MAYBE
Time: 0.010804
TRS:
 {    minus(x, 0()) -> x,
    minus(s x, s y) -> minus(x, y),
     quot(0(), s y) -> 0(),
     quot(s x, s y) -> s quot(minus(x, y), s y),
       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),
     quot#(s x, s y) -> minus#(x, y),
     quot#(s x, s y) -> quot#(minus(x, y), s y),
       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),
      quot(0(), s y) -> 0(),
      quot(s x, s y) -> s quot(minus(x, y), s y),
        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}
  EDG:
   {(plus#(s x, x) -> gt#(x, x), gt#(s x, s y) -> gt#(x, y))
    (quot#(s x, s y) -> quot#(minus(x, y), s y), quot#(s x, s y) -> quot#(minus(x, y), s y))
    (quot#(s x, s y) -> quot#(minus(x, y), s y), quot#(s x, s y) -> minus#(x, y))
    (plus#(s x, s y) -> not# gt(x, y), not# x -> if#(x, false(), true()))
    (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#(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) -> 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#(s x, s y) -> id# 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) -> not# gt(x, 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) -> 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) -> 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, 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) -> 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) -> plus#(if(gt(x, x), id x, id x), s x))
    (quot#(s x, s y) -> minus#(x, y), minus#(s x, s y) -> minus#(x, y))
    (plus#(s x, s y) -> gt#(x, y), gt#(s x, s y) -> gt#(x, y))
    (gt#(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, 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))
    (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) -> gt#(s y, y), gt#(s x, s y) -> gt#(x, y))}
   STATUS:
    arrows: 0.858726
    SCCS (4):
     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:
      {quot#(s x, s y) -> quot#(minus(x, y), s y)}
     Scc:
      {minus#(s x, s y) -> minus#(x, y)}
     Scc:
      {gt#(s x, s y) -> gt#(x, y)}
     
     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),
          quot(0(), s y) -> 0(),
          quot(s x, s y) -> s quot(minus(x, y), s y),
            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:
       {quot#(s x, s y) -> quot#(minus(x, y), s y)}
      Weak:
      {    minus(x, 0()) -> x,
         minus(s x, s y) -> minus(x, y),
          quot(0(), s y) -> 0(),
          quot(s x, s y) -> s quot(minus(x, y), s y),
            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:
       {minus#(s x, s y) -> minus#(x, y)}
      Weak:
      {    minus(x, 0()) -> x,
         minus(s x, s y) -> minus(x, y),
          quot(0(), s y) -> 0(),
          quot(s x, s y) -> s quot(minus(x, y), s y),
            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),
          quot(0(), s y) -> 0(),
          quot(s x, s y) -> s quot(minus(x, y), s y),
            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