MAYBE
Time: 2.432184
TRS:
 { cond2(true(), x) -> cond1(neq(x, 0()), div2 x),
  cond2(false(), x) -> cond1(neq(x, 0()), p x),
           even 0() -> true(),
         even s 0() -> false(),
         even s s x -> even x,
   cond1(true(), x) -> cond2(even x, x),
      neq(0(), 0()) -> false(),
      neq(0(), s x) -> true(),
      neq(s x, 0()) -> true(),
    neq(s x, s y()) -> neq(x, y()),
           div2 0() -> 0(),
         div2 s 0() -> 0(),
         div2 s s x -> s div2 x,
              p 0() -> 0(),
              p s x -> x}
 DP:
  DP:
   { cond2#(true(), x) -> cond1#(neq(x, 0()), div2 x),
     cond2#(true(), x) -> neq#(x, 0()),
     cond2#(true(), x) -> div2# x,
    cond2#(false(), x) -> cond1#(neq(x, 0()), p x),
    cond2#(false(), x) -> neq#(x, 0()),
    cond2#(false(), x) -> p# x,
           even# s s x -> even# x,
     cond1#(true(), x) -> cond2#(even x, x),
     cond1#(true(), x) -> even# x,
      neq#(s x, s y()) -> neq#(x, y()),
           div2# s s x -> div2# x}
  TRS:
  { cond2(true(), x) -> cond1(neq(x, 0()), div2 x),
   cond2(false(), x) -> cond1(neq(x, 0()), p x),
            even 0() -> true(),
          even s 0() -> false(),
          even s s x -> even x,
    cond1(true(), x) -> cond2(even x, x),
       neq(0(), 0()) -> false(),
       neq(0(), s x) -> true(),
       neq(s x, 0()) -> true(),
     neq(s x, s y()) -> neq(x, y()),
            div2 0() -> 0(),
          div2 s 0() -> 0(),
          div2 s s x -> s div2 x,
               p 0() -> 0(),
               p s x -> x}
  EDG:
   {(cond2#(true(), x) -> div2# x, div2# s s x -> div2# x)
    (cond1#(true(), x) -> even# x, even# s s x -> even# x)
    (cond1#(true(), x) -> cond2#(even x, x), cond2#(true(), x) -> cond1#(neq(x, 0()), div2 x))
    (cond1#(true(), x) -> cond2#(even x, x), cond2#(true(), x) -> neq#(x, 0()))
    (cond1#(true(), x) -> cond2#(even x, x), cond2#(true(), x) -> div2# x)
    (cond1#(true(), x) -> cond2#(even x, x), cond2#(false(), x) -> cond1#(neq(x, 0()), p x))
    (cond1#(true(), x) -> cond2#(even x, x), cond2#(false(), x) -> neq#(x, 0()))
    (cond1#(true(), x) -> cond2#(even x, x), cond2#(false(), x) -> p# x)
    (div2# s s x -> div2# x, div2# s s x -> div2# x)
    (even# s s x -> even# x, even# s s x -> even# x)
    (cond2#(false(), x) -> cond1#(neq(x, 0()), p x), cond1#(true(), x) -> cond2#(even x, x))
    (cond2#(false(), x) -> cond1#(neq(x, 0()), p x), cond1#(true(), x) -> even# x)
    (cond2#(true(), x) -> cond1#(neq(x, 0()), div2 x), cond1#(true(), x) -> cond2#(even x, x))
    (cond2#(true(), x) -> cond1#(neq(x, 0()), div2 x), cond1#(true(), x) -> even# x)}
   STATUS:
    arrows: 0.884298
    SCCS (3):
     Scc:
      { cond2#(true(), x) -> cond1#(neq(x, 0()), div2 x),
       cond2#(false(), x) -> cond1#(neq(x, 0()), p x),
        cond1#(true(), x) -> cond2#(even x, x)}
     Scc:
      {even# s s x -> even# x}
     Scc:
      {div2# s s x -> div2# x}
     
     
     SCC (3):
      Strict:
       { cond2#(true(), x) -> cond1#(neq(x, 0()), div2 x),
        cond2#(false(), x) -> cond1#(neq(x, 0()), p x),
         cond1#(true(), x) -> cond2#(even x, x)}
      Weak:
      { cond2(true(), x) -> cond1(neq(x, 0()), div2 x),
       cond2(false(), x) -> cond1(neq(x, 0()), p x),
                even 0() -> true(),
              even s 0() -> false(),
              even s s x -> even x,
        cond1(true(), x) -> cond2(even x, x),
           neq(0(), 0()) -> false(),
           neq(0(), s x) -> true(),
           neq(s x, 0()) -> true(),
         neq(s x, s y()) -> neq(x, y()),
                div2 0() -> 0(),
              div2 s 0() -> 0(),
              div2 s s x -> s div2 x,
                   p 0() -> 0(),
                   p s x -> x}
      Fail
     
     
     
     SCC (1):
      Strict:
       {even# s s x -> even# x}
      Weak:
      { cond2(true(), x) -> cond1(neq(x, 0()), div2 x),
       cond2(false(), x) -> cond1(neq(x, 0()), p x),
                even 0() -> true(),
              even s 0() -> false(),
              even s s x -> even x,
        cond1(true(), x) -> cond2(even x, x),
           neq(0(), 0()) -> false(),
           neq(0(), s x) -> true(),
           neq(s x, 0()) -> true(),
         neq(s x, s y()) -> neq(x, y()),
                div2 0() -> 0(),
              div2 s 0() -> 0(),
              div2 s s x -> s div2 x,
                   p 0() -> 0(),
                   p s x -> x}
      POLY:
       Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
       Interpretation:
        [cond2](x0, x1) = x0 + x1 + 1,
        
        [cond1](x0, x1) = x0 + x1,
        
        [neq](x0, x1) = x0,
        
        [even](x0) = x0 + 1,
        
        [div2](x0) = x0,
        
        [p](x0) = x0,
        
        [s](x0) = x0 + 1,
        
        [true] = 1,
        
        [0] = 1,
        
        [false] = 1,
        
        [y] = 1,
        
        [even#](x0) = x0
       Strict:
        even# s s x -> even# x
        2 + 1x >= 0 + 1x
       Weak:
        p s x -> x
        1 + 1x >= 1x
        p 0() -> 0()
        1 >= 1
        div2 s s x -> s div2 x
        2 + 1x >= 1 + 1x
        div2 s 0() -> 0()
        2 >= 1
        div2 0() -> 0()
        1 >= 1
        neq(s x, s y()) -> neq(x, y())
        1 + 1x >= 0 + 1x
        neq(s x, 0()) -> true()
        1 + 1x >= 1
        neq(0(), s x) -> true()
        1 + 0x >= 1
        neq(0(), 0()) -> false()
        1 >= 1
        cond1(true(), x) -> cond2(even x, x)
        1 + 1x >= 2 + 2x
        even s s x -> even x
        3 + 1x >= 1 + 1x
        even s 0() -> false()
        3 >= 1
        even 0() -> true()
        2 >= 1
        cond2(false(), x) -> cond1(neq(x, 0()), p x)
        2 + 1x >= 0 + 2x
        cond2(true(), x) -> cond1(neq(x, 0()), div2 x)
        2 + 1x >= 0 + 2x
      Qed
    
    SCC (1):
     Strict:
      {div2# s s x -> div2# x}
     Weak:
     { cond2(true(), x) -> cond1(neq(x, 0()), div2 x),
      cond2(false(), x) -> cond1(neq(x, 0()), p x),
               even 0() -> true(),
             even s 0() -> false(),
             even s s x -> even x,
       cond1(true(), x) -> cond2(even x, x),
          neq(0(), 0()) -> false(),
          neq(0(), s x) -> true(),
          neq(s x, 0()) -> true(),
        neq(s x, s y()) -> neq(x, y()),
               div2 0() -> 0(),
             div2 s 0() -> 0(),
             div2 s s x -> s div2 x,
                  p 0() -> 0(),
                  p s x -> x}
     POLY:
      Mode: weak, max_in=1, output_bits=-1, dnum=1, ur=true
      Interpretation:
       [cond2](x0, x1) = x0 + x1 + 1,
       
       [cond1](x0, x1) = x0 + x1,
       
       [neq](x0, x1) = x0,
       
       [even](x0) = x0 + 1,
       
       [div2](x0) = x0,
       
       [p](x0) = x0,
       
       [s](x0) = x0 + 1,
       
       [true] = 1,
       
       [0] = 1,
       
       [false] = 1,
       
       [y] = 1,
       
       [div2#](x0) = x0
      Strict:
       div2# s s x -> div2# x
       2 + 1x >= 0 + 1x
      Weak:
       p s x -> x
       1 + 1x >= 1x
       p 0() -> 0()
       1 >= 1
       div2 s s x -> s div2 x
       2 + 1x >= 1 + 1x
       div2 s 0() -> 0()
       2 >= 1
       div2 0() -> 0()
       1 >= 1
       neq(s x, s y()) -> neq(x, y())
       1 + 1x >= 0 + 1x
       neq(s x, 0()) -> true()
       1 + 1x >= 1
       neq(0(), s x) -> true()
       1 + 0x >= 1
       neq(0(), 0()) -> false()
       1 >= 1
       cond1(true(), x) -> cond2(even x, x)
       1 + 1x >= 2 + 2x
       even s s x -> even x
       3 + 1x >= 1 + 1x
       even s 0() -> false()
       3 >= 1
       even 0() -> true()
       2 >= 1
       cond2(false(), x) -> cond1(neq(x, 0()), p x)
       2 + 1x >= 0 + 2x
       cond2(true(), x) -> cond1(neq(x, 0()), div2 x)
       2 + 1x >= 0 + 2x
     Qed