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
  TDG 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
   graph:
    neq#(s(x),s(y())) -> neq#(x,y()) -> neq#(s(x),s(y())) -> neq#(x,y())
    div2#(s(s(x))) -> div2#(x) -> div2#(s(s(x))) -> div2#(x)
    cond2#(false(),x) -> neq#(x,0()) ->
    neq#(s(x),s(y())) -> neq#(x,y())
    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) -> neq#(x,0()) -> neq#(s(x),s(y())) -> neq#(x,y())
    cond2#(true(),x) -> div2#(x) ->
    div2#(s(s(x))) -> div2#(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)
    even#(s(s(x))) -> even#(x) -> even#(s(s(x))) -> even#(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)
    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) -> even#(x) -> even#(s(s(x))) -> even#(x)
   EDG 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
    graph:
     div2#(s(s(x))) -> div2#(x) ->
     div2#(s(s(x))) -> div2#(x)
     cond2#(false(),x) -> cond1#(neq(x,0()),p(x)) ->
     cond1#(true(),x) -> even#(x)
     cond2#(false(),x) -> cond1#(neq(x,0()),p(x)) ->
     cond1#(true(),x) -> cond2#(even(x),x)
     cond2#(true(),x) -> div2#(x) ->
     div2#(s(s(x))) -> div2#(x)
     cond2#(true(),x) -> cond1#(neq(x,0()),div2(x)) ->
     cond1#(true(),x) -> even#(x)
     cond2#(true(),x) -> cond1#(neq(x,0()),div2(x)) ->
     cond1#(true(),x) -> cond2#(even(x),x)
     even#(s(s(x))) -> even#(x) -> even#(s(s(x))) -> even#(x)
     cond1#(true(),x) -> cond2#(even(x),x) ->
     cond2#(true(),x) -> 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) -> cond1#(neq(x,0()),div2(x))
     cond1#(true(),x) -> cond2#(even(x),x) ->
     cond2#(false(),x) -> 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) -> cond1#(neq(x,0()),p(x))
     cond1#(true(),x) -> even#(x) -> even#(s(s(x))) -> even#(x)
    SCC Processor:
     #sccs: 3
     #rules: 5
     #arcs: 14/121
     DPs:
      cond2#(false(),x) -> cond1#(neq(x,0()),p(x))
      cond1#(true(),x) -> cond2#(even(x),x)
      cond2#(true(),x) -> cond1#(neq(x,0()),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:
       [cond2#](x0, x1) = 3/2x1 + 1/2,
       
       [cond1#](x0, x1) = x0 + 2x1,
       
       [y] = 5/2,
       
       [s](x0) = 2x0 + 2,
       
       [p](x0) = 1/2x0,
       
       [false] = 0,
       
       [div2](x0) = 1/2x0,
       
       [neq](x0, x1) = 1/2x0 + x1,
       
       [0] = 0,
       
       [cond2](x0, x1) = 1/2x0 + 2x1 + 1,
       
       [even](x0) = 1,
       
       [cond1](x0, x1) = x0 + 2x1 + 1/2,
       
       [true] = 1
      orientation:
       cond2#(false(),x) = 3/2x + 1/2 >= 3/2x = cond1#(neq(x,0()),p(x))
       
       cond1#(true(),x) = 2x + 1 >= 3/2x + 1/2 = cond2#(even(x),x)
       
       cond2#(true(),x) = 3/2x + 1/2 >= 3/2x = cond1#(neq(x,0()),div2(x))
       
       cond1(true(),x) = 2x + 3/2 >= 2x + 3/2 = cond2(even(x),x)
       
       cond2(true(),x) = 2x + 3/2 >= 3/2x + 1/2 = cond1(neq(x,0()),div2(x))
       
       cond2(false(),x) = 2x + 1 >= 3/2x + 1/2 = cond1(neq(x,0()),p(x))
       
       neq(0(),0()) = 0 >= 0 = false()
       
       neq(0(),s(x)) = 2x + 2 >= 1 = true()
       
       neq(s(x),0()) = x + 1 >= 1 = true()
       
       neq(s(x),s(y())) = x + 8 >= 1/2x + 5/2 = neq(x,y())
       
       even(0()) = 1 >= 1 = true()
       
       even(s(0())) = 1 >= 0 = false()
       
       even(s(s(x))) = 1 >= 1 = even(x)
       
       div2(0()) = 0 >= 0 = 0()
       
       div2(s(0())) = 1 >= 0 = 0()
       
       div2(s(s(x))) = 2x + 3 >= x + 2 = s(div2(x))
       
       p(0()) = 0 >= 0 = 0()
       
       p(s(x)) = x + 1 >= 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
     
     DPs:
      even#(s(s(x))) -> even#(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
     KBO Processor:
      argument filtering:
       pi(true) = []
       pi(cond1) = 1
       pi(even) = []
       pi(cond2) = 1
       pi(0) = []
       pi(neq) = [0]
       pi(div2) = 0
       pi(false) = []
       pi(p) = 0
       pi(s) = [0]
       pi(y) = []
       pi(even#) = 0
      weight function:
       w0 = 1
       w(even#) = w(y) = w(false) = w(div2) = w(0) = w(cond2) = w(even) = w(
       true) = 1
       w(s) = w(p) = w(neq) = w(cond1) = 0
      precedence:
       y ~ s ~ neq ~ even > even# ~ p ~ false ~ div2 ~ 0 ~ cond2 ~ cond1 ~ true
      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
     
     DPs:
      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
     KBO Processor:
      argument filtering:
       pi(true) = []
       pi(cond1) = 1
       pi(even) = []
       pi(cond2) = 1
       pi(0) = []
       pi(neq) = [0]
       pi(div2) = 0
       pi(false) = []
       pi(p) = 0
       pi(s) = [0]
       pi(y) = []
       pi(div2#) = 0
      weight function:
       w0 = 1
       w(div2#) = w(y) = w(false) = w(div2) = w(0) = w(cond2) = w(even) = w(
       true) = 1
       w(s) = w(p) = w(neq) = w(cond1) = 0
      precedence:
       y ~ s ~ neq ~ even > div2# ~ p ~ false ~ div2 ~ 0 ~ cond2 ~ cond1 ~ true
      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