YES

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

Proof:
 DP Processor:
  DPs:
   cond1#(true(),x,y) -> gr#(y,0())
   cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y)
   cond2#(true(),x,y) -> p#(y)
   cond2#(true(),x,y) -> gr#(y,0())
   cond2#(true(),x,y) -> cond2#(gr(y,0()),x,p(y))
   cond2#(false(),x,y) -> p#(x)
   cond2#(false(),x,y) -> gr#(x,0())
   cond2#(false(),x,y) -> cond1#(gr(x,0()),p(x),y)
   gr#(s(x),s(y)) -> gr#(x,y)
  TRS:
   cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
   cond2(true(),x,y) -> cond2(gr(y,0()),x,p(y))
   cond2(false(),x,y) -> cond1(gr(x,0()),p(x),y)
   gr(0(),x) -> false()
   gr(s(x),0()) -> true()
   gr(s(x),s(y)) -> gr(x,y)
   p(0()) -> 0()
   p(s(x)) -> x
  TDG Processor:
   DPs:
    cond1#(true(),x,y) -> gr#(y,0())
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y)
    cond2#(true(),x,y) -> p#(y)
    cond2#(true(),x,y) -> gr#(y,0())
    cond2#(true(),x,y) -> cond2#(gr(y,0()),x,p(y))
    cond2#(false(),x,y) -> p#(x)
    cond2#(false(),x,y) -> gr#(x,0())
    cond2#(false(),x,y) -> cond1#(gr(x,0()),p(x),y)
    gr#(s(x),s(y)) -> gr#(x,y)
   TRS:
    cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
    cond2(true(),x,y) -> cond2(gr(y,0()),x,p(y))
    cond2(false(),x,y) -> cond1(gr(x,0()),p(x),y)
    gr(0(),x) -> false()
    gr(s(x),0()) -> true()
    gr(s(x),s(y)) -> gr(x,y)
    p(0()) -> 0()
    p(s(x)) -> x
   graph:
    cond2#(false(),x,y) -> gr#(x,0()) ->
    gr#(s(x),s(y)) -> gr#(x,y)
    cond2#(false(),x,y) -> cond1#(gr(x,0()),p(x),y) ->
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y)
    cond2#(false(),x,y) -> cond1#(gr(x,0()),p(x),y) ->
    cond1#(true(),x,y) -> gr#(y,0())
    cond2#(true(),x,y) -> cond2#(gr(y,0()),x,p(y)) ->
    cond2#(false(),x,y) -> cond1#(gr(x,0()),p(x),y)
    cond2#(true(),x,y) -> cond2#(gr(y,0()),x,p(y)) ->
    cond2#(false(),x,y) -> gr#(x,0())
    cond2#(true(),x,y) -> cond2#(gr(y,0()),x,p(y)) ->
    cond2#(false(),x,y) -> p#(x)
    cond2#(true(),x,y) -> cond2#(gr(y,0()),x,p(y)) ->
    cond2#(true(),x,y) -> cond2#(gr(y,0()),x,p(y))
    cond2#(true(),x,y) -> cond2#(gr(y,0()),x,p(y)) ->
    cond2#(true(),x,y) -> gr#(y,0())
    cond2#(true(),x,y) -> cond2#(gr(y,0()),x,p(y)) ->
    cond2#(true(),x,y) -> p#(y)
    cond2#(true(),x,y) -> gr#(y,0()) -> gr#(s(x),s(y)) -> gr#(x,y)
    gr#(s(x),s(y)) -> gr#(x,y) ->
    gr#(s(x),s(y)) -> gr#(x,y)
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y) ->
    cond2#(false(),x,y) -> cond1#(gr(x,0()),p(x),y)
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y) ->
    cond2#(false(),x,y) -> gr#(x,0())
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y) ->
    cond2#(false(),x,y) -> p#(x)
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y) ->
    cond2#(true(),x,y) -> cond2#(gr(y,0()),x,p(y))
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y) ->
    cond2#(true(),x,y) -> gr#(y,0())
    cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y) ->
    cond2#(true(),x,y) -> p#(y)
    cond1#(true(),x,y) -> gr#(y,0()) -> gr#(s(x),s(y)) -> gr#(x,y)
   SCC Processor:
    #sccs: 2
    #rules: 4
    #arcs: 18/81
    DPs:
     cond2#(false(),x,y) -> cond1#(gr(x,0()),p(x),y)
     cond1#(true(),x,y) -> cond2#(gr(y,0()),x,y)
     cond2#(true(),x,y) -> cond2#(gr(y,0()),x,p(y))
    TRS:
     cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
     cond2(true(),x,y) -> cond2(gr(y,0()),x,p(y))
     cond2(false(),x,y) -> cond1(gr(x,0()),p(x),y)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y)) -> gr(x,y)
     p(0()) -> 0()
     p(s(x)) -> x
    Matrix Interpretation Processor: dim=1
     
     interpretation:
      [cond2#](x0, x1, x2) = 5/2x1,
      
      [cond1#](x0, x1, x2) = x0 + 3x1,
      
      [s](x0) = 3x0 + 2,
      
      [false] = 0,
      
      [p](x0) = 1/2x0,
      
      [cond2](x0, x1, x2) = 5/2x1 + 1,
      
      [gr](x0, x1) = x0 + 5/2x1,
      
      [0] = 0,
      
      [cond1](x0, x1, x2) = x0 + 3x1 + 1/2,
      
      [true] = 1
     orientation:
      cond2#(false(),x,y) = 5/2x >= 5/2x = cond1#(gr(x,0()),p(x),y)
      
      cond1#(true(),x,y) = 3x + 1 >= 5/2x = cond2#(gr(y,0()),x,y)
      
      cond2#(true(),x,y) = 5/2x >= 5/2x = cond2#(gr(y,0()),x,p(y))
      
      cond1(true(),x,y) = 3x + 3/2 >= 5/2x + 1 = cond2(gr(y,0()),x,y)
      
      cond2(true(),x,y) = 5/2x + 1 >= 5/2x + 1 = cond2(gr(y,0()),x,p(y))
      
      cond2(false(),x,y) = 5/2x + 1 >= 5/2x + 1/2 = cond1(gr(x,0()),p(x),y)
      
      gr(0(),x) = 5/2x >= 0 = false()
      
      gr(s(x),0()) = 3x + 2 >= 1 = true()
      
      gr(s(x),s(y)) = 3x + 15/2y + 7 >= x + 5/2y = gr(x,y)
      
      p(0()) = 0 >= 0 = 0()
      
      p(s(x)) = 3/2x + 1 >= x = x
     problem:
      DPs:
       cond2#(false(),x,y) -> cond1#(gr(x,0()),p(x),y)
       cond2#(true(),x,y) -> cond2#(gr(y,0()),x,p(y))
      TRS:
       cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
       cond2(true(),x,y) -> cond2(gr(y,0()),x,p(y))
       cond2(false(),x,y) -> cond1(gr(x,0()),p(x),y)
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y)) -> gr(x,y)
       p(0()) -> 0()
       p(s(x)) -> x
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 5/4
      DPs:
       cond2#(true(),x,y) -> cond2#(gr(y,0()),x,p(y))
      TRS:
       cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
       cond2(true(),x,y) -> cond2(gr(y,0()),x,p(y))
       cond2(false(),x,y) -> cond1(gr(x,0()),p(x),y)
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y)) -> gr(x,y)
       p(0()) -> 0()
       p(s(x)) -> x
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [cond2#](x0, x1, x2) = 2x0 + 2x2,
        
        [s](x0) = 2x0 + 1,
        
        [false] = 0,
        
        [p](x0) = 1/2x0,
        
        [cond2](x0, x1, x2) = x2,
        
        [gr](x0, x1) = 1/2x0 + 2x1,
        
        [0] = 0,
        
        [cond1](x0, x1, x2) = x2,
        
        [true] = 1/2
       orientation:
        cond2#(true(),x,y) = 2y + 1 >= 2y = cond2#(gr(y,0()),x,p(y))
        
        cond1(true(),x,y) = y >= y = cond2(gr(y,0()),x,y)
        
        cond2(true(),x,y) = y >= 1/2y = cond2(gr(y,0()),x,p(y))
        
        cond2(false(),x,y) = y >= y = cond1(gr(x,0()),p(x),y)
        
        gr(0(),x) = 2x >= 0 = false()
        
        gr(s(x),0()) = x + 1/2 >= 1/2 = true()
        
        gr(s(x),s(y)) = x + 4y + 5/2 >= 1/2x + 2y = gr(x,y)
        
        p(0()) = 0 >= 0 = 0()
        
        p(s(x)) = x + 1/2 >= x = x
       problem:
        DPs:
         
        TRS:
         cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
         cond2(true(),x,y) -> cond2(gr(y,0()),x,p(y))
         cond2(false(),x,y) -> cond1(gr(x,0()),p(x),y)
         gr(0(),x) -> false()
         gr(s(x),0()) -> true()
         gr(s(x),s(y)) -> gr(x,y)
         p(0()) -> 0()
         p(s(x)) -> x
       Qed
    
    DPs:
     gr#(s(x),s(y)) -> gr#(x,y)
    TRS:
     cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
     cond2(true(),x,y) -> cond2(gr(y,0()),x,p(y))
     cond2(false(),x,y) -> cond1(gr(x,0()),p(x),y)
     gr(0(),x) -> false()
     gr(s(x),0()) -> true()
     gr(s(x),s(y)) -> gr(x,y)
     p(0()) -> 0()
     p(s(x)) -> x
    Subterm Criterion Processor:
     simple projection:
      pi(gr#) = 1
     problem:
      DPs:
       
      TRS:
       cond1(true(),x,y) -> cond2(gr(y,0()),x,y)
       cond2(true(),x,y) -> cond2(gr(y,0()),x,p(y))
       cond2(false(),x,y) -> cond1(gr(x,0()),p(x),y)
       gr(0(),x) -> false()
       gr(s(x),0()) -> true()
       gr(s(x),s(y)) -> gr(x,y)
       p(0()) -> 0()
       p(s(x)) -> x
     Qed