YES

Problem:
 le(0(),y) -> true()
 le(s(x),0()) -> false()
 le(s(x),s(y)) -> le(x,y)
 pred(s(x)) -> x
 minus(x,0()) -> x
 minus(x,s(y)) -> pred(minus(x,y))
 mod(0(),y) -> 0()
 mod(s(x),0()) -> 0()
 mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
 if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
 if_mod(false(),s(x),s(y)) -> s(x)

Proof:
 DP Processor:
  DPs:
   le#(s(x),s(y)) -> le#(x,y)
   minus#(x,s(y)) -> minus#(x,y)
   minus#(x,s(y)) -> pred#(minus(x,y))
   mod#(s(x),s(y)) -> le#(y,x)
   mod#(s(x),s(y)) -> if_mod#(le(y,x),s(x),s(y))
   if_mod#(true(),s(x),s(y)) -> minus#(x,y)
   if_mod#(true(),s(x),s(y)) -> mod#(minus(x,y),s(y))
  TRS:
   le(0(),y) -> true()
   le(s(x),0()) -> false()
   le(s(x),s(y)) -> le(x,y)
   pred(s(x)) -> x
   minus(x,0()) -> x
   minus(x,s(y)) -> pred(minus(x,y))
   mod(0(),y) -> 0()
   mod(s(x),0()) -> 0()
   mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
   if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
   if_mod(false(),s(x),s(y)) -> s(x)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [if_mod#](x0, x1, x2) = x1 + x2 + 4,
    
    [mod#](x0, x1) = 2x0 + x1 + 1,
    
    [minus#](x0, x1) = 2x0 + x1 + 2,
    
    [pred#](x0) = 2x0,
    
    [le#](x0, x1) = 2x1 + 4,
    
    [if_mod](x0, x1, x2) = x0 + x1 + 7,
    
    [mod](x0, x1) = 2x0 + 3,
    
    [minus](x0, x1) = x0 + 2,
    
    [pred](x0) = x0,
    
    [false] = 4,
    
    [s](x0) = 4x0 + 4,
    
    [true] = 0,
    
    [le](x0, x1) = 4x1,
    
    [0] = 1
   orientation:
    le#(s(x),s(y)) = 8y + 12 >= 2y + 4 = le#(x,y)
    
    minus#(x,s(y)) = 2x + 4y + 6 >= 2x + y + 2 = minus#(x,y)
    
    minus#(x,s(y)) = 2x + 4y + 6 >= 2x + 4 = pred#(minus(x,y))
    
    mod#(s(x),s(y)) = 8x + 4y + 13 >= 2x + 4 = le#(y,x)
    
    mod#(s(x),s(y)) = 8x + 4y + 13 >= 4x + 4y + 12 = if_mod#(le(y,x),s(x),s(y))
    
    if_mod#(true(),s(x),s(y)) = 4x + 4y + 12 >= 2x + y + 2 = minus#(x,y)
    
    if_mod#(true(),s(x),s(y)) = 4x + 4y + 12 >= 2x + 4y + 9 = mod#(minus(x,y),s(y))
    
    le(0(),y) = 4y >= 0 = true()
    
    le(s(x),0()) = 4 >= 4 = false()
    
    le(s(x),s(y)) = 16y + 16 >= 4y = le(x,y)
    
    pred(s(x)) = 4x + 4 >= x = x
    
    minus(x,0()) = x + 2 >= x = x
    
    minus(x,s(y)) = x + 2 >= x + 2 = pred(minus(x,y))
    
    mod(0(),y) = 5 >= 1 = 0()
    
    mod(s(x),0()) = 8x + 11 >= 1 = 0()
    
    mod(s(x),s(y)) = 8x + 11 >= 8x + 11 = if_mod(le(y,x),s(x),s(y))
    
    if_mod(true(),s(x),s(y)) = 4x + 11 >= 2x + 7 = mod(minus(x,y),s(y))
    
    if_mod(false(),s(x),s(y)) = 4x + 15 >= 4x + 4 = s(x)
   problem:
    DPs:
     
    TRS:
     le(0(),y) -> true()
     le(s(x),0()) -> false()
     le(s(x),s(y)) -> le(x,y)
     pred(s(x)) -> x
     minus(x,0()) -> x
     minus(x,s(y)) -> pred(minus(x,y))
     mod(0(),y) -> 0()
     mod(s(x),0()) -> 0()
     mod(s(x),s(y)) -> if_mod(le(y,x),s(x),s(y))
     if_mod(true(),s(x),s(y)) -> mod(minus(x,y),s(y))
     if_mod(false(),s(x),s(y)) -> s(x)
   Qed