MAYBE
TRS:
 { cond2(true(), x, y) -> cond1(neq(x, 0()), y, y),
  cond2(false(), x, y) -> cond1(neq(x, 0()), p(x), y),
            gr(0(), x) -> false(),
         gr(s(x), 0()) -> true(),
        gr(s(x), s(y)) -> gr(x, y),
   cond1(true(), x, y) -> cond2(gr(x, y), x, y),
         neq(0(), 0()) -> false(),
        neq(0(), s(x)) -> true(),
        neq(s(x), 0()) -> true(),
       neq(s(x), s(y)) -> neq(x, y),
                p(0()) -> 0(),
               p(s(x)) -> x}
 DP:
  Strict:
   { cond2#(true(), x, y) -> cond1#(neq(x, 0()), y, y),
     cond2#(true(), x, y) -> neq#(x, 0()),
    cond2#(false(), x, y) -> cond1#(neq(x, 0()), p(x), y),
    cond2#(false(), x, y) -> neq#(x, 0()),
    cond2#(false(), x, y) -> p#(x),
          gr#(s(x), s(y)) -> gr#(x, y),
     cond1#(true(), x, y) -> cond2#(gr(x, y), x, y),
     cond1#(true(), x, y) -> gr#(x, y),
         neq#(s(x), s(y)) -> neq#(x, y)}
  Weak:
  { cond2(true(), x, y) -> cond1(neq(x, 0()), y, y),
   cond2(false(), x, y) -> cond1(neq(x, 0()), p(x), y),
             gr(0(), x) -> false(),
          gr(s(x), 0()) -> true(),
         gr(s(x), s(y)) -> gr(x, y),
    cond1(true(), x, y) -> cond2(gr(x, y), x, y),
          neq(0(), 0()) -> false(),
         neq(0(), s(x)) -> true(),
         neq(s(x), 0()) -> true(),
        neq(s(x), s(y)) -> neq(x, y),
                 p(0()) -> 0(),
                p(s(x)) -> x}
  EDG:
   {(cond2#(true(), x, y) -> cond1#(neq(x, 0()), y, y), cond1#(true(), x, y) -> gr#(x, y))
    (cond2#(true(), x, y) -> cond1#(neq(x, 0()), y, y), cond1#(true(), x, y) -> cond2#(gr(x, y), x, y))
    (cond1#(true(), x, y) -> cond2#(gr(x, y), x, y), cond2#(false(), x, y) -> p#(x))
    (cond1#(true(), x, y) -> cond2#(gr(x, y), x, y), cond2#(false(), x, y) -> neq#(x, 0()))
    (cond1#(true(), x, y) -> cond2#(gr(x, y), x, y), cond2#(false(), x, y) -> cond1#(neq(x, 0()), p(x), y))
    (cond1#(true(), x, y) -> cond2#(gr(x, y), x, y), cond2#(true(), x, y) -> neq#(x, 0()))
    (cond1#(true(), x, y) -> cond2#(gr(x, y), x, y), cond2#(true(), x, y) -> cond1#(neq(x, 0()), y, y))
    (neq#(s(x), s(y)) -> neq#(x, y), neq#(s(x), s(y)) -> neq#(x, y))
    (cond1#(true(), x, y) -> gr#(x, y), gr#(s(x), s(y)) -> gr#(x, y))
    (gr#(s(x), s(y)) -> gr#(x, y), gr#(s(x), s(y)) -> gr#(x, y))
    (cond2#(false(), x, y) -> cond1#(neq(x, 0()), p(x), y), cond1#(true(), x, y) -> cond2#(gr(x, y), x, y))
    (cond2#(false(), x, y) -> cond1#(neq(x, 0()), p(x), y), cond1#(true(), x, y) -> gr#(x, y))}
   SCCS:
    Scc:
     {neq#(s(x), s(y)) -> neq#(x, y)}
    Scc:
     {gr#(s(x), s(y)) -> gr#(x, y)}
    Scc:
     { cond2#(true(), x, y) -> cond1#(neq(x, 0()), y, y),
      cond2#(false(), x, y) -> cond1#(neq(x, 0()), p(x), y),
       cond1#(true(), x, y) -> cond2#(gr(x, y), x, y)}
    SCC:
     Strict:
      {neq#(s(x), s(y)) -> neq#(x, y)}
     Weak:
     { cond2(true(), x, y) -> cond1(neq(x, 0()), y, y),
      cond2(false(), x, y) -> cond1(neq(x, 0()), p(x), y),
                gr(0(), x) -> false(),
             gr(s(x), 0()) -> true(),
            gr(s(x), s(y)) -> gr(x, y),
       cond1(true(), x, y) -> cond2(gr(x, y), x, y),
             neq(0(), 0()) -> false(),
            neq(0(), s(x)) -> true(),
            neq(s(x), 0()) -> true(),
           neq(s(x), s(y)) -> neq(x, y),
                    p(0()) -> 0(),
                   p(s(x)) -> x}
     SPSC:
      Simple Projection:
       pi(neq#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {gr#(s(x), s(y)) -> gr#(x, y)}
     Weak:
     { cond2(true(), x, y) -> cond1(neq(x, 0()), y, y),
      cond2(false(), x, y) -> cond1(neq(x, 0()), p(x), y),
                gr(0(), x) -> false(),
             gr(s(x), 0()) -> true(),
            gr(s(x), s(y)) -> gr(x, y),
       cond1(true(), x, y) -> cond2(gr(x, y), x, y),
             neq(0(), 0()) -> false(),
            neq(0(), s(x)) -> true(),
            neq(s(x), 0()) -> true(),
           neq(s(x), s(y)) -> neq(x, y),
                    p(0()) -> 0(),
                   p(s(x)) -> x}
     SPSC:
      Simple Projection:
       pi(gr#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      { cond2#(true(), x, y) -> cond1#(neq(x, 0()), y, y),
       cond2#(false(), x, y) -> cond1#(neq(x, 0()), p(x), y),
        cond1#(true(), x, y) -> cond2#(gr(x, y), x, y)}
     Weak:
     { cond2(true(), x, y) -> cond1(neq(x, 0()), y, y),
      cond2(false(), x, y) -> cond1(neq(x, 0()), p(x), y),
                gr(0(), x) -> false(),
             gr(s(x), 0()) -> true(),
            gr(s(x), s(y)) -> gr(x, y),
       cond1(true(), x, y) -> cond2(gr(x, y), x, y),
             neq(0(), 0()) -> false(),
            neq(0(), s(x)) -> true(),
            neq(s(x), 0()) -> true(),
           neq(s(x), s(y)) -> neq(x, y),
                    p(0()) -> 0(),
                   p(s(x)) -> x}
     Fail