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)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [if_mod#](x0, x1, x2) = x1 + x2,
    
    [mod#](x0, x1) = 2x0 + x1,
    
    [if_minus#](x0, x1, x2) = x1,
    
    [minus#](x0, x1) = 2x0,
    
    [le#](x0, x1) = x0,
    
    [if_mod](x0, x1, x2) = 2x1,
    
    [mod](x0, x1) = 2x0 + 1/2,
    
    [if_minus](x0, x1, x2) = x1,
    
    [minus](x0, x1) = x0,
    
    [false] = 0,
    
    [s](x0) = 5/2x0 + 1/2,
    
    [true] = 0,
    
    [le](x0, x1) = 0,
    
    [0] = 0
   orientation:
    le#(s(x),s(y)) = 5/2x + 1/2 >= x = le#(x,y)
    
    minus#(s(x),y) = 5x + 1 >= 5/2x + 1/2 = le#(s(x),y)
    
    minus#(s(x),y) = 5x + 1 >= 5/2x + 1/2 = if_minus#(le(s(x),y),s(x),y)
    
    if_minus#(false(),s(x),y) = 5/2x + 1/2 >= 2x = minus#(x,y)
    
    mod#(s(x),s(y)) = 5x + 5/2y + 3/2 >= y = le#(y,x)
    
    mod#(s(x),s(y)) = 5x + 5/2y + 3/2 >= 5/2x + 5/2y + 1 = if_mod#(le(y,x),s(x),s(y))
    
    if_mod#(true(),s(x),s(y)) = 5/2x + 5/2y + 1 >= 2x = minus#(x,y)
    
    if_mod#(true(),s(x),s(y)) = 5/2x + 5/2y + 1 >= 2x + 5/2y + 1/2 = mod#(minus(x,y),s(y))
    
    le(0(),y) = 0 >= 0 = true()
    
    le(s(x),0()) = 0 >= 0 = false()
    
    le(s(x),s(y)) = 0 >= 0 = le(x,y)
    
    minus(0(),y) = 0 >= 0 = 0()
    
    minus(s(x),y) = 5/2x + 1/2 >= 5/2x + 1/2 = if_minus(le(s(x),y),s(x),y)
    
    if_minus(true(),s(x),y) = 5/2x + 1/2 >= 0 = 0()
    
    if_minus(false(),s(x),y) = 5/2x + 1/2 >= 5/2x + 1/2 = s(minus(x,y))
    
    mod(0(),y) = 1/2 >= 0 = 0()
    
    mod(s(x),0()) = 5x + 3/2 >= 0 = 0()
    
    mod(s(x),s(y)) = 5x + 3/2 >= 5x + 1 = if_mod(le(y,x),s(x),s(y))
    
    if_mod(true(),s(x),s(y)) = 5x + 1 >= 2x + 1/2 = mod(minus(x,y),s(y))
    
    if_mod(false(),s(x),s(y)) = 5x + 1 >= 5/2x + 1/2 = s(x)
   problem:
    DPs:
     
    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)
   Qed