YES

Problem:
 cond(true(),x,y) -> cond(and(gr(x,0()),gr(y,0())),p(x),p(y))
 and(true(),true()) -> true()
 and(x,false()) -> false()
 and(false(),x) -> false()
 gr(0(),0()) -> false()
 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:
   cond#(true(),x,y) -> p#(y)
   cond#(true(),x,y) -> p#(x)
   cond#(true(),x,y) -> gr#(y,0())
   cond#(true(),x,y) -> gr#(x,0())
   cond#(true(),x,y) -> and#(gr(x,0()),gr(y,0()))
   cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
   gr#(s(x),s(y)) -> gr#(x,y)
  TRS:
   cond(true(),x,y) -> cond(and(gr(x,0()),gr(y,0())),p(x),p(y))
   and(true(),true()) -> true()
   and(x,false()) -> false()
   and(false(),x) -> false()
   gr(0(),0()) -> false()
   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:
    cond#(true(),x,y) -> p#(y)
    cond#(true(),x,y) -> p#(x)
    cond#(true(),x,y) -> gr#(y,0())
    cond#(true(),x,y) -> gr#(x,0())
    cond#(true(),x,y) -> and#(gr(x,0()),gr(y,0()))
    cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
    gr#(s(x),s(y)) -> gr#(x,y)
   TRS:
    cond(true(),x,y) -> cond(and(gr(x,0()),gr(y,0())),p(x),p(y))
    and(true(),true()) -> true()
    and(x,false()) -> false()
    and(false(),x) -> false()
    gr(0(),0()) -> false()
    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:
    gr#(s(x),s(y)) -> gr#(x,y) -> gr#(s(x),s(y)) -> gr#(x,y)
    cond#(true(),x,y) -> gr#(y,0()) -> gr#(s(x),s(y)) -> gr#(x,y)
    cond#(true(),x,y) -> gr#(x,0()) ->
    gr#(s(x),s(y)) -> gr#(x,y)
    cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y)) ->
    cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
    cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y)) ->
    cond#(true(),x,y) -> and#(gr(x,0()),gr(y,0()))
    cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y)) ->
    cond#(true(),x,y) -> gr#(x,0())
    cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y)) ->
    cond#(true(),x,y) -> gr#(y,0())
    cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y)) ->
    cond#(true(),x,y) -> p#(x)
    cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y)) -> 
    cond#(true(),x,y) -> p#(y)
   EDG Processor:
    DPs:
     cond#(true(),x,y) -> p#(y)
     cond#(true(),x,y) -> p#(x)
     cond#(true(),x,y) -> gr#(y,0())
     cond#(true(),x,y) -> gr#(x,0())
     cond#(true(),x,y) -> and#(gr(x,0()),gr(y,0()))
     cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
     gr#(s(x),s(y)) -> gr#(x,y)
    TRS:
     cond(true(),x,y) -> cond(and(gr(x,0()),gr(y,0())),p(x),p(y))
     and(true(),true()) -> true()
     and(x,false()) -> false()
     and(false(),x) -> false()
     gr(0(),0()) -> false()
     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:
     gr#(s(x),s(y)) -> gr#(x,y) ->
     gr#(s(x),s(y)) -> gr#(x,y)
     cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y)) ->
     cond#(true(),x,y) -> p#(y)
     cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y)) ->
     cond#(true(),x,y) -> p#(x)
     cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y)) ->
     cond#(true(),x,y) -> gr#(y,0())
     cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y)) ->
     cond#(true(),x,y) -> gr#(x,0())
     cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y)) ->
     cond#(true(),x,y) -> and#(gr(x,0()),gr(y,0()))
     cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y)) ->
     cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
    SCC Processor:
     #sccs: 2
     #rules: 2
     #arcs: 7/49
     DPs:
      cond#(true(),x,y) -> cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
     TRS:
      cond(true(),x,y) -> cond(and(gr(x,0()),gr(y,0())),p(x),p(y))
      and(true(),true()) -> true()
      and(x,false()) -> false()
      and(false(),x) -> false()
      gr(0(),0()) -> false()
      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:
       [cond#](x0, x1, x2) = x0 + 2x2,
       
       [s](x0) = 2x0 + 1,
       
       [false] = 0,
       
       [p](x0) = 1/2x0,
       
       [and](x0, x1) = 2x1,
       
       [gr](x0, x1) = 1/2x0,
       
       [0] = 0,
       
       [cond](x0, x1, x2) = x0 + x1 + 2x2,
       
       [true] = 1/2
      orientation:
       cond#(true(),x,y) = 2y + 1/2 >= 2y = cond#(and(gr(x,0()),gr(y,0())),p(x),p(y))
       
       cond(true(),x,y) = x + 2y + 1/2 >= 1/2x + 2y = cond(and(gr(x,0()),gr(y,0())),p(x),p(y))
       
       and(true(),true()) = 1 >= 1/2 = true()
       
       and(x,false()) = 0 >= 0 = false()
       
       and(false(),x) = 2x >= 0 = false()
       
       gr(0(),0()) = 0 >= 0 = false()
       
       gr(0(),x) = 0 >= 0 = false()
       
       gr(s(x),0()) = x + 1/2 >= 1/2 = true()
       
       gr(s(x),s(y)) = x + 1/2 >= 1/2x = gr(x,y)
       
       p(0()) = 0 >= 0 = 0()
       
       p(s(x)) = x + 1/2 >= x = x
      problem:
       DPs:
        
       TRS:
        cond(true(),x,y) -> cond(and(gr(x,0()),gr(y,0())),p(x),p(y))
        and(true(),true()) -> true()
        and(x,false()) -> false()
        and(false(),x) -> false()
        gr(0(),0()) -> false()
        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:
      cond(true(),x,y) -> cond(and(gr(x,0()),gr(y,0())),p(x),p(y))
      and(true(),true()) -> true()
      and(x,false()) -> false()
      and(false(),x) -> false()
      gr(0(),0()) -> false()
      gr(0(),x) -> false()
      gr(s(x),0()) -> true()
      gr(s(x),s(y)) -> gr(x,y)
      p(0()) -> 0()
      p(s(x)) -> x
     KBO Processor:
      argument filtering:
       pi(true) = []
       pi(cond) = 1
       pi(0) = []
       pi(gr) = [1]
       pi(and) = [1]
       pi(p) = 0
       pi(false) = []
       pi(s) = [0]
       pi(gr#) = 0
      weight function:
       w0 = 1
       w(gr#) = w(false) = w(and) = w(0) = w(cond) = w(true) = 1
       w(s) = w(p) = w(gr) = 0
      precedence:
       s ~ and ~ gr ~ 0 ~ cond > gr# ~ false ~ p ~ true
      problem:
       DPs:
        
       TRS:
        cond(true(),x,y) -> cond(and(gr(x,0()),gr(y,0())),p(x),p(y))
        and(true(),true()) -> true()
        and(x,false()) -> false()
        and(false(),x) -> false()
        gr(0(),0()) -> false()
        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