MAYBE
Time: 0.044764
TRS:
 { cond2(true(), x, y, z) -> cond1(gr(add(x, y), z), p x, y, z),
  cond2(false(), x, y, z) -> cond3(gr(y, 0()), 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(x, 0()), x, y, z),
              add(0(), x) -> x,
              add(s x, y) -> s add(x, y),
                    p 0() -> 0(),
                    p s x -> x,
   cond3(true(), x, y, z) -> cond1(gr(add(x, y), z), x, p y, z),
  cond3(false(), x, y, z) -> cond1(gr(add(x, y), z), x, y, z)}
 DP:
  DP:
   { cond2#(true(), x, y, z) -> gr#(add(x, y), z),
     cond2#(true(), x, y, z) -> cond1#(gr(add(x, y), z), p x, y, z),
     cond2#(true(), x, y, z) -> add#(x, y),
     cond2#(true(), x, y, z) -> p# x,
    cond2#(false(), x, y, z) -> gr#(y, 0()),
    cond2#(false(), x, y, z) -> cond3#(gr(y, 0()), x, y, z),
               gr#(s x, s y) -> gr#(x, y),
     cond1#(true(), x, y, z) -> cond2#(gr(x, 0()), x, y, z),
     cond1#(true(), x, y, z) -> gr#(x, 0()),
                add#(s x, y) -> add#(x, y),
     cond3#(true(), x, y, z) -> gr#(add(x, y), z),
     cond3#(true(), x, y, z) -> cond1#(gr(add(x, y), z), x, p y, z),
     cond3#(true(), x, y, z) -> add#(x, y),
     cond3#(true(), x, y, z) -> p# y,
    cond3#(false(), x, y, z) -> gr#(add(x, y), z),
    cond3#(false(), x, y, z) -> cond1#(gr(add(x, y), z), x, y, z),
    cond3#(false(), x, y, z) -> add#(x, y)}
  TRS:
  { cond2(true(), x, y, z) -> cond1(gr(add(x, y), z), p x, y, z),
   cond2(false(), x, y, z) -> cond3(gr(y, 0()), 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(x, 0()), x, y, z),
               add(0(), x) -> x,
               add(s x, y) -> s add(x, y),
                     p 0() -> 0(),
                     p s x -> x,
    cond3(true(), x, y, z) -> cond1(gr(add(x, y), z), x, p y, z),
   cond3(false(), x, y, z) -> cond1(gr(add(x, y), z), x, y, z)}
  UR:
   {  gr(0(), x) -> false(),
    gr(s x, 0()) -> true(),
    gr(s x, s y) -> gr(x, y),
     add(0(), x) -> x,
     add(s x, y) -> s add(x, y),
           p 0() -> 0(),
           p s x -> x,
         a(w, v) -> w,
         a(w, v) -> v}
   EDG:
    {(cond2#(false(), x, y, z) -> cond3#(gr(y, 0()), x, y, z), cond3#(false(), x, y, z) -> add#(x, y))
     (cond2#(false(), x, y, z) -> cond3#(gr(y, 0()), x, y, z), cond3#(false(), x, y, z) -> cond1#(gr(add(x, y), z), x, y, z))
     (cond2#(false(), x, y, z) -> cond3#(gr(y, 0()), x, y, z), cond3#(false(), x, y, z) -> gr#(add(x, y), z))
     (cond2#(false(), x, y, z) -> cond3#(gr(y, 0()), x, y, z), cond3#(true(), x, y, z) -> p# y)
     (cond2#(false(), x, y, z) -> cond3#(gr(y, 0()), x, y, z), cond3#(true(), x, y, z) -> add#(x, y))
     (cond2#(false(), x, y, z) -> cond3#(gr(y, 0()), x, y, z), cond3#(true(), x, y, z) -> cond1#(gr(add(x, y), z), x, p y, z))
     (cond2#(false(), x, y, z) -> cond3#(gr(y, 0()), x, y, z), cond3#(true(), x, y, z) -> gr#(add(x, y), z))
     (cond3#(true(), x, y, z) -> cond1#(gr(add(x, y), z), x, p y, z), cond1#(true(), x, y, z) -> gr#(x, 0()))
     (cond3#(true(), x, y, z) -> cond1#(gr(add(x, y), z), x, p y, z), cond1#(true(), x, y, z) -> cond2#(gr(x, 0()), x, y, z))
     (cond2#(true(), x, y, z) -> gr#(add(x, y), z), gr#(s x, s y) -> gr#(x, y))
     (cond3#(false(), x, y, z) -> gr#(add(x, 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))
     (cond3#(true(), x, y, z) -> add#(x, y), add#(s x, y) -> add#(x, y))
     (cond3#(false(), x, y, z) -> 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, z) -> add#(x, y), add#(s x, y) -> add#(x, y))
     (cond3#(true(), x, y, z) -> gr#(add(x, y), z), gr#(s x, s y) -> gr#(x, y))
     (cond3#(false(), x, y, z) -> cond1#(gr(add(x, y), z), x, y, z), cond1#(true(), x, y, z) -> cond2#(gr(x, 0()), x, y, z))
     (cond3#(false(), x, y, z) -> cond1#(gr(add(x, y), z), x, y, z), cond1#(true(), x, y, z) -> gr#(x, 0()))
     (cond1#(true(), x, y, z) -> cond2#(gr(x, 0()), x, y, z), cond2#(true(), x, y, z) -> gr#(add(x, y), z))
     (cond1#(true(), x, y, z) -> cond2#(gr(x, 0()), x, y, z), cond2#(true(), x, y, z) -> cond1#(gr(add(x, y), z), p x, y, z))
     (cond1#(true(), x, y, z) -> cond2#(gr(x, 0()), x, y, z), cond2#(true(), x, y, z) -> add#(x, y))
     (cond1#(true(), x, y, z) -> cond2#(gr(x, 0()), x, y, z), cond2#(true(), x, y, z) -> p# x)
     (cond1#(true(), x, y, z) -> cond2#(gr(x, 0()), x, y, z), cond2#(false(), x, y, z) -> gr#(y, 0()))
     (cond1#(true(), x, y, z) -> cond2#(gr(x, 0()), x, y, z), cond2#(false(), x, y, z) -> cond3#(gr(y, 0()), x, y, z))
     (cond2#(true(), x, y, z) -> cond1#(gr(add(x, y), z), p x, y, z), cond1#(true(), x, y, z) -> cond2#(gr(x, 0()), x, y, z))
     (cond2#(true(), x, y, z) -> cond1#(gr(add(x, y), z), p x, y, z), cond1#(true(), x, y, z) -> gr#(x, 0()))}
    STATUS:
     arrows: 0.906574
     SCCS (3):
      Scc:
       { cond2#(true(), x, y, z) -> cond1#(gr(add(x, y), z), p x, y, z),
        cond2#(false(), x, y, z) -> cond3#(gr(y, 0()), x, y, z),
         cond1#(true(), x, y, z) -> cond2#(gr(x, 0()), x, y, z),
         cond3#(true(), x, y, z) -> cond1#(gr(add(x, y), z), x, p y, z),
        cond3#(false(), x, y, z) -> cond1#(gr(add(x, y), z), x, y, z)}
      Scc:
       {add#(s x, y) -> add#(x, y)}
      Scc:
       {gr#(s x, s y) -> gr#(x, y)}
      
      SCC (5):
       Strict:
        { cond2#(true(), x, y, z) -> cond1#(gr(add(x, y), z), p x, y, z),
         cond2#(false(), x, y, z) -> cond3#(gr(y, 0()), x, y, z),
          cond1#(true(), x, y, z) -> cond2#(gr(x, 0()), x, y, z),
          cond3#(true(), x, y, z) -> cond1#(gr(add(x, y), z), x, p y, z),
         cond3#(false(), x, y, z) -> cond1#(gr(add(x, y), z), x, y, z)}
       Weak:
       { cond2(true(), x, y, z) -> cond1(gr(add(x, y), z), p x, y, z),
        cond2(false(), x, y, z) -> cond3(gr(y, 0()), 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(x, 0()), x, y, z),
                    add(0(), x) -> x,
                    add(s x, y) -> s add(x, y),
                          p 0() -> 0(),
                          p s x -> x,
         cond3(true(), x, y, z) -> cond1(gr(add(x, y), z), x, p y, z),
        cond3(false(), x, y, z) -> cond1(gr(add(x, y), z), x, y, z)}
       Fail
      
      
      
      
      
      
      
      
      
      SCC (1):
       Strict:
        {add#(s x, y) -> add#(x, y)}
       Weak:
       { cond2(true(), x, y, z) -> cond1(gr(add(x, y), z), p x, y, z),
        cond2(false(), x, y, z) -> cond3(gr(y, 0()), 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(x, 0()), x, y, z),
                    add(0(), x) -> x,
                    add(s x, y) -> s add(x, y),
                          p 0() -> 0(),
                          p s x -> x,
         cond3(true(), x, y, z) -> cond1(gr(add(x, y), z), x, p y, z),
        cond3(false(), x, y, z) -> cond1(gr(add(x, y), z), x, y, z)}
       POLY:
        Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
        Interpretation:
         [cond2](x0, x1, x2, x3) = x0 + x1 + 1,
         
         [cond1](x0, x1, x2, x3) = 0,
         
         [cond3](x0, x1, x2, x3) = x0 + x1,
         
         [gr](x0, x1) = x0 + x1 + 1,
         
         [add](x0, x1) = 1,
         
         [p](x0) = x0 + 1,
         
         [s](x0) = x0 + 1,
         
         [0] = 1,
         
         [true] = 1,
         
         [false] = 1,
         
         [add#](x0, x1) = x0
        Strict:
         add#(s x, y) -> add#(x, y)
         1 + 1x + 0y >= 0 + 1x + 0y
        Weak:
         cond3(false(), x, y, z) -> cond1(gr(add(x, y), z), x, y, z)
         1 + 0x + 1y + 0z >= 0 + 0x + 0y + 0z
         cond3(true(), x, y, z) -> cond1(gr(add(x, y), z), x, p y, z)
         1 + 0x + 1y + 0z >= 0 + 0x + 0y + 0z
         p s x -> x
         2 + 1x >= 1x
         p 0() -> 0()
         2 >= 1
         add(s x, y) -> s add(x, y)
         1 + 0x + 0y >= 2 + 0x + 0y
         add(0(), x) -> x
         1 + 0x >= 1x
         cond1(true(), x, y, z) -> cond2(gr(x, 0()), x, y, z)
         0 + 0x + 0y + 0z >= 3 + 2x + 0y + 0z
         gr(s x, s y) -> gr(x, y)
         3 + 1x + 1y >= 1 + 1x + 1y
         gr(s x, 0()) -> true()
         3 + 1x >= 1
         gr(0(), x) -> false()
         2 + 1x >= 1
         cond2(false(), x, y, z) -> cond3(gr(y, 0()), x, y, z)
         2 + 1x + 0y + 0z >= 2 + 0x + 2y + 0z
         cond2(true(), x, y, z) -> cond1(gr(add(x, y), z), p x, y, z)
         2 + 1x + 0y + 0z >= 0 + 0x + 0y + 0z
       Qed
     
     SCC (1):
      Strict:
       {gr#(s x, s y) -> gr#(x, y)}
      Weak:
      { cond2(true(), x, y, z) -> cond1(gr(add(x, y), z), p x, y, z),
       cond2(false(), x, y, z) -> cond3(gr(y, 0()), 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(x, 0()), x, y, z),
                   add(0(), x) -> x,
                   add(s x, y) -> s add(x, y),
                         p 0() -> 0(),
                         p s x -> x,
        cond3(true(), x, y, z) -> cond1(gr(add(x, y), z), x, p y, z),
       cond3(false(), x, y, z) -> cond1(gr(add(x, y), z), x, y, z)}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [cond2](x0, x1, x2, x3) = x0 + x1 + 1,
        
        [cond1](x0, x1, x2, x3) = 0,
        
        [cond3](x0, x1, x2, x3) = x0 + x1,
        
        [gr](x0, x1) = x0 + x1 + 1,
        
        [add](x0, x1) = 1,
        
        [p](x0) = x0 + 1,
        
        [s](x0) = x0 + 1,
        
        [0] = 1,
        
        [true] = 1,
        
        [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, z) -> cond1(gr(add(x, y), z), x, y, z)
        1 + 0x + 1y + 0z >= 0 + 0x + 0y + 0z
        cond3(true(), x, y, z) -> cond1(gr(add(x, y), z), x, p y, z)
        1 + 0x + 1y + 0z >= 0 + 0x + 0y + 0z
        p s x -> x
        2 + 1x >= 1x
        p 0() -> 0()
        2 >= 1
        add(s x, y) -> s add(x, y)
        1 + 0x + 0y >= 2 + 0x + 0y
        add(0(), x) -> x
        1 + 0x >= 1x
        cond1(true(), x, y, z) -> cond2(gr(x, 0()), x, y, z)
        0 + 0x + 0y + 0z >= 3 + 2x + 0y + 0z
        gr(s x, s y) -> gr(x, y)
        3 + 1x + 1y >= 1 + 1x + 1y
        gr(s x, 0()) -> true()
        3 + 1x >= 1
        gr(0(), x) -> false()
        2 + 1x >= 1
        cond2(false(), x, y, z) -> cond3(gr(y, 0()), x, y, z)
        2 + 1x + 0y + 0z >= 2 + 0x + 2y + 0z
        cond2(true(), x, y, z) -> cond1(gr(add(x, y), z), p x, y, z)
        2 + 1x + 0y + 0z >= 0 + 0x + 0y + 0z
      Qed