YES

Problem:
 cond(true(),x,y,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
 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,z) -> p#(y)
   cond#(true(),x,y,z) -> p#(x)
   cond#(true(),x,y,z) -> gr#(y,z)
   cond#(true(),x,y,z) -> gr#(x,z)
   cond#(true(),x,y,z) -> and#(gr(x,z),gr(y,z))
   cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z)
   gr#(s(x),s(y)) -> gr#(x,y)
  TRS:
   cond(true(),x,y,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
   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,z) -> p#(y)
    cond#(true(),x,y,z) -> p#(x)
    cond#(true(),x,y,z) -> gr#(y,z)
    cond#(true(),x,y,z) -> gr#(x,z)
    cond#(true(),x,y,z) -> and#(gr(x,z),gr(y,z))
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z)
    gr#(s(x),s(y)) -> gr#(x,y)
   TRS:
    cond(true(),x,y,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
    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,z) -> gr#(y,z) -> gr#(s(x),s(y)) -> gr#(x,y)
    cond#(true(),x,y,z) -> gr#(x,z) ->
    gr#(s(x),s(y)) -> gr#(x,y)
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z) ->
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z)
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z) ->
    cond#(true(),x,y,z) -> and#(gr(x,z),gr(y,z))
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z) ->
    cond#(true(),x,y,z) -> gr#(x,z)
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z) ->
    cond#(true(),x,y,z) -> gr#(y,z)
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z) ->
    cond#(true(),x,y,z) -> p#(x)
    cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z) -> 
    cond#(true(),x,y,z) -> p#(y)
   SCC Processor:
    #sccs: 2
    #rules: 2
    #arcs: 9/49
    DPs:
     cond#(true(),x,y,z) -> cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z)
    TRS:
     cond(true(),x,y,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
     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
    Arctic Interpretation Processor:
     dimension: 1
     interpretation:
      [cond#](x0, x1, x2, x3) = x0 + -1x1 + -1x2 + 0,
      
      [s](x0) = 8x0 + 11,
      
      [0] = 0,
      
      [false] = 0,
      
      [p](x0) = -7x0 + 4,
      
      [and](x0, x1) = x0 + x1 + 0,
      
      [gr](x0, x1) = -7x0 + 0,
      
      [cond](x0, x1, x2, x3) = 15x3,
      
      [true] = 4
     orientation:
      cond#(true(),x,y,z) = -1x + -1y + 4 >= -7x + -7y + 3 = cond#(and(gr(x,z),gr(y,z)),p(x),p(y),z)
      
      cond(true(),x,y,z) = 15z >= 15z = cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
      
      and(true(),true()) = 4 >= 4 = true()
      
      and(x,false()) = x + 0 >= 0 = false()
      
      and(false(),x) = x + 0 >= 0 = false()
      
      gr(0(),0()) = 0 >= 0 = false()
      
      gr(0(),x) = 0 >= 0 = false()
      
      gr(s(x),0()) = 1x + 4 >= 4 = true()
      
      gr(s(x),s(y)) = 1x + 4 >= -7x + 0 = gr(x,y)
      
      p(0()) = 4 >= 0 = 0()
      
      p(s(x)) = 1x + 4 >= x = x
     problem:
      DPs:
       
      TRS:
       cond(true(),x,y,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
       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,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
     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
    Subterm Criterion Processor:
     simple projection:
      pi(gr#) = 1
     problem:
      DPs:
       
      TRS:
       cond(true(),x,y,z) -> cond(and(gr(x,z),gr(y,z)),p(x),p(y),z)
       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