MAYBE
Time: 23.639729
TRS:
 {  cons(mark X1, X2) -> mark cons(X1, X2),
   cons(ok X1, ok X2) -> ok cons(X1, X2),
             f mark X -> mark f X,
               f ok X -> ok f X,
             s mark X -> mark s X,
               s ok X -> ok s X,
  active cons(X1, X2) -> cons(active X1, X2),
           active f X -> f active X,
         active f 0() -> mark cons(0(), f s 0()),
       active f s 0() -> mark f p s 0(),
           active s X -> s active X,
           active p X -> p active X,
         active p s X -> mark X,
             p mark X -> mark p X,
               p ok X -> ok p X,
  proper cons(X1, X2) -> cons(proper X1, proper X2),
           proper 0() -> ok 0(),
           proper f X -> f proper X,
           proper s X -> s proper X,
           proper p X -> p proper X,
           top mark X -> top proper X,
             top ok X -> top active X}
 DP:
  DP:
   {  cons#(mark X1, X2) -> cons#(X1, X2),
     cons#(ok X1, ok X2) -> cons#(X1, X2),
               f# mark X -> f# X,
                 f# ok X -> f# X,
               s# mark X -> s# X,
                 s# ok X -> s# X,
    active# cons(X1, X2) -> cons#(active X1, X2),
    active# cons(X1, X2) -> active# X1,
             active# f X -> f# active X,
             active# f X -> active# X,
           active# f 0() -> cons#(0(), f s 0()),
           active# f 0() -> f# s 0(),
           active# f 0() -> s# 0(),
         active# f s 0() -> f# p s 0(),
         active# f s 0() -> p# s 0(),
             active# s X -> s# active X,
             active# s X -> active# X,
             active# p X -> active# X,
             active# p X -> p# active X,
               p# mark X -> p# X,
                 p# ok X -> p# X,
    proper# cons(X1, X2) -> cons#(proper X1, proper X2),
    proper# cons(X1, X2) -> proper# X1,
    proper# cons(X1, X2) -> proper# X2,
             proper# f X -> f# proper X,
             proper# f X -> proper# X,
             proper# s X -> s# proper X,
             proper# s X -> proper# X,
             proper# p X -> p# proper X,
             proper# p X -> proper# X,
             top# mark X -> proper# X,
             top# mark X -> top# proper X,
               top# ok X -> active# X,
               top# ok X -> top# active X}
  TRS:
  {  cons(mark X1, X2) -> mark cons(X1, X2),
    cons(ok X1, ok X2) -> ok cons(X1, X2),
              f mark X -> mark f X,
                f ok X -> ok f X,
              s mark X -> mark s X,
                s ok X -> ok s X,
   active cons(X1, X2) -> cons(active X1, X2),
            active f X -> f active X,
          active f 0() -> mark cons(0(), f s 0()),
        active f s 0() -> mark f p s 0(),
            active s X -> s active X,
            active p X -> p active X,
          active p s X -> mark X,
              p mark X -> mark p X,
                p ok X -> ok p X,
   proper cons(X1, X2) -> cons(proper X1, proper X2),
            proper 0() -> ok 0(),
            proper f X -> f proper X,
            proper s X -> s proper X,
            proper p X -> p proper X,
            top mark X -> top proper X,
              top ok X -> top active X}
  UR:
   {  cons(mark X1, X2) -> mark cons(X1, X2),
     cons(ok X1, ok X2) -> ok cons(X1, X2),
               f mark X -> mark f X,
                 f ok X -> ok f X,
               s mark X -> mark s X,
                 s ok X -> ok s X,
    active cons(X1, X2) -> cons(active X1, X2),
             active f X -> f active X,
           active f 0() -> mark cons(0(), f s 0()),
         active f s 0() -> mark f p s 0(),
             active s X -> s active X,
             active p X -> p active X,
           active p s X -> mark X,
               p mark X -> mark p X,
                 p ok X -> ok p X,
    proper cons(X1, X2) -> cons(proper X1, proper X2),
             proper 0() -> ok 0(),
             proper f X -> f proper X,
             proper s X -> s proper X,
             proper p X -> p proper X}
   EDG:
    {(active# f X -> f# active X, f# mark X -> f# X)
     (active# p X -> p# active X, p# mark X -> p# X)
     (top# mark X -> top# proper X, top# ok X -> top# active X)
     (top# mark X -> top# proper X, top# ok X -> active# X)
     (active# s X -> active# X, active# p X -> p# active X)
     (active# s X -> active# X, active# p X -> active# X)
     (top# ok X -> active# X, active# p X -> p# active X)
     (top# ok X -> active# X, active# p X -> active# X)
     (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# p X -> active# X, active# p X -> active# X)
     (active# p 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# p X -> p# active X)
     (top# ok X -> top# active X, top# mark X -> proper# X)
     (top# ok X -> top# active X, top# mark X -> top# proper X)
     (active# s X -> s# active X, s# mark X -> s# X)}
    STATUS:
     arrows: 0.984429
     SCCS (2):
      Scc:
       {top# mark X -> top# proper X,
          top# ok X -> top# active X}
      Scc:
       {active# p X -> active# X}
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      
      SCC (2):
       Strict:
        {top# mark X -> top# proper X,
           top# ok X -> top# active X}
       Weak:
       {  cons(mark X1, X2) -> mark cons(X1, X2),
         cons(ok X1, ok X2) -> ok cons(X1, X2),
                   f mark X -> mark f X,
                     f ok X -> ok f X,
                   s mark X -> mark s X,
                     s ok X -> ok s X,
        active cons(X1, X2) -> cons(active X1, X2),
                 active f X -> f active X,
               active f 0() -> mark cons(0(), f s 0()),
             active f s 0() -> mark f p s 0(),
                 active s X -> s active X,
                 active p X -> p active X,
               active p s X -> mark X,
                   p mark X -> mark p X,
                     p ok X -> ok p X,
        proper cons(X1, X2) -> cons(proper X1, proper X2),
                 proper 0() -> ok 0(),
                 proper f X -> f proper X,
                 proper s X -> s proper X,
                 proper p X -> p proper X,
                 top mark X -> top proper X,
                   top ok X -> top active X}
       Open
      
      
      SCC (1):
       Strict:
        {active# p X -> active# X}
       Weak:
       {  cons(mark X1, X2) -> mark cons(X1, X2),
         cons(ok X1, ok X2) -> ok cons(X1, X2),
                   f mark X -> mark f X,
                     f ok X -> ok f X,
                   s mark X -> mark s X,
                     s ok X -> ok s X,
        active cons(X1, X2) -> cons(active X1, X2),
                 active f X -> f active X,
               active f 0() -> mark cons(0(), f s 0()),
             active f s 0() -> mark f p s 0(),
                 active s X -> s active X,
                 active p X -> p active X,
               active p s X -> mark X,
                   p mark X -> mark p X,
                     p ok X -> ok p X,
        proper cons(X1, X2) -> cons(proper X1, proper X2),
                 proper 0() -> ok 0(),
                 proper f X -> f proper X,
                 proper s X -> s proper X,
                 proper p X -> p proper X,
                 top mark X -> top proper X,
                   top ok X -> top active X}
       Open