MAYBE
Time: 0.016389
TRS:
 {           app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                     app(app(plus(), 0()), y) -> y,
            app(app(times(), app(s(), x)), y) -> app(app(plus(), app(app(times(), x), y)), y),
                    app(app(times(), 0()), y) -> 0(),
  app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                    app(app(map(), f), nil()) -> nil(),
                                        inc() -> app(map(), app(plus(), app(s(), 0()))),
                                     double() -> app(map(), app(times(), app(s(), app(s(), 0()))))}
 DP:
  DP:
   {           app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y),
               app#(app(plus(), app(s(), x)), y) -> app#(plus(), x),
               app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)),
              app#(app(times(), app(s(), x)), y) -> app#(app(plus(), app(app(times(), x), y)), y),
              app#(app(times(), app(s(), x)), y) -> app#(app(times(), x), y),
              app#(app(times(), app(s(), x)), y) -> app#(plus(), app(app(times(), x), y)),
              app#(app(times(), app(s(), x)), y) -> app#(times(), x),
    app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
    app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs),
    app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)),
    app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)),
                                          inc#() -> app#(plus(), app(s(), 0())),
                                          inc#() -> app#(s(), 0()),
                                          inc#() -> app#(map(), app(plus(), app(s(), 0()))),
                                       double#() -> app#(s(), app(s(), 0())),
                                       double#() -> app#(s(), 0()),
                                       double#() -> app#(times(), app(s(), app(s(), 0()))),
                                       double#() -> app#(map(), app(times(), app(s(), app(s(), 0()))))}
  TRS:
  {           app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                      app(app(plus(), 0()), y) -> y,
             app(app(times(), app(s(), x)), y) -> app(app(plus(), app(app(times(), x), y)), y),
                     app(app(times(), 0()), y) -> 0(),
   app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                     app(app(map(), f), nil()) -> nil(),
                                         inc() -> app(map(), app(plus(), app(s(), 0()))),
                                      double() -> app(map(), app(times(), app(s(), app(s(), 0()))))}
  UR:
   {           app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                       app(app(plus(), 0()), y) -> y,
              app(app(times(), app(s(), x)), y) -> app(app(plus(), app(app(times(), x), y)), y),
                      app(app(times(), 0()), y) -> 0(),
    app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                      app(app(map(), f), nil()) -> nil(),
                                        a(z, w) -> z,
                                        a(z, w) -> w}
   EDG:
    {(app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(times(), app(s(), x)), y) -> app#(app(times(), x), y), app#(app(times(), app(s(), x)), y) -> app#(times(), x))
     (app#(app(times(), app(s(), x)), y) -> app#(app(times(), x), y), app#(app(times(), app(s(), x)), y) -> app#(plus(), app(app(times(), x), y)))
     (app#(app(times(), app(s(), x)), y) -> app#(app(times(), x), y), app#(app(times(), app(s(), x)), y) -> app#(app(times(), x), y))
     (app#(app(times(), app(s(), x)), y) -> app#(app(times(), x), y), app#(app(times(), app(s(), x)), y) -> app#(app(plus(), app(app(times(), x), y)), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), app(s(), x)), y) -> app#(app(plus(), app(app(times(), x), y)), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), app(s(), x)), y) -> app#(app(times(), x), y))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), app(s(), x)), y) -> app#(plus(), app(app(times(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(times(), app(s(), x)), y) -> app#(times(), x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))
     (app#(app(times(), app(s(), x)), y) -> app#(app(plus(), app(app(times(), x), y)), y), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(times(), app(s(), x)), y) -> app#(app(plus(), app(app(times(), x), y)), y), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(times(), app(s(), x)), y) -> app#(app(plus(), app(app(times(), x), y)), y), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(cons(), app(f, x)), app(app(map(), f), xs)))
     (app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs), app#(app(map(), f), app(app(cons(), x), xs)) -> app#(cons(), app(f, x)))}
    STATUS:
     arrows: 0.922840
     SCCS (3):
      Scc:
       {app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
        app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)}
      Scc:
       {app#(app(times(), app(s(), x)), y) -> app#(app(times(), x), y)}
      Scc:
       {app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)}
      
      
      
      
      
      
      
      
      SCC (2):
       Strict:
        {app#(app(map(), f), app(app(cons(), x), xs)) -> app#(f, x),
         app#(app(map(), f), app(app(cons(), x), xs)) -> app#(app(map(), f), xs)}
       Weak:
       {           app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                           app(app(plus(), 0()), y) -> y,
                  app(app(times(), app(s(), x)), y) -> app(app(plus(), app(app(times(), x), y)), y),
                          app(app(times(), 0()), y) -> 0(),
        app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                          app(app(map(), f), nil()) -> nil(),
                                              inc() -> app(map(), app(plus(), app(s(), 0()))),
                                           double() -> app(map(), app(times(), app(s(), app(s(), 0()))))}
       Open
      
      
      SCC (1):
       Strict:
        {app#(app(times(), app(s(), x)), y) -> app#(app(times(), x), y)}
       Weak:
       {           app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                           app(app(plus(), 0()), y) -> y,
                  app(app(times(), app(s(), x)), y) -> app(app(plus(), app(app(times(), x), y)), y),
                          app(app(times(), 0()), y) -> 0(),
        app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                          app(app(map(), f), nil()) -> nil(),
                                              inc() -> app(map(), app(plus(), app(s(), 0()))),
                                           double() -> app(map(), app(times(), app(s(), app(s(), 0()))))}
       Open
      
      
      
      SCC (1):
       Strict:
        {app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)}
       Weak:
       {           app(app(plus(), app(s(), x)), y) -> app(s(), app(app(plus(), x), y)),
                           app(app(plus(), 0()), y) -> y,
                  app(app(times(), app(s(), x)), y) -> app(app(plus(), app(app(times(), x), y)), y),
                          app(app(times(), 0()), y) -> 0(),
        app(app(map(), f), app(app(cons(), x), xs)) -> app(app(cons(), app(f, x)), app(app(map(), f), xs)),
                          app(app(map(), f), nil()) -> nil(),
                                              inc() -> app(map(), app(plus(), app(s(), 0()))),
                                           double() -> app(map(), app(times(), app(s(), app(s(), 0()))))}
       Open