MAYBE
Time: 1.034766
TRS:
 { cond2(true(), x, y) -> cond1(or(gr(x, 0()), gr(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),
         or(x, true()) -> true(),
         or(true(), x) -> true(),
  or(false(), false()) -> false(),
                 p 0() -> 0(),
                 p s x -> x,
   cond3(true(), x, y) -> cond1(or(gr(x, 0()), gr(y, 0())), x, p y),
  cond3(false(), x, y) -> cond1(or(gr(x, 0()), gr(y, 0())), x, y)}
 DP:
  DP:
   { cond2#(true(), x, y) -> gr#(x, 0()),
     cond2#(true(), x, y) -> gr#(y, 0()),
     cond2#(true(), x, y) -> cond1#(or(gr(x, 0()), gr(y, 0())), p x, y),
     cond2#(true(), x, y) -> or#(gr(x, 0()), gr(y, 0())),
     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()),
     cond3#(true(), x, y) -> gr#(x, 0()),
     cond3#(true(), x, y) -> gr#(y, 0()),
     cond3#(true(), x, y) -> cond1#(or(gr(x, 0()), gr(y, 0())), x, p y),
     cond3#(true(), x, y) -> or#(gr(x, 0()), gr(y, 0())),
     cond3#(true(), x, y) -> p# y,
    cond3#(false(), x, y) -> gr#(x, 0()),
    cond3#(false(), x, y) -> gr#(y, 0()),
    cond3#(false(), x, y) -> cond1#(or(gr(x, 0()), gr(y, 0())), x, y),
    cond3#(false(), x, y) -> or#(gr(x, 0()), gr(y, 0()))}
  TRS:
  { cond2(true(), x, y) -> cond1(or(gr(x, 0()), gr(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),
          or(x, true()) -> true(),
          or(true(), x) -> true(),
   or(false(), false()) -> false(),
                  p 0() -> 0(),
                  p s x -> x,
    cond3(true(), x, y) -> cond1(or(gr(x, 0()), gr(y, 0())), x, p y),
   cond3(false(), x, y) -> cond1(or(gr(x, 0()), gr(y, 0())), x, y)}
  UR:
   {          gr(0(), x) -> false(),
            gr(s x, 0()) -> true(),
           or(x, true()) -> true(),
           or(true(), x) -> true(),
    or(false(), false()) -> false(),
                   p 0() -> 0(),
                   p s x -> x,
                 a(z, w) -> z,
                 a(z, w) -> w}
   EDG:
    {(cond3#(true(), x, y) -> cond1#(or(gr(x, 0()), gr(y, 0())), x, p y), cond1#(true(), x, y) -> gr#(x, 0()))
     (cond3#(true(), x, y) -> cond1#(or(gr(x, 0()), gr(y, 0())), x, p y), cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y))
     (cond2#(true(), x, y) -> cond1#(or(gr(x, 0()), gr(y, 0())), p x, y), cond1#(true(), x, y) -> gr#(x, 0()))
     (cond2#(true(), x, y) -> cond1#(or(gr(x, 0()), gr(y, 0())), p x, 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#(false(), x, y) -> cond1#(or(gr(x, 0()), gr(y, 0())), x, y), cond1#(true(), x, y) -> gr#(x, 0()))
     (cond3#(false(), x, y) -> cond1#(or(gr(x, 0()), gr(y, 0())), x, y), cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y))
     (cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y), cond2#(true(), x, y) -> gr#(x, 0()))
     (cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y), cond2#(true(), x, y) -> gr#(y, 0()))
     (cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y), cond2#(true(), x, y) -> cond1#(or(gr(x, 0()), gr(y, 0())), p x, y))
     (cond1#(true(), x, y) -> cond2#(gr(x, 0()), x, y), cond2#(true(), x, y) -> or#(gr(x, 0()), 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#(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#(false(), x, y) -> cond3#(gr(y, 0()), x, y), cond3#(true(), x, y) -> gr#(x, 0()))
     (cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y), cond3#(true(), x, y) -> gr#(y, 0()))
     (cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y), cond3#(true(), x, y) -> cond1#(or(gr(x, 0()), gr(y, 0())), x, p y))
     (cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y), cond3#(true(), x, y) -> or#(gr(x, 0()), gr(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#(false(), x, y) -> gr#(x, 0()))
     (cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y), cond3#(false(), x, y) -> gr#(y, 0()))
     (cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y), cond3#(false(), x, y) -> cond1#(or(gr(x, 0()), gr(y, 0())), x, y))
     (cond2#(false(), x, y) -> cond3#(gr(y, 0()), x, y), cond3#(false(), x, y) -> or#(gr(x, 0()), gr(y, 0())))}
    STATUS:
     arrows: 0.936288
     SCCS (2):
      Scc:
       {gr#(s x, s y) -> gr#(x, y)}
      Scc:
       { cond2#(true(), x, y) -> cond1#(or(gr(x, 0()), gr(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#(or(gr(x, 0()), gr(y, 0())), x, p y),
        cond3#(false(), x, y) -> cond1#(or(gr(x, 0()), gr(y, 0())), x, y)}
      
      SCC (1):
       Strict:
        {gr#(s x, s y) -> gr#(x, y)}
       Weak:
       { cond2(true(), x, y) -> cond1(or(gr(x, 0()), gr(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),
               or(x, true()) -> true(),
               or(true(), x) -> true(),
        or(false(), false()) -> false(),
                       p 0() -> 0(),
                       p s x -> x,
         cond3(true(), x, y) -> cond1(or(gr(x, 0()), gr(y, 0())), x, p y),
        cond3(false(), x, y) -> cond1(or(gr(x, 0()), gr(y, 0())), x, y)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [cond2](x0, x1, x2) = 0,
         
         [cond1](x0, x1, x2) = 0,
         
         [cond3](x0, x1, x2) = 0,
         
         [gr](x0, x1) = x0 + 1,
         
         [or](x0, x1) = x0 + 1,
         
         [p](x0) = 0,
         
         [s](x0) = x0 + 1,
         
         [0] = 0,
         
         [true] = 0,
         
         [false] = 1,
         
         [gr#](x0, x1) = x0
        Strict:
         gr#(s x, s y) -> gr#(x, y)
         1 + 0x + 1y >= 0 + 0x + 1y
        Weak:
         cond3(false(), x, y) -> cond1(or(gr(x, 0()), gr(y, 0())), x, y)
         0 + 0x + 0y >= 0 + 0x + 0y
         cond3(true(), x, y) -> cond1(or(gr(x, 0()), gr(y, 0())), x, p y)
         0 + 0x + 0y >= 0 + 0x + 0y
         p s x -> x
         0 + 0x >= 1x
         p 0() -> 0()
         0 >= 0
         or(false(), false()) -> false()
         2 >= 1
         or(true(), x) -> true()
         1 + 1x >= 0
         or(x, true()) -> true()
         1 + 0x >= 0
         cond1(true(), x, y) -> cond2(gr(x, 0()), x, y)
         0 + 0x + 0y >= 0 + 0x + 0y
         gr(s x, s y) -> gr(x, y)
         2 + 0x + 1y >= 1 + 0x + 1y
         gr(s x, 0()) -> true()
         1 + 0x >= 0
         gr(0(), x) -> false()
         1 + 1x >= 1
         cond2(false(), x, y) -> cond3(gr(y, 0()), x, y)
         0 + 0x + 0y >= 0 + 0x + 0y
         cond2(true(), x, y) -> cond1(or(gr(x, 0()), gr(y, 0())), p x, y)
         0 + 0x + 0y >= 0 + 0x + 0y
       Qed
     SCC (5):
      Strict:
       { cond2#(true(), x, y) -> cond1#(or(gr(x, 0()), gr(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#(or(gr(x, 0()), gr(y, 0())), x, p y),
        cond3#(false(), x, y) -> cond1#(or(gr(x, 0()), gr(y, 0())), x, y)}
      Weak:
      { cond2(true(), x, y) -> cond1(or(gr(x, 0()), gr(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),
              or(x, true()) -> true(),
              or(true(), x) -> true(),
       or(false(), false()) -> false(),
                      p 0() -> 0(),
                      p s x -> x,
        cond3(true(), x, y) -> cond1(or(gr(x, 0()), gr(y, 0())), x, p y),
       cond3(false(), x, y) -> cond1(or(gr(x, 0()), gr(y, 0())), x, y)}
      Fail