MAYBE
TRS:
 {f(true(), x, y) -> f(gt(x, y), trunc(x), s(y)),
   gt(s(u), s(v)) -> gt(u, v),
    gt(s(u), 0()) -> true(),
       gt(0(), v) -> false(),
   trunc(s(s(x))) -> s(s(trunc(x))),
    trunc(s(0())) -> 0(),
       trunc(0()) -> 0()}
 DP:
  Strict:
   {f#(true(), x, y) -> f#(gt(x, y), trunc(x), s(y)),
    f#(true(), x, y) -> gt#(x, y),
    f#(true(), x, y) -> trunc#(x),
     gt#(s(u), s(v)) -> gt#(u, v),
     trunc#(s(s(x))) -> trunc#(x)}
  Weak:
  {f(true(), x, y) -> f(gt(x, y), trunc(x), s(y)),
    gt(s(u), s(v)) -> gt(u, v),
     gt(s(u), 0()) -> true(),
        gt(0(), v) -> false(),
    trunc(s(s(x))) -> s(s(trunc(x))),
     trunc(s(0())) -> 0(),
        trunc(0()) -> 0()}
  EDG:
   {(gt#(s(u), s(v)) -> gt#(u, v), gt#(s(u), s(v)) -> gt#(u, v))
    (f#(true(), x, y) -> f#(gt(x, y), trunc(x), s(y)), f#(true(), x, y) -> trunc#(x))
    (f#(true(), x, y) -> f#(gt(x, y), trunc(x), s(y)), f#(true(), x, y) -> gt#(x, y))
    (f#(true(), x, y) -> f#(gt(x, y), trunc(x), s(y)), f#(true(), x, y) -> f#(gt(x, y), trunc(x), s(y)))
    (f#(true(), x, y) -> gt#(x, y), gt#(s(u), s(v)) -> gt#(u, v))
    (trunc#(s(s(x))) -> trunc#(x), trunc#(s(s(x))) -> trunc#(x))
    (f#(true(), x, y) -> trunc#(x), trunc#(s(s(x))) -> trunc#(x))}
   SCCS:
    Scc:
     {trunc#(s(s(x))) -> trunc#(x)}
    Scc:
     {gt#(s(u), s(v)) -> gt#(u, v)}
    Scc:
     {f#(true(), x, y) -> f#(gt(x, y), trunc(x), s(y))}
    SCC:
     Strict:
      {trunc#(s(s(x))) -> trunc#(x)}
     Weak:
     {f(true(), x, y) -> f(gt(x, y), trunc(x), s(y)),
       gt(s(u), s(v)) -> gt(u, v),
        gt(s(u), 0()) -> true(),
           gt(0(), v) -> false(),
       trunc(s(s(x))) -> s(s(trunc(x))),
        trunc(s(0())) -> 0(),
           trunc(0()) -> 0()}
     SPSC:
      Simple Projection:
       pi(trunc#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {gt#(s(u), s(v)) -> gt#(u, v)}
     Weak:
     {f(true(), x, y) -> f(gt(x, y), trunc(x), s(y)),
       gt(s(u), s(v)) -> gt(u, v),
        gt(s(u), 0()) -> true(),
           gt(0(), v) -> false(),
       trunc(s(s(x))) -> s(s(trunc(x))),
        trunc(s(0())) -> 0(),
           trunc(0()) -> 0()}
     SPSC:
      Simple Projection:
       pi(gt#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {f#(true(), x, y) -> f#(gt(x, y), trunc(x), s(y))}
     Weak:
     {f(true(), x, y) -> f(gt(x, y), trunc(x), s(y)),
       gt(s(u), s(v)) -> gt(u, v),
        gt(s(u), 0()) -> true(),
           gt(0(), v) -> false(),
       trunc(s(s(x))) -> s(s(trunc(x))),
        trunc(s(0())) -> 0(),
           trunc(0()) -> 0()}
     Fail