YES

Problem:
 active(f(0())) -> mark(cons(0(),f(s(0()))))
 active(f(s(0()))) -> mark(f(p(s(0()))))
 active(p(s(0()))) -> mark(0())
 active(f(X)) -> f(active(X))
 active(cons(X1,X2)) -> cons(active(X1),X2)
 active(s(X)) -> s(active(X))
 active(p(X)) -> p(active(X))
 f(mark(X)) -> mark(f(X))
 cons(mark(X1),X2) -> mark(cons(X1,X2))
 s(mark(X)) -> mark(s(X))
 p(mark(X)) -> mark(p(X))
 proper(f(X)) -> f(proper(X))
 proper(0()) -> ok(0())
 proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
 proper(s(X)) -> s(proper(X))
 proper(p(X)) -> p(proper(X))
 f(ok(X)) -> ok(f(X))
 cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
 s(ok(X)) -> ok(s(X))
 p(ok(X)) -> ok(p(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
               [1 1 0]     [0]
   [top](x0) = [1 1 1]x0 + [1]
               [0 0 0]     [0],
   
                
   [ok](x0) = x0
                ,
   
                    
   [proper](x0) = x0
                    ,
   
             [1 1 0]  
   [p](x0) = [0 0 0]x0
             [0 0 0]  ,
   
                [1 1 1]  
   [mark](x0) = [0 0 0]x0
                [0 0 0]  ,
   
                    [1 0 0]     [1 0 0]  
   [cons](x0, x1) = [0 1 0]x0 + [0 0 0]x1
                    [0 0 0]     [0 0 0]  ,
   
             [1 0 0]  
   [s](x0) = [0 1 1]x0
             [0 0 0]  ,
   
                  [1 1 0]  
   [active](x0) = [0 0 0]x0
                  [0 0 0]  ,
   
             [1 0 0]  
   [f](x0) = [0 1 1]x0
             [0 0 0]  ,
   
         [0]
   [0] = [0]
         [1]
  orientation:
                    [1]    [0]                            
   active(f(0())) = [0] >= [0] = mark(cons(0(),f(s(0()))))
                    [0]    [0]                            
   
                       [1]    [1]                     
   active(f(s(0()))) = [0] >= [0] = mark(f(p(s(0()))))
                       [0]    [0]                     
   
                       [1]    [1]            
   active(p(s(0()))) = [0] >= [0] = mark(0())
                       [0]    [0]            
   
                  [1 1 1]     [1 1 0]                
   active(f(X)) = [0 0 0]X >= [0 0 0]X = f(active(X))
                  [0 0 0]     [0 0 0]                
   
                         [1 1 0]     [1 0 0]      [1 1 0]     [1 0 0]                        
   active(cons(X1,X2)) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = cons(active(X1),X2)
                         [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                        
   
                  [1 1 1]     [1 1 0]                
   active(s(X)) = [0 0 0]X >= [0 0 0]X = s(active(X))
                  [0 0 0]     [0 0 0]                
   
                  [1 1 0]     [1 1 0]                
   active(p(X)) = [0 0 0]X >= [0 0 0]X = p(active(X))
                  [0 0 0]     [0 0 0]                
   
                [1 1 1]     [1 1 1]              
   f(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(f(X))
                [0 0 0]     [0 0 0]              
   
                       [1 1 1]     [1 0 0]      [1 1 0]     [1 0 0]                      
   cons(mark(X1),X2) = [0 0 0]X1 + [0 0 0]X2 >= [0 0 0]X1 + [0 0 0]X2 = mark(cons(X1,X2))
                       [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                      
   
                [1 1 1]     [1 1 1]              
   s(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(s(X))
                [0 0 0]     [0 0 0]              
   
                [1 1 1]     [1 1 0]              
   p(mark(X)) = [0 0 0]X >= [0 0 0]X = mark(p(X))
                [0 0 0]     [0 0 0]              
   
                  [1 0 0]     [1 0 0]                
   proper(f(X)) = [0 1 1]X >= [0 1 1]X = f(proper(X))
                  [0 0 0]     [0 0 0]                
   
                 [0]    [0]          
   proper(0()) = [0] >= [0] = ok(0())
                 [1]    [1]          
   
                         [1 0 0]     [1 0 0]      [1 0 0]     [1 0 0]                                
   proper(cons(X1,X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = cons(proper(X1),proper(X2))
                         [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                                
   
                  [1 0 0]     [1 0 0]                
   proper(s(X)) = [0 1 1]X >= [0 1 1]X = s(proper(X))
                  [0 0 0]     [0 0 0]                
   
                  [1 1 0]     [1 1 0]                
   proper(p(X)) = [0 0 0]X >= [0 0 0]X = p(proper(X))
                  [0 0 0]     [0 0 0]                
   
              [1 0 0]     [1 0 0]            
   f(ok(X)) = [0 1 1]X >= [0 1 1]X = ok(f(X))
              [0 0 0]     [0 0 0]            
   
                         [1 0 0]     [1 0 0]      [1 0 0]     [1 0 0]                    
   cons(ok(X1),ok(X2)) = [0 1 0]X1 + [0 0 0]X2 >= [0 1 0]X1 + [0 0 0]X2 = ok(cons(X1,X2))
                         [0 0 0]     [0 0 0]      [0 0 0]     [0 0 0]                    
   
              [1 0 0]     [1 0 0]            
   s(ok(X)) = [0 1 1]X >= [0 1 1]X = ok(s(X))
              [0 0 0]     [0 0 0]            
   
              [1 1 0]     [1 1 0]            
   p(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(p(X))
              [0 0 0]     [0 0 0]            
   
                  [1 1 1]    [0]    [1 1 0]    [0]                 
   top(mark(X)) = [1 1 1]X + [1] >= [1 1 1]X + [1] = top(proper(X))
                  [0 0 0]    [0]    [0 0 0]    [0]                 
   
                [1 1 0]    [0]    [1 1 0]    [0]                 
   top(ok(X)) = [1 1 1]X + [1] >= [1 1 0]X + [1] = top(active(X))
                [0 0 0]    [0]    [0 0 0]    [0]                 
  problem:
   active(f(s(0()))) -> mark(f(p(s(0()))))
   active(p(s(0()))) -> mark(0())
   active(f(X)) -> f(active(X))
   active(cons(X1,X2)) -> cons(active(X1),X2)
   active(s(X)) -> s(active(X))
   active(p(X)) -> p(active(X))
   f(mark(X)) -> mark(f(X))
   cons(mark(X1),X2) -> mark(cons(X1,X2))
   s(mark(X)) -> mark(s(X))
   p(mark(X)) -> mark(p(X))
   proper(f(X)) -> f(proper(X))
   proper(0()) -> ok(0())
   proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
   proper(s(X)) -> s(proper(X))
   proper(p(X)) -> p(proper(X))
   f(ok(X)) -> ok(f(X))
   cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
   s(ok(X)) -> ok(s(X))
   p(ok(X)) -> ok(p(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  DP Processor:
   DPs:
    active#(f(s(0()))) -> p#(s(0()))
    active#(f(s(0()))) -> f#(p(s(0())))
    active#(f(X)) -> active#(X)
    active#(f(X)) -> f#(active(X))
    active#(cons(X1,X2)) -> active#(X1)
    active#(cons(X1,X2)) -> cons#(active(X1),X2)
    active#(s(X)) -> active#(X)
    active#(s(X)) -> s#(active(X))
    active#(p(X)) -> active#(X)
    active#(p(X)) -> p#(active(X))
    f#(mark(X)) -> f#(X)
    cons#(mark(X1),X2) -> cons#(X1,X2)
    s#(mark(X)) -> s#(X)
    p#(mark(X)) -> p#(X)
    proper#(f(X)) -> proper#(X)
    proper#(f(X)) -> f#(proper(X))
    proper#(cons(X1,X2)) -> proper#(X2)
    proper#(cons(X1,X2)) -> proper#(X1)
    proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
    proper#(s(X)) -> proper#(X)
    proper#(s(X)) -> s#(proper(X))
    proper#(p(X)) -> proper#(X)
    proper#(p(X)) -> p#(proper(X))
    f#(ok(X)) -> f#(X)
    cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
    s#(ok(X)) -> s#(X)
    p#(ok(X)) -> p#(X)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    active(f(s(0()))) -> mark(f(p(s(0()))))
    active(p(s(0()))) -> mark(0())
    active(f(X)) -> f(active(X))
    active(cons(X1,X2)) -> cons(active(X1),X2)
    active(s(X)) -> s(active(X))
    active(p(X)) -> p(active(X))
    f(mark(X)) -> mark(f(X))
    cons(mark(X1),X2) -> mark(cons(X1,X2))
    s(mark(X)) -> mark(s(X))
    p(mark(X)) -> mark(p(X))
    proper(f(X)) -> f(proper(X))
    proper(0()) -> ok(0())
    proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
    proper(s(X)) -> s(proper(X))
    proper(p(X)) -> p(proper(X))
    f(ok(X)) -> ok(f(X))
    cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
    s(ok(X)) -> ok(s(X))
    p(ok(X)) -> ok(p(X))
    top(mark(X)) -> top(proper(X))
    top(ok(X)) -> top(active(X))
   TDG Processor:
    DPs:
     active#(f(s(0()))) -> p#(s(0()))
     active#(f(s(0()))) -> f#(p(s(0())))
     active#(f(X)) -> active#(X)
     active#(f(X)) -> f#(active(X))
     active#(cons(X1,X2)) -> active#(X1)
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     active#(s(X)) -> active#(X)
     active#(s(X)) -> s#(active(X))
     active#(p(X)) -> active#(X)
     active#(p(X)) -> p#(active(X))
     f#(mark(X)) -> f#(X)
     cons#(mark(X1),X2) -> cons#(X1,X2)
     s#(mark(X)) -> s#(X)
     p#(mark(X)) -> p#(X)
     proper#(f(X)) -> proper#(X)
     proper#(f(X)) -> f#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(s(X)) -> proper#(X)
     proper#(s(X)) -> s#(proper(X))
     proper#(p(X)) -> proper#(X)
     proper#(p(X)) -> p#(proper(X))
     f#(ok(X)) -> f#(X)
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     s#(ok(X)) -> s#(X)
     p#(ok(X)) -> p#(X)
     top#(mark(X)) -> proper#(X)
     top#(mark(X)) -> top#(proper(X))
     top#(ok(X)) -> active#(X)
     top#(ok(X)) -> top#(active(X))
    TRS:
     active(f(s(0()))) -> mark(f(p(s(0()))))
     active(p(s(0()))) -> mark(0())
     active(f(X)) -> f(active(X))
     active(cons(X1,X2)) -> cons(active(X1),X2)
     active(s(X)) -> s(active(X))
     active(p(X)) -> p(active(X))
     f(mark(X)) -> mark(f(X))
     cons(mark(X1),X2) -> mark(cons(X1,X2))
     s(mark(X)) -> mark(s(X))
     p(mark(X)) -> mark(p(X))
     proper(f(X)) -> f(proper(X))
     proper(0()) -> ok(0())
     proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
     proper(s(X)) -> s(proper(X))
     proper(p(X)) -> p(proper(X))
     f(ok(X)) -> ok(f(X))
     cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
     s(ok(X)) -> ok(s(X))
     p(ok(X)) -> ok(p(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
    graph:
     top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X))
     top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X)
     top#(ok(X)) -> top#(active(X)) ->
     top#(mark(X)) -> top#(proper(X))
     top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X)
     top#(ok(X)) -> active#(X) -> active#(p(X)) -> p#(active(X))
     top#(ok(X)) -> active#(X) -> active#(p(X)) -> active#(X)
     top#(ok(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
     top#(ok(X)) -> active#(X) -> active#(s(X)) -> active#(X)
     top#(ok(X)) -> active#(X) ->
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     top#(ok(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
     top#(ok(X)) -> active#(X) -> active#(f(X)) -> f#(active(X))
     top#(ok(X)) -> active#(X) -> active#(f(X)) -> active#(X)
     top#(ok(X)) -> active#(X) -> active#(f(s(0()))) -> f#(p(s(0())))
     top#(ok(X)) -> active#(X) -> active#(f(s(0()))) -> p#(s(0()))
     top#(mark(X)) -> top#(proper(X)) ->
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X)
     top#(mark(X)) -> top#(proper(X)) ->
     top#(mark(X)) -> top#(proper(X))
     top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X)
     top#(mark(X)) -> proper#(X) -> proper#(p(X)) -> p#(proper(X))
     top#(mark(X)) -> proper#(X) -> proper#(p(X)) -> proper#(X)
     top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
     top#(mark(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
     top#(mark(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
     top#(mark(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
     top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
     top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
     proper#(p(X)) -> proper#(X) -> proper#(p(X)) -> p#(proper(X))
     proper#(p(X)) -> proper#(X) -> proper#(p(X)) -> proper#(X)
     proper#(p(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
     proper#(p(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
     proper#(p(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(p(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
     proper#(p(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
     proper#(p(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
     proper#(p(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
     proper#(p(X)) -> p#(proper(X)) -> p#(ok(X)) -> p#(X)
     proper#(p(X)) -> p#(proper(X)) -> p#(mark(X)) -> p#(X)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(p(X)) -> p#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(p(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(s(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(f(X)) -> f#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X2) ->
     proper#(f(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(p(X)) -> p#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(p(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(s(X)) -> s#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(s(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(cons(X1,X2)) -> proper#(X1)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(cons(X1,X2)) -> proper#(X2)
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(f(X)) -> f#(proper(X))
     proper#(cons(X1,X2)) -> proper#(X1) ->
     proper#(f(X)) -> proper#(X)
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) ->
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2)) ->
     cons#(mark(X1),X2) -> cons#(X1,X2)
     proper#(s(X)) -> proper#(X) -> proper#(p(X)) -> p#(proper(X))
     proper#(s(X)) -> proper#(X) -> proper#(p(X)) -> proper#(X)
     proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
     proper#(s(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
     proper#(s(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
     proper#(s(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
     proper#(s(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
     proper#(s(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
     proper#(s(X)) -> s#(proper(X)) -> s#(ok(X)) -> s#(X)
     proper#(s(X)) -> s#(proper(X)) -> s#(mark(X)) -> s#(X)
     proper#(f(X)) -> proper#(X) -> proper#(p(X)) -> p#(proper(X))
     proper#(f(X)) -> proper#(X) -> proper#(p(X)) -> proper#(X)
     proper#(f(X)) -> proper#(X) -> proper#(s(X)) -> s#(proper(X))
     proper#(f(X)) -> proper#(X) -> proper#(s(X)) -> proper#(X)
     proper#(f(X)) -> proper#(X) ->
     proper#(cons(X1,X2)) -> cons#(proper(X1),proper(X2))
     proper#(f(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X1)
     proper#(f(X)) -> proper#(X) -> proper#(cons(X1,X2)) -> proper#(X2)
     proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
     proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
     proper#(f(X)) -> f#(proper(X)) -> f#(ok(X)) -> f#(X)
     proper#(f(X)) -> f#(proper(X)) -> f#(mark(X)) -> f#(X)
     s#(ok(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
     s#(ok(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
     s#(mark(X)) -> s#(X) -> s#(ok(X)) -> s#(X)
     s#(mark(X)) -> s#(X) -> s#(mark(X)) -> s#(X)
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2) ->
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2) ->
     cons#(mark(X1),X2) -> cons#(X1,X2)
     cons#(mark(X1),X2) -> cons#(X1,X2) ->
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     cons#(mark(X1),X2) -> cons#(X1,X2) -> cons#(mark(X1),X2) -> cons#(X1,X2)
     f#(ok(X)) -> f#(X) -> f#(ok(X)) -> f#(X)
     f#(ok(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
     f#(mark(X)) -> f#(X) -> f#(ok(X)) -> f#(X)
     f#(mark(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
     p#(ok(X)) -> p#(X) -> p#(ok(X)) -> p#(X)
     p#(ok(X)) -> p#(X) -> p#(mark(X)) -> p#(X)
     p#(mark(X)) -> p#(X) -> p#(ok(X)) -> p#(X)
     p#(mark(X)) -> p#(X) -> p#(mark(X)) -> p#(X)
     active#(p(X)) -> p#(active(X)) -> p#(ok(X)) -> p#(X)
     active#(p(X)) -> p#(active(X)) -> p#(mark(X)) -> p#(X)
     active#(p(X)) -> active#(X) -> active#(p(X)) -> p#(active(X))
     active#(p(X)) -> active#(X) -> active#(p(X)) -> active#(X)
     active#(p(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
     active#(p(X)) -> active#(X) -> active#(s(X)) -> active#(X)
     active#(p(X)) -> active#(X) ->
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     active#(p(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
     active#(p(X)) -> active#(X) -> active#(f(X)) -> f#(active(X))
     active#(p(X)) -> active#(X) -> active#(f(X)) -> active#(X)
     active#(p(X)) -> active#(X) -> active#(f(s(0()))) -> f#(p(s(0())))
     active#(p(X)) -> active#(X) ->
     active#(f(s(0()))) -> p#(s(0()))
     active#(cons(X1,X2)) -> cons#(active(X1),X2) ->
     cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     active#(cons(X1,X2)) -> cons#(active(X1),X2) ->
     cons#(mark(X1),X2) -> cons#(X1,X2)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(p(X)) -> p#(active(X))
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(p(X)) -> active#(X)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(s(X)) -> s#(active(X))
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(s(X)) -> active#(X)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(cons(X1,X2)) -> active#(X1)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(f(X)) -> f#(active(X))
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(f(X)) -> active#(X)
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(f(s(0()))) -> f#(p(s(0())))
     active#(cons(X1,X2)) -> active#(X1) ->
     active#(f(s(0()))) -> p#(s(0()))
     active#(s(X)) -> s#(active(X)) -> s#(ok(X)) -> s#(X)
     active#(s(X)) -> s#(active(X)) -> s#(mark(X)) -> s#(X)
     active#(s(X)) -> active#(X) -> active#(p(X)) -> p#(active(X))
     active#(s(X)) -> active#(X) -> active#(p(X)) -> active#(X)
     active#(s(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
     active#(s(X)) -> active#(X) -> active#(s(X)) -> active#(X)
     active#(s(X)) -> active#(X) ->
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     active#(s(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
     active#(s(X)) -> active#(X) -> active#(f(X)) -> f#(active(X))
     active#(s(X)) -> active#(X) -> active#(f(X)) -> active#(X)
     active#(s(X)) -> active#(X) -> active#(f(s(0()))) -> f#(p(s(0())))
     active#(s(X)) -> active#(X) ->
     active#(f(s(0()))) -> p#(s(0()))
     active#(f(s(0()))) -> f#(p(s(0()))) -> f#(ok(X)) -> f#(X)
     active#(f(s(0()))) -> f#(p(s(0()))) -> f#(mark(X)) -> f#(X)
     active#(f(s(0()))) -> p#(s(0())) -> p#(ok(X)) -> p#(X)
     active#(f(s(0()))) -> p#(s(0())) -> p#(mark(X)) -> p#(X)
     active#(f(X)) -> f#(active(X)) -> f#(ok(X)) -> f#(X)
     active#(f(X)) -> f#(active(X)) -> f#(mark(X)) -> f#(X)
     active#(f(X)) -> active#(X) -> active#(p(X)) -> p#(active(X))
     active#(f(X)) -> active#(X) -> active#(p(X)) -> active#(X)
     active#(f(X)) -> active#(X) -> active#(s(X)) -> s#(active(X))
     active#(f(X)) -> active#(X) -> active#(s(X)) -> active#(X)
     active#(f(X)) -> active#(X) ->
     active#(cons(X1,X2)) -> cons#(active(X1),X2)
     active#(f(X)) -> active#(X) -> active#(cons(X1,X2)) -> active#(X1)
     active#(f(X)) -> active#(X) -> active#(f(X)) -> f#(active(X))
     active#(f(X)) -> active#(X) -> active#(f(X)) -> active#(X)
     active#(f(X)) -> active#(X) -> active#(f(s(0()))) -> f#(p(s(0())))
     active#(f(X)) -> active#(X) -> active#(f(s(0()))) -> p#(s(0()))
    SCC Processor:
     #sccs: 7
     #rules: 19
     #arcs: 148/961
     DPs:
      top#(ok(X)) -> top#(active(X))
      top#(mark(X)) -> top#(proper(X))
     TRS:
      active(f(s(0()))) -> mark(f(p(s(0()))))
      active(p(s(0()))) -> mark(0())
      active(f(X)) -> f(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(p(X)) -> p(active(X))
      f(mark(X)) -> mark(f(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      s(mark(X)) -> mark(s(X))
      p(mark(X)) -> mark(p(X))
      proper(f(X)) -> f(proper(X))
      proper(0()) -> ok(0())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(p(X)) -> p(proper(X))
      f(ok(X)) -> ok(f(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      s(ok(X)) -> ok(s(X))
      p(ok(X)) -> ok(p(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Matrix Interpretation Processor: dim=3
      
      interpretation:
       [top#](x0) = [0 1 0]x0,
       
                   [0 1 0]     [0]
       [top](x0) = [1 1 0]x0 + [0]
                   [1 0 0]     [1],
       
                  [1 0 0]  
       [ok](x0) = [0 1 1]x0
                  [0 0 0]  ,
       
                      [1 0 0]  
       [proper](x0) = [0 1 1]x0
                      [0 0 0]  ,
       
                 [0 1 1]     [1]
       [p](x0) = [1 0 0]x0 + [1]
                 [0 0 0]     [0],
       
                    [1 0 0]     [1]
       [mark](x0) = [0 1 1]x0 + [1]
                    [0 0 0]     [0],
       
                          
       [cons](x0, x1) = x0
                          ,
       
                 [0 1 1]  
       [s](x0) = [1 0 0]x0
                 [0 0 0]  ,
       
                      [1 0 0]  
       [active](x0) = [0 1 0]x0
                      [0 0 0]  ,
       
                 [1 0 0]  
       [f](x0) = [1 0 0]x0
                 [0 0 0]  ,
       
             [0]
       [0] = [1]
             [1]
      orientation:
       top#(ok(X)) = [0 1 1]X >= [0 1 0]X = top#(active(X))
       
       top#(mark(X)) = [0 1 1]X + [1] >= [0 1 1]X = top#(proper(X))
       
                           [2]    [2]                     
       active(f(s(0()))) = [2] >= [2] = mark(f(p(s(0()))))
                           [0]    [0]                     
       
                           [1]    [1]            
       active(p(s(0()))) = [3] >= [3] = mark(0())
                           [0]    [0]            
       
                      [1 0 0]     [1 0 0]                
       active(f(X)) = [1 0 0]X >= [1 0 0]X = f(active(X))
                      [0 0 0]     [0 0 0]                
       
                             [1 0 0]      [1 0 0]                        
       active(cons(X1,X2)) = [0 1 0]X1 >= [0 1 0]X1 = cons(active(X1),X2)
                             [0 0 0]      [0 0 0]                        
       
                      [0 1 1]     [0 1 0]                
       active(s(X)) = [1 0 0]X >= [1 0 0]X = s(active(X))
                      [0 0 0]     [0 0 0]                
       
                      [0 1 1]    [1]    [0 1 0]    [1]               
       active(p(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = p(active(X))
                      [0 0 0]    [0]    [0 0 0]    [0]               
       
                    [1 0 0]    [1]    [1 0 0]    [1]             
       f(mark(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = mark(f(X))
                    [0 0 0]    [0]    [0 0 0]    [0]             
       
                           [1 0 0]     [1]    [1 0 0]     [1]                    
       cons(mark(X1),X2) = [0 1 1]X1 + [1] >= [0 1 1]X1 + [1] = mark(cons(X1,X2))
                           [0 0 0]     [0]    [0 0 0]     [0]                    
       
                    [0 1 1]    [1]    [0 1 1]    [1]             
       s(mark(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = mark(s(X))
                    [0 0 0]    [0]    [0 0 0]    [0]             
       
                    [0 1 1]    [2]    [0 1 1]    [2]             
       p(mark(X)) = [1 0 0]X + [2] >= [1 0 0]X + [2] = mark(p(X))
                    [0 0 0]    [0]    [0 0 0]    [0]             
       
                      [1 0 0]     [1 0 0]                
       proper(f(X)) = [1 0 0]X >= [1 0 0]X = f(proper(X))
                      [0 0 0]     [0 0 0]                
       
                     [0]    [0]          
       proper(0()) = [2] >= [2] = ok(0())
                     [0]    [0]          
       
                             [1 0 0]      [1 0 0]                                
       proper(cons(X1,X2)) = [0 1 1]X1 >= [0 1 1]X1 = cons(proper(X1),proper(X2))
                             [0 0 0]      [0 0 0]                                
       
                      [0 1 1]     [0 1 1]                
       proper(s(X)) = [1 0 0]X >= [1 0 0]X = s(proper(X))
                      [0 0 0]     [0 0 0]                
       
                      [0 1 1]    [1]    [0 1 1]    [1]               
       proper(p(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = p(proper(X))
                      [0 0 0]    [0]    [0 0 0]    [0]               
       
                  [1 0 0]     [1 0 0]            
       f(ok(X)) = [1 0 0]X >= [1 0 0]X = ok(f(X))
                  [0 0 0]     [0 0 0]            
       
                             [1 0 0]      [1 0 0]                    
       cons(ok(X1),ok(X2)) = [0 1 1]X1 >= [0 1 1]X1 = ok(cons(X1,X2))
                             [0 0 0]      [0 0 0]                    
       
                  [0 1 1]     [0 1 1]            
       s(ok(X)) = [1 0 0]X >= [1 0 0]X = ok(s(X))
                  [0 0 0]     [0 0 0]            
       
                  [0 1 1]    [1]    [0 1 1]    [1]           
       p(ok(X)) = [1 0 0]X + [1] >= [1 0 0]X + [1] = ok(p(X))
                  [0 0 0]    [0]    [0 0 0]    [0]           
       
                      [0 1 1]    [1]    [0 1 1]    [0]                 
       top(mark(X)) = [1 1 1]X + [2] >= [1 1 1]X + [0] = top(proper(X))
                      [1 0 0]    [2]    [1 0 0]    [1]                 
       
                    [0 1 1]    [0]    [0 1 0]    [0]                 
       top(ok(X)) = [1 1 1]X + [0] >= [1 1 0]X + [0] = top(active(X))
                    [1 0 0]    [1]    [1 0 0]    [1]                 
      problem:
       DPs:
        top#(ok(X)) -> top#(active(X))
       TRS:
        active(f(s(0()))) -> mark(f(p(s(0()))))
        active(p(s(0()))) -> mark(0())
        active(f(X)) -> f(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        active(p(X)) -> p(active(X))
        f(mark(X)) -> mark(f(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        s(mark(X)) -> mark(s(X))
        p(mark(X)) -> mark(p(X))
        proper(f(X)) -> f(proper(X))
        proper(0()) -> ok(0())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(p(X)) -> p(proper(X))
        f(ok(X)) -> ok(f(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        s(ok(X)) -> ok(s(X))
        p(ok(X)) -> ok(p(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      KBO Processor:
       argument filtering:
        pi(0) = []
        pi(f) = 0
        pi(active) = []
        pi(s) = 0
        pi(cons) = 0
        pi(mark) = 0
        pi(p) = 0
        pi(proper) = []
        pi(ok) = []
        pi(top) = []
        pi(top#) = 0
       weight function:
        w0 = 1
        w(top#) = w(top) = w(ok) = w(proper) = w(p) = w(mark) = w(s) = w(
        active) = w(f) = w(0) = 1
        w(cons) = 0
       precedence:
        top# ~ top > proper > ok > active > p ~ mark ~ cons ~ s ~ f ~ 0
       problem:
        DPs:
         
        TRS:
         active(f(s(0()))) -> mark(f(p(s(0()))))
         active(p(s(0()))) -> mark(0())
         active(f(X)) -> f(active(X))
         active(cons(X1,X2)) -> cons(active(X1),X2)
         active(s(X)) -> s(active(X))
         active(p(X)) -> p(active(X))
         f(mark(X)) -> mark(f(X))
         cons(mark(X1),X2) -> mark(cons(X1,X2))
         s(mark(X)) -> mark(s(X))
         p(mark(X)) -> mark(p(X))
         proper(f(X)) -> f(proper(X))
         proper(0()) -> ok(0())
         proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
         proper(s(X)) -> s(proper(X))
         proper(p(X)) -> p(proper(X))
         f(ok(X)) -> ok(f(X))
         cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
         s(ok(X)) -> ok(s(X))
         p(ok(X)) -> ok(p(X))
         top(mark(X)) -> top(proper(X))
         top(ok(X)) -> top(active(X))
       Qed
     
     DPs:
      active#(f(X)) -> active#(X)
      active#(cons(X1,X2)) -> active#(X1)
      active#(s(X)) -> active#(X)
      active#(p(X)) -> active#(X)
     TRS:
      active(f(s(0()))) -> mark(f(p(s(0()))))
      active(p(s(0()))) -> mark(0())
      active(f(X)) -> f(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(p(X)) -> p(active(X))
      f(mark(X)) -> mark(f(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      s(mark(X)) -> mark(s(X))
      p(mark(X)) -> mark(p(X))
      proper(f(X)) -> f(proper(X))
      proper(0()) -> ok(0())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(p(X)) -> p(proper(X))
      f(ok(X)) -> ok(f(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      s(ok(X)) -> ok(s(X))
      p(ok(X)) -> ok(p(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(active#) = 0
      problem:
       DPs:
        
       TRS:
        active(f(s(0()))) -> mark(f(p(s(0()))))
        active(p(s(0()))) -> mark(0())
        active(f(X)) -> f(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        active(p(X)) -> p(active(X))
        f(mark(X)) -> mark(f(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        s(mark(X)) -> mark(s(X))
        p(mark(X)) -> mark(p(X))
        proper(f(X)) -> f(proper(X))
        proper(0()) -> ok(0())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(p(X)) -> p(proper(X))
        f(ok(X)) -> ok(f(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        s(ok(X)) -> ok(s(X))
        p(ok(X)) -> ok(p(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
     
     DPs:
      proper#(f(X)) -> proper#(X)
      proper#(cons(X1,X2)) -> proper#(X2)
      proper#(cons(X1,X2)) -> proper#(X1)
      proper#(s(X)) -> proper#(X)
      proper#(p(X)) -> proper#(X)
     TRS:
      active(f(s(0()))) -> mark(f(p(s(0()))))
      active(p(s(0()))) -> mark(0())
      active(f(X)) -> f(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(p(X)) -> p(active(X))
      f(mark(X)) -> mark(f(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      s(mark(X)) -> mark(s(X))
      p(mark(X)) -> mark(p(X))
      proper(f(X)) -> f(proper(X))
      proper(0()) -> ok(0())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(p(X)) -> p(proper(X))
      f(ok(X)) -> ok(f(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      s(ok(X)) -> ok(s(X))
      p(ok(X)) -> ok(p(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(proper#) = 0
      problem:
       DPs:
        
       TRS:
        active(f(s(0()))) -> mark(f(p(s(0()))))
        active(p(s(0()))) -> mark(0())
        active(f(X)) -> f(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        active(p(X)) -> p(active(X))
        f(mark(X)) -> mark(f(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        s(mark(X)) -> mark(s(X))
        p(mark(X)) -> mark(p(X))
        proper(f(X)) -> f(proper(X))
        proper(0()) -> ok(0())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(p(X)) -> p(proper(X))
        f(ok(X)) -> ok(f(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        s(ok(X)) -> ok(s(X))
        p(ok(X)) -> ok(p(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
     
     DPs:
      p#(mark(X)) -> p#(X)
      p#(ok(X)) -> p#(X)
     TRS:
      active(f(s(0()))) -> mark(f(p(s(0()))))
      active(p(s(0()))) -> mark(0())
      active(f(X)) -> f(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(p(X)) -> p(active(X))
      f(mark(X)) -> mark(f(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      s(mark(X)) -> mark(s(X))
      p(mark(X)) -> mark(p(X))
      proper(f(X)) -> f(proper(X))
      proper(0()) -> ok(0())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(p(X)) -> p(proper(X))
      f(ok(X)) -> ok(f(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      s(ok(X)) -> ok(s(X))
      p(ok(X)) -> ok(p(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(p#) = 0
      problem:
       DPs:
        
       TRS:
        active(f(s(0()))) -> mark(f(p(s(0()))))
        active(p(s(0()))) -> mark(0())
        active(f(X)) -> f(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        active(p(X)) -> p(active(X))
        f(mark(X)) -> mark(f(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        s(mark(X)) -> mark(s(X))
        p(mark(X)) -> mark(p(X))
        proper(f(X)) -> f(proper(X))
        proper(0()) -> ok(0())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(p(X)) -> p(proper(X))
        f(ok(X)) -> ok(f(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        s(ok(X)) -> ok(s(X))
        p(ok(X)) -> ok(p(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
     
     DPs:
      s#(mark(X)) -> s#(X)
      s#(ok(X)) -> s#(X)
     TRS:
      active(f(s(0()))) -> mark(f(p(s(0()))))
      active(p(s(0()))) -> mark(0())
      active(f(X)) -> f(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(p(X)) -> p(active(X))
      f(mark(X)) -> mark(f(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      s(mark(X)) -> mark(s(X))
      p(mark(X)) -> mark(p(X))
      proper(f(X)) -> f(proper(X))
      proper(0()) -> ok(0())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(p(X)) -> p(proper(X))
      f(ok(X)) -> ok(f(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      s(ok(X)) -> ok(s(X))
      p(ok(X)) -> ok(p(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(s#) = 0
      problem:
       DPs:
        
       TRS:
        active(f(s(0()))) -> mark(f(p(s(0()))))
        active(p(s(0()))) -> mark(0())
        active(f(X)) -> f(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        active(p(X)) -> p(active(X))
        f(mark(X)) -> mark(f(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        s(mark(X)) -> mark(s(X))
        p(mark(X)) -> mark(p(X))
        proper(f(X)) -> f(proper(X))
        proper(0()) -> ok(0())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(p(X)) -> p(proper(X))
        f(ok(X)) -> ok(f(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        s(ok(X)) -> ok(s(X))
        p(ok(X)) -> ok(p(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed
     
     DPs:
      cons#(mark(X1),X2) -> cons#(X1,X2)
      cons#(ok(X1),ok(X2)) -> cons#(X1,X2)
     TRS:
      active(f(s(0()))) -> mark(f(p(s(0()))))
      active(p(s(0()))) -> mark(0())
      active(f(X)) -> f(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(p(X)) -> p(active(X))
      f(mark(X)) -> mark(f(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      s(mark(X)) -> mark(s(X))
      p(mark(X)) -> mark(p(X))
      proper(f(X)) -> f(proper(X))
      proper(0()) -> ok(0())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(p(X)) -> p(proper(X))
      f(ok(X)) -> ok(f(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      s(ok(X)) -> ok(s(X))
      p(ok(X)) -> ok(p(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(cons#) = 1
      problem:
       DPs:
        cons#(mark(X1),X2) -> cons#(X1,X2)
       TRS:
        active(f(s(0()))) -> mark(f(p(s(0()))))
        active(p(s(0()))) -> mark(0())
        active(f(X)) -> f(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        active(p(X)) -> p(active(X))
        f(mark(X)) -> mark(f(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        s(mark(X)) -> mark(s(X))
        p(mark(X)) -> mark(p(X))
        proper(f(X)) -> f(proper(X))
        proper(0()) -> ok(0())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(p(X)) -> p(proper(X))
        f(ok(X)) -> ok(f(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        s(ok(X)) -> ok(s(X))
        p(ok(X)) -> ok(p(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Subterm Criterion Processor:
       simple projection:
        pi(cons#) = 0
       problem:
        DPs:
         
        TRS:
         active(f(s(0()))) -> mark(f(p(s(0()))))
         active(p(s(0()))) -> mark(0())
         active(f(X)) -> f(active(X))
         active(cons(X1,X2)) -> cons(active(X1),X2)
         active(s(X)) -> s(active(X))
         active(p(X)) -> p(active(X))
         f(mark(X)) -> mark(f(X))
         cons(mark(X1),X2) -> mark(cons(X1,X2))
         s(mark(X)) -> mark(s(X))
         p(mark(X)) -> mark(p(X))
         proper(f(X)) -> f(proper(X))
         proper(0()) -> ok(0())
         proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
         proper(s(X)) -> s(proper(X))
         proper(p(X)) -> p(proper(X))
         f(ok(X)) -> ok(f(X))
         cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
         s(ok(X)) -> ok(s(X))
         p(ok(X)) -> ok(p(X))
         top(mark(X)) -> top(proper(X))
         top(ok(X)) -> top(active(X))
       Qed
     
     DPs:
      f#(mark(X)) -> f#(X)
      f#(ok(X)) -> f#(X)
     TRS:
      active(f(s(0()))) -> mark(f(p(s(0()))))
      active(p(s(0()))) -> mark(0())
      active(f(X)) -> f(active(X))
      active(cons(X1,X2)) -> cons(active(X1),X2)
      active(s(X)) -> s(active(X))
      active(p(X)) -> p(active(X))
      f(mark(X)) -> mark(f(X))
      cons(mark(X1),X2) -> mark(cons(X1,X2))
      s(mark(X)) -> mark(s(X))
      p(mark(X)) -> mark(p(X))
      proper(f(X)) -> f(proper(X))
      proper(0()) -> ok(0())
      proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
      proper(s(X)) -> s(proper(X))
      proper(p(X)) -> p(proper(X))
      f(ok(X)) -> ok(f(X))
      cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
      s(ok(X)) -> ok(s(X))
      p(ok(X)) -> ok(p(X))
      top(mark(X)) -> top(proper(X))
      top(ok(X)) -> top(active(X))
     Subterm Criterion Processor:
      simple projection:
       pi(f#) = 0
      problem:
       DPs:
        
       TRS:
        active(f(s(0()))) -> mark(f(p(s(0()))))
        active(p(s(0()))) -> mark(0())
        active(f(X)) -> f(active(X))
        active(cons(X1,X2)) -> cons(active(X1),X2)
        active(s(X)) -> s(active(X))
        active(p(X)) -> p(active(X))
        f(mark(X)) -> mark(f(X))
        cons(mark(X1),X2) -> mark(cons(X1,X2))
        s(mark(X)) -> mark(s(X))
        p(mark(X)) -> mark(p(X))
        proper(f(X)) -> f(proper(X))
        proper(0()) -> ok(0())
        proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
        proper(s(X)) -> s(proper(X))
        proper(p(X)) -> p(proper(X))
        f(ok(X)) -> ok(f(X))
        cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
        s(ok(X)) -> ok(s(X))
        p(ok(X)) -> ok(p(X))
        top(mark(X)) -> top(proper(X))
        top(ok(X)) -> top(active(X))
      Qed