MAYBE
Time: 0.003395
TRS:
 {    minus(x, 0()) -> x,
    minus(s x, s y) -> minus(x, y),
         double 0() -> 0(),
         double s x -> s s double x,
       plus(s x, x) -> plus(if(gt(x, x), id x, id x), s x),
     plus(s x, s y) -> s s plus(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)),
    plus(id x, s y) -> s plus(x, if(gt(s y, y), y, s y)),
    plus(zero(), y) -> y,
   if(true(), x, y) -> x,
  if(false(), x, y) -> y,
       gt(s x, s y) -> gt(x, y),
    gt(s x, zero()) -> true(),
      gt(zero(), y) -> false(),
              not x -> if(x, false(), true()),
               id x -> x}
 DP:
  DP:
   {minus#(s x, s y) -> minus#(x, y),
         double# s x -> double# x,
       plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x),
       plus#(s x, x) -> if#(gt(x, x), id x, id x),
       plus#(s x, x) -> gt#(x, x),
       plus#(s x, x) -> id# x,
     plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)),
     plus#(s x, s y) -> if#(gt(x, y), x, y),
     plus#(s x, s y) -> if#(not gt(x, y), id x, id y),
     plus#(s x, s y) -> gt#(x, y),
     plus#(s x, s y) -> not# gt(x, y),
     plus#(s x, s y) -> id# x,
     plus#(s x, s y) -> id# y,
    plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)),
    plus#(id x, s y) -> if#(gt(s y, y), y, s y),
    plus#(id x, s y) -> gt#(s y, y),
       gt#(s x, s y) -> gt#(x, y),
              not# x -> if#(x, false(), true())}
  TRS:
  {    minus(x, 0()) -> x,
     minus(s x, s y) -> minus(x, y),
          double 0() -> 0(),
          double s x -> s s double x,
        plus(s x, x) -> plus(if(gt(x, x), id x, id x), s x),
      plus(s x, s y) -> s s plus(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)),
     plus(id x, s y) -> s plus(x, if(gt(s y, y), y, s y)),
     plus(zero(), y) -> y,
    if(true(), x, y) -> x,
   if(false(), x, y) -> y,
        gt(s x, s y) -> gt(x, y),
     gt(s x, zero()) -> true(),
       gt(zero(), y) -> false(),
               not x -> if(x, false(), true()),
                id x -> x}
  UR:
   { if(true(), x, y) -> x,
    if(false(), x, y) -> y,
         gt(s x, s y) -> gt(x, y),
      gt(s x, zero()) -> true(),
        gt(zero(), y) -> false(),
                not x -> if(x, false(), true()),
                 id x -> x,
              a(z, w) -> z,
              a(z, w) -> w}
   EDG:
    {(plus#(id x, s y) -> gt#(s y, y), gt#(s x, s y) -> gt#(x, y))
     (double# s x -> double# x, double# s x -> double# x)
     (gt#(s x, s y) -> gt#(x, y), gt#(s x, s y) -> gt#(x, y))
     (plus#(s x, s y) -> not# gt(x, y), not# x -> if#(x, false(), true()))
     (plus#(s x, x) -> gt#(x, x), gt#(s x, s y) -> gt#(x, y))
     (plus#(s x, s y) -> gt#(x, y), gt#(s x, s y) -> gt#(x, y))
     (minus#(s x, s y) -> minus#(x, y), minus#(s x, s y) -> minus#(x, y))
     (plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x), plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x))
     (plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x), plus#(s x, x) -> if#(gt(x, x), id x, id x))
     (plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x), plus#(s x, x) -> gt#(x, x))
     (plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x), plus#(s x, x) -> id# x)
     (plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x), plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)))
     (plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x), plus#(s x, s y) -> if#(gt(x, y), x, y))
     (plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x), plus#(s x, s y) -> if#(not gt(x, y), id x, id y))
     (plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x), plus#(s x, s y) -> gt#(x, y))
     (plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x), plus#(s x, s y) -> not# gt(x, y))
     (plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x), plus#(s x, s y) -> id# x)
     (plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x), plus#(s x, s y) -> id# y)
     (plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x), plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)))
     (plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x), plus#(id x, s y) -> if#(gt(s y, y), y, s y))
     (plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x), plus#(id x, s y) -> gt#(s y, y))
     (plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)), plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x))
     (plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)), plus#(s x, x) -> if#(gt(x, x), id x, id x))
     (plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)), plus#(s x, x) -> gt#(x, x))
     (plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)), plus#(s x, x) -> id# x)
     (plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)), plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)))
     (plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)), plus#(s x, s y) -> if#(gt(x, y), x, y))
     (plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)), plus#(s x, s y) -> if#(not gt(x, y), id x, id y))
     (plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)), plus#(s x, s y) -> gt#(x, y))
     (plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)), plus#(s x, s y) -> not# gt(x, y))
     (plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)), plus#(s x, s y) -> id# x)
     (plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)), plus#(s x, s y) -> id# y)
     (plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)), plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)))
     (plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)), plus#(id x, s y) -> if#(gt(s y, y), y, s y))
     (plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)), plus#(id x, s y) -> gt#(s y, y))
     (plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)), plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x))
     (plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)), plus#(s x, x) -> if#(gt(x, x), id x, id x))
     (plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)), plus#(s x, x) -> gt#(x, x))
     (plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)), plus#(s x, x) -> id# x)
     (plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)), plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)))
     (plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)), plus#(s x, s y) -> if#(gt(x, y), x, y))
     (plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)), plus#(s x, s y) -> if#(not gt(x, y), id x, id y))
     (plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)), plus#(s x, s y) -> gt#(x, y))
     (plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)), plus#(s x, s y) -> not# gt(x, y))
     (plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)), plus#(s x, s y) -> id# x)
     (plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)), plus#(s x, s y) -> id# y)
     (plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)), plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y)))
     (plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)), plus#(id x, s y) -> if#(gt(s y, y), y, s y))
     (plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)), plus#(id x, s y) -> gt#(s y, y))}
    STATUS:
     arrows: 0.848765
     SCCS (4):
      Scc:
       {minus#(s x, s y) -> minus#(x, y)}
      Scc:
       {double# s x -> double# x}
      Scc:
       {   plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x),
         plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)),
        plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y))}
      Scc:
       {gt#(s x, s y) -> gt#(x, y)}
      
      SCC (1):
       Strict:
        {minus#(s x, s y) -> minus#(x, y)}
       Weak:
       {    minus(x, 0()) -> x,
          minus(s x, s y) -> minus(x, y),
               double 0() -> 0(),
               double s x -> s s double x,
             plus(s x, x) -> plus(if(gt(x, x), id x, id x), s x),
           plus(s x, s y) -> s s plus(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)),
          plus(id x, s y) -> s plus(x, if(gt(s y, y), y, s y)),
          plus(zero(), y) -> y,
         if(true(), x, y) -> x,
        if(false(), x, y) -> y,
             gt(s x, s y) -> gt(x, y),
          gt(s x, zero()) -> true(),
            gt(zero(), y) -> false(),
                    not x -> if(x, false(), true()),
                     id x -> x}
       Open
      SCC (1):
       Strict:
        {double# s x -> double# x}
       Weak:
       {    minus(x, 0()) -> x,
          minus(s x, s y) -> minus(x, y),
               double 0() -> 0(),
               double s x -> s s double x,
             plus(s x, x) -> plus(if(gt(x, x), id x, id x), s x),
           plus(s x, s y) -> s s plus(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)),
          plus(id x, s y) -> s plus(x, if(gt(s y, y), y, s y)),
          plus(zero(), y) -> y,
         if(true(), x, y) -> x,
        if(false(), x, y) -> y,
             gt(s x, s y) -> gt(x, y),
          gt(s x, zero()) -> true(),
            gt(zero(), y) -> false(),
                    not x -> if(x, false(), true()),
                     id x -> x}
       Open
      SCC (3):
       Strict:
        {   plus#(s x, x) -> plus#(if(gt(x, x), id x, id x), s x),
          plus#(s x, s y) -> plus#(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)),
         plus#(id x, s y) -> plus#(x, if(gt(s y, y), y, s y))}
       Weak:
       {    minus(x, 0()) -> x,
          minus(s x, s y) -> minus(x, y),
               double 0() -> 0(),
               double s x -> s s double x,
             plus(s x, x) -> plus(if(gt(x, x), id x, id x), s x),
           plus(s x, s y) -> s s plus(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)),
          plus(id x, s y) -> s plus(x, if(gt(s y, y), y, s y)),
          plus(zero(), y) -> y,
         if(true(), x, y) -> x,
        if(false(), x, y) -> y,
             gt(s x, s y) -> gt(x, y),
          gt(s x, zero()) -> true(),
            gt(zero(), y) -> false(),
                    not x -> if(x, false(), true()),
                     id x -> x}
       Open
      
      
      
      
      
      
      
      
      
      
      
      SCC (1):
       Strict:
        {gt#(s x, s y) -> gt#(x, y)}
       Weak:
       {    minus(x, 0()) -> x,
          minus(s x, s y) -> minus(x, y),
               double 0() -> 0(),
               double s x -> s s double x,
             plus(s x, x) -> plus(if(gt(x, x), id x, id x), s x),
           plus(s x, s y) -> s s plus(if(gt(x, y), x, y), if(not gt(x, y), id x, id y)),
          plus(id x, s y) -> s plus(x, if(gt(s y, y), y, s y)),
          plus(zero(), y) -> y,
         if(true(), x, y) -> x,
        if(false(), x, y) -> y,
             gt(s x, s y) -> gt(x, y),
          gt(s x, zero()) -> true(),
            gt(zero(), y) -> false(),
                    not x -> if(x, false(), true()),
                     id x -> x}
       Open