MAYBE
Time: 0.443598
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:
  DP:
   { 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)}
  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)}
  UR:
   {  gr(0(), x) -> false(),
    gr(s x, 0()) -> true(),
     add(0(), x) -> x,
     add(s x, y) -> s add(x, y),
           p 0() -> 0(),
           p s x -> x,
         a(z, w) -> z,
         a(z, w) -> w}
   EDG:
    {(cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y), cond3#(false(), x, y) -> add#(x, y))
     (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) -> gr#(add(x, y), 0()))
     (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#(true(), x, y) -> add#(x, y))
     (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) -> 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))
     (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))
     (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))
     (cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y), cond2#(true(), x, y) -> gr#(add(x, y), 0()))
     (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) -> add#(x, y))
     (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#(false(), x, y) -> gr#(y, 0()))
     (cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y), cond2#(false(), x, y) -> cond3#(gr(y, 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) -> cond1#(gr(add(x, y), 0()), p x, y), cond1#(true(), x, y) -> gr#(x, 0()))}
    STATUS:
     arrows: 0.916955
     SCCS (3):
      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:
       {add#(s x, y) -> add#(x, y)}
      
      SCC (1):
       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)}
       Open
      SCC (5):
       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)}
       Open
      
      
      
      
      
      
      
      
      
      SCC (1):
       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)}
       Open