YES

Problem:
 plus(x,0()) -> x
 plus(x,s(y)) -> s(plus(x,y))
 d(0()) -> 0()
 d(s(x)) -> s(s(d(x)))
 q(0()) -> 0()
 q(s(x)) -> s(plus(q(x),d(x)))

Proof:
 DP Processor:
  DPs:
   plus#(x,s(y)) -> plus#(x,y)
   d#(s(x)) -> d#(x)
   q#(s(x)) -> d#(x)
   q#(s(x)) -> q#(x)
   q#(s(x)) -> plus#(q(x),d(x))
  TRS:
   plus(x,0()) -> x
   plus(x,s(y)) -> s(plus(x,y))
   d(0()) -> 0()
   d(s(x)) -> s(s(d(x)))
   q(0()) -> 0()
   q(s(x)) -> s(plus(q(x),d(x)))
  Matrix Interpretation Processor: dim=1
   
   usable rules:
    d(0()) -> 0()
    d(s(x)) -> s(s(d(x)))
   interpretation:
    [q#](x0) = 3x0 + 4,
    
    [d#](x0) = 3x0 + 4,
    
    [plus#](x0, x1) = x1,
    
    [q](x0) = 5x0 + 1,
    
    [d](x0) = 3x0,
    
    [s](x0) = x0 + 1,
    
    [plus](x0, x1) = 4x1 + 2,
    
    [0] = 3
   orientation:
    plus#(x,s(y)) = y + 1 >= y = plus#(x,y)
    
    d#(s(x)) = 3x + 7 >= 3x + 4 = d#(x)
    
    q#(s(x)) = 3x + 7 >= 3x + 4 = d#(x)
    
    q#(s(x)) = 3x + 7 >= 3x + 4 = q#(x)
    
    q#(s(x)) = 3x + 7 >= 3x = plus#(q(x),d(x))
    
    plus(x,0()) = 14 >= x = x
    
    plus(x,s(y)) = 4y + 6 >= 4y + 3 = s(plus(x,y))
    
    d(0()) = 9 >= 3 = 0()
    
    d(s(x)) = 3x + 3 >= 3x + 2 = s(s(d(x)))
    
    q(0()) = 16 >= 3 = 0()
    
    q(s(x)) = 5x + 6 >= 12x + 3 = s(plus(q(x),d(x)))
   problem:
    DPs:
     
    TRS:
     plus(x,0()) -> x
     plus(x,s(y)) -> s(plus(x,y))
     d(0()) -> 0()
     d(s(x)) -> s(s(d(x)))
     q(0()) -> 0()
     q(s(x)) -> s(plus(q(x),d(x)))
   Qed