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())
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [divp#](x0, x1) = 3x0,
    
    [prime1#](x0, x1) = 4x1,
    
    [prime#](x0) = 4x0,
    
    [=](x0, x1) = 0,
    
    [rem](x0, x1) = 0,
    
    [and](x0, x1) = 4x0 + 6,
    
    [not](x0) = 3,
    
    [divp](x0, x1) = 0,
    
    [true] = 0,
    
    [prime1](x0, x1) = 3x1 + 6,
    
    [s](x0) = x0 + 2,
    
    [false] = 0,
    
    [prime](x0) = 3x0,
    
    [0] = 0
   orientation:
    prime#(s(s(x))) = 4x + 16 >= 4x + 8 = prime1#(s(s(x)),s(x))
    
    prime1#(x,s(s(y))) = 4y + 16 >= 4y + 8 = prime1#(x,s(y))
    
    prime1#(x,s(s(y))) = 4y + 16 >= 3y + 12 = divp#(s(s(y)),x)
    
    prime(0()) = 0 >= 0 = false()
    
    prime(s(0())) = 6 >= 0 = false()
    
    prime(s(s(x))) = 3x + 12 >= 3x + 12 = prime1(s(s(x)),s(x))
    
    prime1(x,0()) = 6 >= 0 = false()
    
    prime1(x,s(0())) = 12 >= 0 = true()
    
    prime1(x,s(s(y))) = 3y + 18 >= 18 = and(not(divp(s(s(y)),x)),prime1(x,s(y)))
    
    divp(x,y) = 0 >= 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