17 = cons(proper(X1),proper(X2))
     
     proper(0()) = 3 >= 3 = ok(0())
     
     proper(s(X)) = 7X + 3 >= 7X + 3 = s(proper(X))
     
     proper(sieve(X)) = 7X + 3 >= 7X + 3 = sieve(proper(X))
     
     proper(nats(X)) = 28X + 17 >= 28X + 14 = nats(proper(X))
     
     filter(ok(X1),ok(X2),ok(X3)) = 4X1 + 8X2 + 4X3 + 15 >= 4X1 + 8X2 + 4X3 + 15 = ok(filter(X1,X2,X3))
     
     cons(ok(X1),ok(X2)) = 16X1 + 4X2 + 17 >= 16X1 + 4X2 + 11 = ok(cons(X1,X2))
     
     s(ok(X)) = 4X + 3 >= 4X + 3 = ok(s(X))
     
     sieve(ok(X)) = 4X + 3 >= 4X + 3 = ok(sieve(X))
     
     nats(ok(X)) = 16X + 14 >= 16X + 11 = ok(nats(X))
     
     top(ok(X)) = 8X + 10 >= 8X + 8 = top(active(X))
    problem:
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(s(X)) -> s(active(X))
     active(sieve(X)) -> sieve(active(X))
     active(nats(X)) -> nats(active(X))
     filter(mark(X1),X2,X3) -> mark(filter(X1,X2,X3))
     filter(X1,X2,mark(X3)) -> mark(filter(X1,X2,X3))
     s(mark(X)) -> mark(s(X))
     sieve(mark(X)) -> mark(sieve(X))
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(0()) -> ok(0())
     proper(s(X)) -> s(proper(X))
     proper(sieve(X)) -> sieve(proper(X))
     filter(ok(X1),ok(X2),ok(X3)) -> ok(filter(X1,X2,X3))
     s(ok(X)) -> ok(s(X))
     sieve(ok(X)) -> ok(sieve(X))
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [mark](x0) = x0 + 2,
      
      [0] = 1,
      
      [active](x0) = x0,
      
      [s](x0) = x0,
      
      [ok](x0) = 5x0,
      
      [cons](x0, x1) = 4x0 + 2x1 + 5,
      
      [nats](x0) = x0 + 6,
      
      [proper](x0) = 3x0 + 2,
      
      [sieve](x0) = x0,
      
      [filter](x0, x1, x2) = 4x0 + 2x1 + 4x2
     orientation:
      active(cons(X1,X2)) = 4X1 + 2X2 + 5 >= 4X1 + 2X2 + 5 = cons(active(X1),X2)
      
      active(s(X)) = X >= X = s(active(X))
      
      active(sieve(X)) = X >= X = sieve(active(X))
      
      active(nats(X)) = X + 6 >= X + 6 = nats(active(X))
      
      filter(mark(X1),X2,X3) = 4X1 + 2X2 + 4X3 + 8 >= 4X1 + 2X2 + 4X3 + 2 = mark(filter(X1,X2,X3))
      
      filter(X1,X2,mark(X3)) = 4X1 + 2X2 + 4X3 + 8 >= 4X1 + 2X2 + 4X3 + 2 = mark(filter(X1,X2,X3))
      
      s(mark(X)) = X + 2 >= X + 2 = mark(s(X))
      
      sieve(mark(X)) = X + 2 >= X + 2 = mark(sieve(X))
      
      proper(cons(X1,X2)) = 12X1 + 6X2 + 17 >= 12X1 + 6X2 + 17 = cons(proper(X1),proper(X2))
      
      proper(0()) = 5 >= 5 = ok(0())
      
      proper(s(X)) = 3X + 2 >= 3X + 2 = s(proper(X))
      
      proper(sieve(X)) = 3X + 2 >= 3X + 2 = sieve(proper(X))
      
      filter(ok(X1),ok(X2),ok(X3)) = 20X1 + 10X2 + 20X3 >= 20X1 + 10X2 + 20X3 = ok(filter(X1,X2,X3))
      
      s(ok(X)) = 5X >= 5X = ok(s(X))
      
      sieve(ok(X)) = 5X >= 5X = ok(sieve(X))
     problem:
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(sieve(X)) -> sieve(active(X))
      active(nats(X)) -> nats(active(X))
      s(mark(X)) -> mark(s(X))
      sieve(mark(X)) -> mark(sieve(X))
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(0()) -> ok(0())
      proper(s(X)) -> s(proper(X))
      proper(sieve(X)) -> sieve(proper(X))
      filter(ok(X1),ok(X2),ok(X3)) -> ok(filter(X1,X2,X3))
      s(ok(X)) -> ok(s(X))
      sieve(ok(X)) -> ok(sieve(X))
     Matrix Interpretation Processor: dim=1
      
      interpretation:
       [mark](x0) = x0 + 6,
       
       [0] = 4,
       
       [active](x0) = x0,
       
       [s](x0) = x0,
       
       [ok](x0) = 4x0,
       
       [cons](x0, x1) = 4x0 + x1 + 4,
       
       [nats](x0) = x0 + 2,
       
       [proper](x0) = 4x0,
       
       [sieve](x0) = 4x0,
       
       [filter](x0, x1, x2) = x0 + x1 + x2
      orientation:
       active(cons(X1,X2)) = 4X1 + X2 + 4 >= 4X1 + X2 + 4 = cons(active(X1),X2)
       
       active(s(X)) = X >= X = s(active(X))
       
       active(sieve(X)) = 4X >= 4X = sieve(active(X))
       
       active(nats(X)) = X + 2 >= X + 2 = nats(active(X))
       
       s(mark(X)) = X + 6 >= X + 6 = mark(s(X))
       
       sieve(mark(X)) = 4X + 24 >= 4X + 6 = mark(sieve(X))
       
       proper(cons(X1,X2)) = 16X1 + 4X2 + 16 >= 16X1 + 4X2 + 4 = cons(proper(X1),proper(X2))
       
       proper(0()) = 16 >= 16 = ok(0())
       
       proper(s(X)) = 4X >= 4X = s(proper(X))
       
       proper(sieve(X)) = 16X >= 16X = sieve(proper(X))
       
       filter(ok(X1),ok(X2),ok(X3)) = 4X1 + 4X2 + 4X3 >= 4X1 + 4X2 + 4X3 = ok(filter(X1,X2,X3))
       
       s(ok(X)) = 4X >= 4X = ok(s(X))
       
       sieve(ok(X)) = 16X >= 16X = ok(sieve(X))
      problem:
       active(cons(X1,X2)) -> cons(active(X1),X2)
       active(s(X)) -> s(active(X))
       active(sieve(X)) -> sieve(active(X))
       active(nats(X)) -> nats(active(X))
       s(mark(X)) -> mark(s(X))
       proper(0()) -> ok(0())
       proper(s(X)) -> s(proper(X))
       proper(sieve(X)) -> sieve(proper(X))
       filter(ok(X1),ok(X2),ok(X3)) -> ok(filter(X1,X2,X3))
       s(ok(X)) -> ok(s(X))
       sieve(ok(X)) -> ok(sieve(X))
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [mark](x0) = x0 + 6,
        
        [0] = 0,
        
        [active](x0) = 2x0 + 3,
        
        [s](x0) = 2x0 + 3,
        
        [ok](x0) = x0,
        
        [cons](x0, x1) = x0 + 6x1,
        
        [nats](x0) = x0,
        
        [proper](x0) = 2x0,
        
        [sieve](x0) = x0,
        
        [filter](x0, x1, x2) = 4x0 + x1 + 4x2
       orientation:
        active(cons(X1,X2)) = 2X1 + 12X2 + 3 >= 2X1 + 6X2 + 3 = cons(active(X1),X2)
        
        active(s(X)) = 4X + 9 >= 4X + 9 = s(active(X))
        
        active(sieve(X)) = 2X + 3 >= 2X + 3 = sieve(active(X))
        
        active(nats(X)) = 2X + 3 >= 2X + 3 = nats(active(X))
        
        s(mark(X)) = 2X + 15 >= 2X + 9 = mark(s(X))
        
        proper(0()) = 0 >= 0 = ok(0())
        
        proper(s(X)) = 4X + 6 >= 4X + 3 = s(proper(X))
        
        proper(sieve(X)) = 2X >= 2X = sieve(proper(X))
        
        filter(ok(X1),ok(X2),ok(X3)) = 4X1 + X2 + 4X3 >= 4X1 + X2 + 4X3 = ok(filter(X1,X2,X3))
        
        s(ok(X)) = 2X + 3 >= 2X + 3 = ok(s(X))
        
        sieve(ok(X)) = X >= X = ok(sieve(X))
       problem:
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        active(sieve(X)) -> sieve(active(X))
        active(nats(X)) -> nats(active(X))
        proper(0()) -> ok(0())
        proper(sieve(X)) -> sieve(proper(X))
        filter(ok(X1),ok(X2),ok(X3)) -> ok(filter(X1,X2,X3))
        s(ok(X)) -> ok(s(X))
        sieve(ok(X)) -> ok(sieve(X))
       Matrix Interpretation Processor: dim=1
        
        interpretation:
         [0] = 4,
         
         [active](x0) = 4x0,
         
         [s](x0) = 4x0 + 6,
         
         [ok](x0) = x0 + 1,
         
         [cons](x0, x1) = 4x0 + x1 + 1,
         
         [nats](x0) = x0,
         
         [proper](x0) = 5x0 + 1,
         
         [sieve](x0) = x0,
         
         [filter](x0, x1, x2) = 2x0 + 4x1 + x2 + 4
        orientation:
         active(cons(X1,X2)) = 16X1 + 4X2 + 4 >= 16X1 + X2 + 1 = cons(active(X1),X2)
         
         active(s(X)) = 16X + 24 >= 16X + 6 = s(active(X))
         
         active(sieve(X)) = 4X >= 4X = sieve(active(X))
         
         active(nats(X)) = 4X >= 4X = nats(active(X))
         
         proper(0()) = 21 >= 5 = ok(0())
         
         proper(sieve(X)) = 5X + 1 >= 5X + 1 = sieve(proper(X))
         
         filter(ok(X1),ok(X2),ok(X3)) = 2X1 + 4X2 + X3 + 11 >= 2X1 + 4X2 + X3 + 5 = ok(filter(X1,X2,X3))
         
         s(ok(X)) = 4X + 10 >= 4X + 7 = ok(s(X))
         
         sieve(ok(X)) = X + 1 >= X + 1 = ok(sieve(X))
        problem:
         active(sieve(X)) -> sieve(active(X))
         active(nats(X)) -> nats(active(X))
         proper(sieve(X)) -> sieve(proper(X))
         sieve(ok(X)) -> ok(sieve(X))
        Matrix Interpretation Processor: dim=1
         
         interpretation:
          [active](x0) = x0,
          
          [ok](x0) = 4x0 + 4,
          
          [nats](x0) = x0,
          
          [proper](x0) = x0,
          
          [sieve](x0) = 4x0 + 3
         orientation:
          active(sieve(X)) = 4X + 3 >= 4X + 3 = sieve(active(X))
          
          active(nats(X)) = X >= X = nats(active(X))
          
          proper(sieve(X)) = 4X + 3 >= 4X + 3 = sieve(proper(X))
          
          sieve(ok(X)) = 16X + 19 >= 16X + 16 = ok(sieve(X))
         problem:
          active(sieve(X)) -> sieve(active(X))
          active(nats(X)) -> nats(active(X))
          proper(sieve(X)) -> sieve(proper(X))
         Matrix Interpretation Processor: dim=1
          
          interpretation:
           [active](x0) = x0,
           
           [nats](x0) = x0,
           
           [proper](x0) = 2x0 + 1,
           
           [sieve](x0) = x0 + 3
          orientation:
           active(sieve(X)) = X + 3 >= X + 3 = sieve(active(X))
           
           active(nats(X)) = X >= X = nats(active(X))
           
           proper(sieve(X)) = 2X + 7 >= 2X + 4 = sieve(proper(X))
          problem:
           active(sieve(X)) -> sieve(active(X))
           active(nats(X)) -> nats(active(X))
          Matrix Interpretation Processor: dim=3
           
           interpretation:
                           [1 0 1]  
            [active](x0) = [0 1 0]x0
                           [0 1 0]  ,
            
                         [1 0 1]     [1]
            [nats](x0) = [0 1 0]x0 + [0]
                         [0 1 0]     [0],
            
                          [1 0 1]     [0]
            [sieve](x0) = [0 1 0]x0 + [1]
                          [0 1 0]     [1]
           orientation:
                               [1 1 1]    [1]    [1 1 1]    [0]                   
            active(sieve(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = sieve(active(X))
                               [0 1 0]    [1]    [0 1 0]    [1]                   
            
                              [1 1 1]    [1]    [1 1 1]    [1]                  
            active(nats(X)) = [0 1 0]X + [0] >= [0 1 0]X + [0] = nats(active(X))
                              [0 1 0]    [0]    [0 1 0]    [0]                  
           problem:
            active(nats(X)) -> nats(active(X))
           Matrix Interpretation Processor: dim=3
            
            interpretation:
                            [1 1 0]  
             [active](x0) = [0 1 0]x0
                            [0 0 0]  ,
             
                          [1 0 0]     [0]
             [nats](x0) = [0 1 0]x0 + [1]
                          [0 0 0]     [0]
            orientation:
                               [1 1 0]    [1]    [1 1 0]    [0]                  
             active(nats(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = nats(active(X))
                               [0 0 0]    [0]    [0 0 0]    [0]                  
            problem:
             
            Qed