MAYBE
TRS:
 { cond2(true(), x, y) -> cond1(gr(add(x, y), 0()), p(x), y),
  cond2(false(), x, y) -> cond3(gr(y, 0()), 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, 0()), x, y),
           add(0(), x) -> x,
          add(s(x), y) -> s(add(x, y)),
                p(0()) -> 0(),
               p(s(x)) -> x,
   cond3(true(), x, y) -> cond1(gr(add(x, y), 0()), x, p(y)),
  cond3(false(), x, y) -> cond1(gr(add(x, y), 0()), x, y)}
 DP:
  Strict:
   { cond2#(true(), x, y) -> gr#(add(x, y), 0()),
     cond2#(true(), x, y) -> cond1#(gr(add(x, y), 0()), p(x), y),
     cond2#(true(), x, y) -> add#(x, y),
     cond2#(true(), x, y) -> p#(x),
    cond2#(false(), x, y) -> gr#(y, 0()),
    cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y),
          gr#(s(x), s(y)) -> gr#(x, y),
     cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y),
     cond1#(true(), x, y) -> gr#(x, 0()),
            add#(s(x), y) -> add#(x, y),
     cond3#(true(), x, y) -> gr#(add(x, y), 0()),
     cond3#(true(), x, y) -> cond1#(gr(add(x, y), 0()), x, p(y)),
     cond3#(true(), x, y) -> add#(x, y),
     cond3#(true(), x, y) -> p#(y),
    cond3#(false(), x, y) -> gr#(add(x, y), 0()),
    cond3#(false(), x, y) -> cond1#(gr(add(x, y), 0()), x, y),
    cond3#(false(), x, y) -> add#(x, y)}
  Weak:
  { cond2(true(), x, y) -> cond1(gr(add(x, y), 0()), p(x), y),
   cond2(false(), x, y) -> cond3(gr(y, 0()), 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, 0()), x, y),
            add(0(), x) -> x,
           add(s(x), y) -> s(add(x, y)),
                 p(0()) -> 0(),
                p(s(x)) -> x,
    cond3(true(), x, y) -> cond1(gr(add(x, y), 0()), x, p(y)),
   cond3(false(), x, y) -> cond1(gr(add(x, y), 0()), x, y)}
  EDG:
   {(cond3#(true(), x, y) -> cond1#(gr(add(x, y), 0()), x, p(y)), cond1#(true(), x, y) -> gr#(x, 0()))
    (cond3#(true(), x, y) -> cond1#(gr(add(x, y), 0()), x, p(y)), cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y))
    (gr#(s(x), s(y)) -> gr#(x, y), gr#(s(x), s(y)) -> gr#(x, y))
    (cond3#(true(), x, y) -> add#(x, y), add#(s(x), y) -> add#(x, y))
    (cond2#(true(), x, y) -> cond1#(gr(add(x, y), 0()), p(x), y), cond1#(true(), x, y) -> gr#(x, 0()))
    (cond2#(true(), x, y) -> cond1#(gr(add(x, y), 0()), p(x), y), cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y))
    (cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y), cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y))
    (cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y), cond2#(false(), x, y) -> gr#(y, 0()))
    (cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y), cond2#(true(), x, y) -> p#(x))
    (cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y), cond2#(true(), x, y) -> add#(x, y))
    (cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y), cond2#(true(), x, y) -> cond1#(gr(add(x, y), 0()), p(x), y))
    (cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y), cond2#(true(), x, y) -> gr#(add(x, y), 0()))
    (cond3#(false(), x, y) -> cond1#(gr(add(x, y), 0()), x, y), cond1#(true(), x, y) -> gr#(x, 0()))
    (cond3#(false(), x, y) -> cond1#(gr(add(x, y), 0()), x, y), cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y))
    (cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y), cond3#(true(), x, y) -> gr#(add(x, y), 0()))
    (cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y), cond3#(true(), x, y) -> cond1#(gr(add(x, y), 0()), x, p(y)))
    (cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y), cond3#(true(), x, y) -> add#(x, y))
    (cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y), cond3#(true(), x, y) -> p#(y))
    (cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y), cond3#(false(), x, y) -> gr#(add(x, y), 0()))
    (cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y), cond3#(false(), x, y) -> cond1#(gr(add(x, y), 0()), x, y))
    (cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y), cond3#(false(), x, y) -> add#(x, y))
    (cond3#(false(), x, y) -> add#(x, y), add#(s(x), y) -> add#(x, y))
    (add#(s(x), y) -> add#(x, y), add#(s(x), y) -> add#(x, y))
    (cond2#(true(), x, y) -> add#(x, y), add#(s(x), y) -> add#(x, y))}
   SCCS:
    Scc:
     {add#(s(x), y) -> add#(x, y)}
    Scc:
     {gr#(s(x), s(y)) -> gr#(x, y)}
    Scc:
     { cond2#(true(), x, y) -> cond1#(gr(add(x, y), 0()), p(x), y),
      cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y),
       cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y),
       cond3#(true(), x, y) -> cond1#(gr(add(x, y), 0()), x, p(y)),
      cond3#(false(), x, y) -> cond1#(gr(add(x, y), 0()), x, y)}
    SCC:
     Strict:
      {add#(s(x), y) -> add#(x, y)}
     Weak:
     { cond2(true(), x, y) -> cond1(gr(add(x, y), 0()), p(x), y),
      cond2(false(), x, y) -> cond3(gr(y, 0()), 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, 0()), x, y),
               add(0(), x) -> x,
              add(s(x), y) -> s(add(x, y)),
                    p(0()) -> 0(),
                   p(s(x)) -> x,
       cond3(true(), x, y) -> cond1(gr(add(x, y), 0()), x, p(y)),
      cond3(false(), x, y) -> cond1(gr(add(x, y), 0()), x, y)}
     SPSC:
      Simple Projection:
       pi(add#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      {gr#(s(x), s(y)) -> gr#(x, y)}
     Weak:
     { cond2(true(), x, y) -> cond1(gr(add(x, y), 0()), p(x), y),
      cond2(false(), x, y) -> cond3(gr(y, 0()), 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, 0()), x, y),
               add(0(), x) -> x,
              add(s(x), y) -> s(add(x, y)),
                    p(0()) -> 0(),
                   p(s(x)) -> x,
       cond3(true(), x, y) -> cond1(gr(add(x, y), 0()), x, p(y)),
      cond3(false(), x, y) -> cond1(gr(add(x, y), 0()), x, y)}
     SPSC:
      Simple Projection:
       pi(gr#) = 0
      Strict:
       {}
      Qed
    SCC:
     Strict:
      { cond2#(true(), x, y) -> cond1#(gr(add(x, y), 0()), p(x), y),
       cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y),
        cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y),
        cond3#(true(), x, y) -> cond1#(gr(add(x, y), 0()), x, p(y)),
       cond3#(false(), x, y) -> cond1#(gr(add(x, y), 0()), x, y)}
     Weak:
     { cond2(true(), x, y) -> cond1(gr(add(x, y), 0()), p(x), y),
      cond2(false(), x, y) -> cond3(gr(y, 0()), 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, 0()), x, y),
               add(0(), x) -> x,
              add(s(x), y) -> s(add(x, y)),
                    p(0()) -> 0(),
                   p(s(x)) -> x,
       cond3(true(), x, y) -> cond1(gr(add(x, y), 0()), x, p(y)),
      cond3(false(), x, y) -> cond1(gr(add(x, y), 0()), x, y)}
     Fail