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