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)))
  TDG 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)))
   graph:
    q#(s(x)) -> q#(x) -> q#(s(x)) -> plus#(q(x),d(x))
    q#(s(x)) -> q#(x) -> q#(s(x)) -> q#(x)
    q#(s(x)) -> q#(x) -> q#(s(x)) -> d#(x)
    q#(s(x)) -> d#(x) -> d#(s(x)) -> d#(x)
    q#(s(x)) -> plus#(q(x),d(x)) -> plus#(x,s(y)) -> plus#(x,y)
    d#(s(x)) -> d#(x) -> d#(s(x)) -> d#(x)
    plus#(x,s(y)) -> plus#(x,y) -> plus#(x,s(y)) -> plus#(x,y)
   SCC Processor:
    #sccs: 3
    #rules: 3
    #arcs: 7/25
    DPs:
     q#(s(x)) -> q#(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)))
    LPO Processor:
     argument filtering:
      pi(0) = []
      pi(plus) = [0,1]
      pi(s) = [0]
      pi(d) = [0]
      pi(q) = [0]
      pi(q#) = 0
     precedence:
      q > plus > d > q# ~ s ~ 0
     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
    
    DPs:
     plus#(x,s(y)) -> plus#(x,y)
    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)))
    LPO Processor:
     argument filtering:
      pi(0) = []
      pi(plus) = [0,1]
      pi(s) = [0]
      pi(d) = [0]
      pi(q) = [0]
      pi(plus#) = 1
     precedence:
      q > plus > d > plus# ~ s ~ 0
     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
    
    DPs:
     d#(s(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)))
    LPO Processor:
     argument filtering:
      pi(0) = []
      pi(plus) = [0,1]
      pi(s) = [0]
      pi(d) = [0]
      pi(q) = [0]
      pi(d#) = 0
     precedence:
      q > plus > d > d# ~ s ~ 0
     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