YES

Problem:
 cond1(true(),x) -> cond2(even(x),x)
 cond2(true(),x) -> cond1(neq(x,0()),div2(x))
 cond2(false(),x) -> cond1(neq(x,0()),p(x))
 neq(0(),0()) -> false()
 neq(0(),s(x)) -> true()
 neq(s(x),0()) -> true()
 neq(s(x),s(y())) -> neq(x,y())
 even(0()) -> true()
 even(s(0())) -> false()
 even(s(s(x))) -> even(x)
 div2(0()) -> 0()
 div2(s(0())) -> 0()
 div2(s(s(x))) -> s(div2(x))
 p(0()) -> 0()
 p(s(x)) -> x

Proof:
 DP Processor:
  DPs:
   cond1#(true(),x) -> even#(x)
   cond1#(true(),x) -> cond2#(even(x),x)
   cond2#(true(),x) -> div2#(x)
   cond2#(true(),x) -> neq#(x,0())
   cond2#(true(),x) -> cond1#(neq(x,0()),div2(x))
   cond2#(false(),x) -> p#(x)
   cond2#(false(),x) -> neq#(x,0())
   cond2#(false(),x) -> cond1#(neq(x,0()),p(x))
   neq#(s(x),s(y())) -> neq#(x,y())
   even#(s(s(x))) -> even#(x)
   div2#(s(s(x))) -> div2#(x)
  TRS:
   cond1(true(),x) -> cond2(even(x),x)
   cond2(true(),x) -> cond1(neq(x,0()),div2(x))
   cond2(false(),x) -> cond1(neq(x,0()),p(x))
   neq(0(),0()) -> false()
   neq(0(),s(x)) -> true()
   neq(s(x),0()) -> true()
   neq(s(x),s(y())) -> neq(x,y())
   even(0()) -> true()
   even(s(0())) -> false()
   even(s(s(x))) -> even(x)
   div2(0()) -> 0()
   div2(s(0())) -> 0()
   div2(s(s(x))) -> s(div2(x))
   p(0()) -> 0()
   p(s(x)) -> x
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [p#](x0) = 0,
    
    [neq#](x0, x1) = 3/2x0,
    
    [div2#](x0) = 2x0,
    
    [cond2#](x0, x1) = 2x1 + 1/2,
    
    [even#](x0) = 2x0,
    
    [cond1#](x0, x1) = 1/2x0 + 2x1,
    
    [y] = 1,
    
    [s](x0) = 3x0 + 1,
    
    [p](x0) = 1/2x0,
    
    [false] = 0,
    
    [div2](x0) = 1/2x0,
    
    [neq](x0, x1) = 2x0 + 2x1,
    
    [0] = 0,
    
    [cond2](x0, x1) = 2,
    
    [even](x0) = 2,
    
    [cond1](x0, x1) = 2,
    
    [true] = 2
   orientation:
    cond1#(true(),x) = 2x + 1 >= 2x = even#(x)
    
    cond1#(true(),x) = 2x + 1 >= 2x + 1/2 = cond2#(even(x),x)
    
    cond2#(true(),x) = 2x + 1/2 >= 2x = div2#(x)
    
    cond2#(true(),x) = 2x + 1/2 >= 3/2x = neq#(x,0())
    
    cond2#(true(),x) = 2x + 1/2 >= 2x = cond1#(neq(x,0()),div2(x))
    
    cond2#(false(),x) = 2x + 1/2 >= 0 = p#(x)
    
    cond2#(false(),x) = 2x + 1/2 >= 3/2x = neq#(x,0())
    
    cond2#(false(),x) = 2x + 1/2 >= 2x = cond1#(neq(x,0()),p(x))
    
    neq#(s(x),s(y())) = 9/2x + 3/2 >= 3/2x = neq#(x,y())
    
    even#(s(s(x))) = 18x + 8 >= 2x = even#(x)
    
    div2#(s(s(x))) = 18x + 8 >= 2x = div2#(x)
    
    cond1(true(),x) = 2 >= 2 = cond2(even(x),x)
    
    cond2(true(),x) = 2 >= 2 = cond1(neq(x,0()),div2(x))
    
    cond2(false(),x) = 2 >= 2 = cond1(neq(x,0()),p(x))
    
    neq(0(),0()) = 0 >= 0 = false()
    
    neq(0(),s(x)) = 6x + 2 >= 2 = true()
    
    neq(s(x),0()) = 6x + 2 >= 2 = true()
    
    neq(s(x),s(y())) = 6x + 10 >= 2x + 2 = neq(x,y())
    
    even(0()) = 2 >= 2 = true()
    
    even(s(0())) = 2 >= 0 = false()
    
    even(s(s(x))) = 2 >= 2 = even(x)
    
    div2(0()) = 0 >= 0 = 0()
    
    div2(s(0())) = 1/2 >= 0 = 0()
    
    div2(s(s(x))) = 9/2x + 2 >= 3/2x + 1 = s(div2(x))
    
    p(0()) = 0 >= 0 = 0()
    
    p(s(x)) = 3/2x + 1/2 >= x = x
   problem:
    DPs:
     
    TRS:
     cond1(true(),x) -> cond2(even(x),x)
     cond2(true(),x) -> cond1(neq(x,0()),div2(x))
     cond2(false(),x) -> cond1(neq(x,0()),p(x))
     neq(0(),0()) -> false()
     neq(0(),s(x)) -> true()
     neq(s(x),0()) -> true()
     neq(s(x),s(y())) -> neq(x,y())
     even(0()) -> true()
     even(s(0())) -> false()
     even(s(s(x))) -> even(x)
     div2(0()) -> 0()
     div2(s(0())) -> 0()
     div2(s(s(x))) -> s(div2(x))
     p(0()) -> 0()
     p(s(x)) -> x
   Qed