YES

Problem:
 le(0(),y) -> true()
 le(s(x),0()) -> false()
 le(s(x),s(y)) -> le(x,y)
 minus(0(),y) -> 0()
 minus(s(x),y) -> if_minus(le(s(x),y),s(x),y)
 if_minus(true(),s(x),y) -> 0()
 if_minus(false(),s(x),y) -> s(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#(s(x),y) -> le#(s(x),y)
   minus#(s(x),y) -> if_minus#(le(s(x),y),s(x),y)
   if_minus#(false(),s(x),y) -> 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)
   minus(0(),y) -> 0()
   minus(s(x),y) -> if_minus(le(s(x),y),s(x),y)
   if_minus(true(),s(x),y) -> 0()
   if_minus(false(),s(x),y) -> s(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)
  Usable Rule Processor:
   DPs:
    le#(s(x),s(y)) -> le#(x,y)
    minus#(s(x),y) -> le#(s(x),y)
    minus#(s(x),y) -> if_minus#(le(s(x),y),s(x),y)
    if_minus#(false(),s(x),y) -> 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(s(x),0()) -> false()
    le(s(x),s(y)) -> le(x,y)
    le(0(),y) -> true()
    minus(0(),y) -> 0()
    minus(s(x),y) -> if_minus(le(s(x),y),s(x),y)
    if_minus(true(),s(x),y) -> 0()
    if_minus(false(),s(x),y) -> s(minus(x,y))
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     minus(0(),y) -> 0()
     minus(s(x),y) -> if_minus(le(s(x),y),s(x),y)
     if_minus(true(),s(x),y) -> 0()
     if_minus(false(),s(x),y) -> s(minus(x,y))
    interpretation:
     [if_mod#](x0, x1, x2) = 2x1 + x2,
     
     [mod#](x0, x1) = 2x0 + x1 + 5,
     
     [if_minus#](x0, x1, x2) = x1 + 2,
     
     [minus#](x0, x1) = x0 + 3,
     
     [le#](x0, x1) = x0,
     
     [if_minus](x0, x1, x2) = x1,
     
     [minus](x0, x1) = x0,
     
     [false] = 0,
     
     [s](x0) = x0 + 4,
     
     [true] = 0,
     
     [le](x0, x1) = 0,
     
     [0] = 0
    orientation:
     le#(s(x),s(y)) = x + 4 >= x = le#(x,y)
     
     minus#(s(x),y) = x + 7 >= x + 4 = le#(s(x),y)
     
     minus#(s(x),y) = x + 7 >= x + 6 = if_minus#(le(s(x),y),s(x),y)
     
     if_minus#(false(),s(x),y) = x + 6 >= x + 3 = minus#(x,y)
     
     mod#(s(x),s(y)) = 2x + y + 17 >= y = le#(y,x)
     
     mod#(s(x),s(y)) = 2x + y + 17 >= 2x + y + 12 = if_mod#(le(y,x),s(x),s(y))
     
     if_mod#(true(),s(x),s(y)) = 2x + y + 12 >= x + 3 = minus#(x,y)
     
     if_mod#(true(),s(x),s(y)) = 2x + y + 12 >= 2x + y + 9 = mod#(minus(x,y),s(y))
     
     le(s(x),0()) = 0 >= 0 = false()
     
     le(s(x),s(y)) = 0 >= 0 = le(x,y)
     
     le(0(),y) = 0 >= 0 = true()
     
     minus(0(),y) = 0 >= 0 = 0()
     
     minus(s(x),y) = x + 4 >= x + 4 = if_minus(le(s(x),y),s(x),y)
     
     if_minus(true(),s(x),y) = x + 4 >= 0 = 0()
     
     if_minus(false(),s(x),y) = x + 4 >= x + 4 = s(minus(x,y))
    problem:
     DPs:
      
     TRS:
      le(s(x),0()) -> false()
      le(s(x),s(y)) -> le(x,y)
      le(0(),y) -> true()
      minus(0(),y) -> 0()
      minus(s(x),y) -> if_minus(le(s(x),y),s(x),y)
      if_minus(true(),s(x),y) -> 0()
      if_minus(false(),s(x),y) -> s(minus(x,y))
    Qed