YES

Problem:
 prime(0()) -> false()
 prime(s(0())) -> false()
 prime(s(s(x))) -> prime1(s(s(x)),s(x))
 prime1(x,0()) -> false()
 prime1(x,s(0())) -> true()
 prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y)))
 divp(x,y) -> =(rem(x,y),0())

Proof:
 DP Processor:
  DPs:
   prime#(s(s(x))) -> prime1#(s(s(x)),s(x))
   prime1#(x,s(s(y))) -> prime1#(x,s(y))
   prime1#(x,s(s(y))) -> divp#(s(s(y)),x)
  TRS:
   prime(0()) -> false()
   prime(s(0())) -> false()
   prime(s(s(x))) -> prime1(s(s(x)),s(x))
   prime1(x,0()) -> false()
   prime1(x,s(0())) -> true()
   prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y)))
   divp(x,y) -> =(rem(x,y),0())
  Usable Rule Processor:
   DPs:
    prime#(s(s(x))) -> prime1#(s(s(x)),s(x))
    prime1#(x,s(s(y))) -> prime1#(x,s(y))
    prime1#(x,s(s(y))) -> divp#(s(s(y)),x)
   TRS:
    f14(x,y) -> x
    f14(x,y) -> y
   EDG Processor:
    DPs:
     prime#(s(s(x))) -> prime1#(s(s(x)),s(x))
     prime1#(x,s(s(y))) -> prime1#(x,s(y))
     prime1#(x,s(s(y))) -> divp#(s(s(y)),x)
    TRS:
     f14(x,y) -> x
     f14(x,y) -> y
    graph:
     prime1#(x,s(s(y))) -> prime1#(x,s(y)) ->
     prime1#(x,s(s(y))) -> prime1#(x,s(y))
     prime1#(x,s(s(y))) -> prime1#(x,s(y)) ->
     prime1#(x,s(s(y))) -> divp#(s(s(y)),x)
     prime#(s(s(x))) -> prime1#(s(s(x)),s(x)) ->
     prime1#(x,s(s(y))) -> prime1#(x,s(y))
     prime#(s(s(x))) -> prime1#(s(s(x)),s(x)) -> prime1#(x,s(s(y))) -> divp#(s(s(y)),x)
    Restore Modifier:
     DPs:
      prime#(s(s(x))) -> prime1#(s(s(x)),s(x))
      prime1#(x,s(s(y))) -> prime1#(x,s(y))
      prime1#(x,s(s(y))) -> divp#(s(s(y)),x)
     TRS:
      prime(0()) -> false()
      prime(s(0())) -> false()
      prime(s(s(x))) -> prime1(s(s(x)),s(x))
      prime1(x,0()) -> false()
      prime1(x,s(0())) -> true()
      prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y)))
      divp(x,y) -> =(rem(x,y),0())
     SCC Processor:
      #sccs: 1
      #rules: 1
      #arcs: 4/9
      DPs:
       prime1#(x,s(s(y))) -> prime1#(x,s(y))
      TRS:
       prime(0()) -> false()
       prime(s(0())) -> false()
       prime(s(s(x))) -> prime1(s(s(x)),s(x))
       prime1(x,0()) -> false()
       prime1(x,s(0())) -> true()
       prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y)))
       divp(x,y) -> =(rem(x,y),0())
      Matrix Interpretation Processor:
       dimension: 1
       interpretation:
        [prime1#](x0, x1) = x1,
        
        [=](x0, x1) = 0,
        
        [rem](x0, x1) = 0,
        
        [and](x0, x1) = 0,
        
        [not](x0) = 0,
        
        [divp](x0, x1) = 1,
        
        [true] = 1,
        
        [prime1](x0, x1) = x0 + 1,
        
        [s](x0) = x0 + 1,
        
        [false] = 0,
        
        [prime](x0) = x0 + 1,
        
        [0] = 1
       orientation:
        prime1#(x,s(s(y))) = y + 2 >= y + 1 = prime1#(x,s(y))
        
        prime(0()) = 2 >= 0 = false()
        
        prime(s(0())) = 3 >= 0 = false()
        
        prime(s(s(x))) = x + 3 >= x + 3 = prime1(s(s(x)),s(x))
        
        prime1(x,0()) = x + 1 >= 0 = false()
        
        prime1(x,s(0())) = x + 1 >= 1 = true()
        
        prime1(x,s(s(y))) = x + 1 >= 0 = and(not(divp(s(s(y)),x)),prime1(x,s(y)))
        
        divp(x,y) = 1 >= 0 = =(rem(x,y),0())
       problem:
        DPs:
         
        TRS:
         prime(0()) -> false()
         prime(s(0())) -> false()
         prime(s(s(x))) -> prime1(s(s(x)),s(x))
         prime1(x,0()) -> false()
         prime1(x,s(0())) -> true()
         prime1(x,s(s(y))) -> and(not(divp(s(s(y)),x)),prime1(x,s(y)))
         divp(x,y) -> =(rem(x,y),0())
       Qed