MAYBE
Time: 17.968967
TRS:
 {   app(app(app(comp(), f), g), x) -> app(f, app(g, x)),
   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(twice(), f) -> app(app(comp(), f), f)}
 DP:
  DP:
   {   app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)),
       app#(app(app(comp(), f), g), x) -> app#(g, x),
     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#(twice(), f) -> app#(app(comp(), f), f),
                      app#(twice(), f) -> app#(comp(), f)}
  TRS:
  {   app(app(app(comp(), f), g), x) -> app(f, app(g, x)),
    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(twice(), f) -> app(app(comp(), f), f)}
  UR:
   {   app(app(app(comp(), f), g), x) -> app(f, app(g, x)),
     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(twice(), f) -> app(app(comp(), f), f),
                              a(z, w) -> z,
                              a(z, w) -> w}
   EDG:
    {(app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(twice(), f) -> app#(comp(), f))
     (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(twice(), f) -> app#(app(comp(), f), f))
     (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(times(), app(s(), x)), y) -> app#(times(), x))
     (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(times(), app(s(), x)), y) -> app#(plus(), app(app(times(), x), y)))
     (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(times(), app(s(), x)), y) -> app#(app(times(), x), y))
     (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(times(), app(s(), x)), y) -> app#(app(plus(), app(app(times(), x), y)), y))
     (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(app(comp(), f), g), x) -> app#(g, x))
     (app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)), app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)))
     (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(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(app(comp(), f), g), x) -> app#(g, x), app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)))
     (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(app(comp(), f), g), x) -> app#(g, x))
     (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y))
     (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(plus(), app(s(), x)), y) -> app#(plus(), x))
     (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(plus(), app(s(), x)), y) -> app#(s(), app(app(plus(), x), y)))
     (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(times(), app(s(), x)), y) -> app#(app(plus(), app(app(times(), x), y)), y))
     (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(times(), app(s(), x)), y) -> app#(app(times(), x), y))
     (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(times(), app(s(), x)), y) -> app#(plus(), app(app(times(), x), y)))
     (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(app(times(), app(s(), x)), y) -> app#(times(), x))
     (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(twice(), f) -> app#(app(comp(), f), f))
     (app#(app(app(comp(), f), g), x) -> app#(g, x), app#(twice(), f) -> app#(comp(), f))}
    STATUS:
     arrows: 0.735537
     SCCS (3):
      Scc:
       {app#(app(app(comp(), f), g), x) -> app#(f, app(g, x)),
        app#(app(app(comp(), f), g), x) -> app#(g, x)}
      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(app(comp(), f), g), x) -> app#(f, app(g, x)),
         app#(app(app(comp(), f), g), x) -> app#(g, x)}
       Weak:
       {   app(app(app(comp(), f), g), x) -> app(f, app(g, x)),
         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(twice(), f) -> app(app(comp(), f), f)}
       Open
      
      
      SCC (1):
       Strict:
        {app#(app(times(), app(s(), x)), y) -> app#(app(times(), x), y)}
       Weak:
       {   app(app(app(comp(), f), g), x) -> app(f, app(g, x)),
         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(twice(), f) -> app(app(comp(), f), f)}
       Open
      
      
      SCC (1):
       Strict:
        {app#(app(plus(), app(s(), x)), y) -> app#(app(plus(), x), y)}
       Weak:
       {   app(app(app(comp(), f), g), x) -> app(f, app(g, x)),
         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(twice(), f) -> app(app(comp(), f), f)}
       Open