YES

Problem:
 int(0(),0()) -> .(0(),nil())
 int(0(),s(y)) -> .(0(),int(s(0()),s(y)))
 int(s(x),0()) -> nil()
 int(s(x),s(y)) -> int_list(int(x,y))
 int_list(nil()) -> nil()
 int_list(.(x,y)) -> .(s(x),int_list(y))

Proof:
 DP Processor:
  DPs:
   int#(0(),s(y)) -> int#(s(0()),s(y))
   int#(s(x),s(y)) -> int#(x,y)
   int#(s(x),s(y)) -> int_list#(int(x,y))
   int_list#(.(x,y)) -> int_list#(y)
  TRS:
   int(0(),0()) -> .(0(),nil())
   int(0(),s(y)) -> .(0(),int(s(0()),s(y)))
   int(s(x),0()) -> nil()
   int(s(x),s(y)) -> int_list(int(x,y))
   int_list(nil()) -> nil()
   int_list(.(x,y)) -> .(s(x),int_list(y))
  EDG Processor:
   DPs:
    int#(0(),s(y)) -> int#(s(0()),s(y))
    int#(s(x),s(y)) -> int#(x,y)
    int#(s(x),s(y)) -> int_list#(int(x,y))
    int_list#(.(x,y)) -> int_list#(y)
   TRS:
    int(0(),0()) -> .(0(),nil())
    int(0(),s(y)) -> .(0(),int(s(0()),s(y)))
    int(s(x),0()) -> nil()
    int(s(x),s(y)) -> int_list(int(x,y))
    int_list(nil()) -> nil()
    int_list(.(x,y)) -> .(s(x),int_list(y))
   graph:
    int_list#(.(x,y)) -> int_list#(y) ->
    int_list#(.(x,y)) -> int_list#(y)
    int#(s(x),s(y)) -> int_list#(int(x,y)) ->
    int_list#(.(x,y)) -> int_list#(y)
    int#(s(x),s(y)) -> int#(x,y) -> int#(0(),s(y)) -> int#(s(0()),s(y))
    int#(s(x),s(y)) -> int#(x,y) -> int#(s(x),s(y)) -> int#(x,y)
    int#(s(x),s(y)) -> int#(x,y) ->
    int#(s(x),s(y)) -> int_list#(int(x,y))
    int#(0(),s(y)) -> int#(s(0()),s(y)) ->
    int#(s(x),s(y)) -> int#(x,y)
    int#(0(),s(y)) -> int#(s(0()),s(y)) -> int#(s(x),s(y)) -> int_list#(int(x,y))
   SCC Processor:
    #sccs: 2
    #rules: 3
    #arcs: 7/16
    DPs:
     int#(s(x),s(y)) -> int#(x,y)
     int#(0(),s(y)) -> int#(s(0()),s(y))
    TRS:
     int(0(),0()) -> .(0(),nil())
     int(0(),s(y)) -> .(0(),int(s(0()),s(y)))
     int(s(x),0()) -> nil()
     int(s(x),s(y)) -> int_list(int(x,y))
     int_list(nil()) -> nil()
     int_list(.(x,y)) -> .(s(x),int_list(y))
    Subterm Criterion Processor:
     simple projection:
      pi(int#) = 1
     problem:
      DPs:
       int#(0(),s(y)) -> int#(s(0()),s(y))
      TRS:
       int(0(),0()) -> .(0(),nil())
       int(0(),s(y)) -> .(0(),int(s(0()),s(y)))
       int(s(x),0()) -> nil()
       int(s(x),s(y)) -> int_list(int(x,y))
       int_list(nil()) -> nil()
       int_list(.(x,y)) -> .(s(x),int_list(y))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [int#](x0, x1) = x0,
       
       [int_list](x0) = 1,
       
       [s](x0) = 0,
       
       [.](x0, x1) = 0,
       
       [nil] = 0,
       
       [int](x0, x1) = x1 + 1,
       
       [0] = 1
      orientation:
       int#(0(),s(y)) = 1 >= 0 = int#(s(0()),s(y))
       
       int(0(),0()) = 2 >= 0 = .(0(),nil())
       
       int(0(),s(y)) = 1 >= 0 = .(0(),int(s(0()),s(y)))
       
       int(s(x),0()) = 2 >= 0 = nil()
       
       int(s(x),s(y)) = 1 >= 1 = int_list(int(x,y))
       
       int_list(nil()) = 1 >= 0 = nil()
       
       int_list(.(x,y)) = 1 >= 0 = .(s(x),int_list(y))
      problem:
       DPs:
        
       TRS:
        int(0(),0()) -> .(0(),nil())
        int(0(),s(y)) -> .(0(),int(s(0()),s(y)))
        int(s(x),0()) -> nil()
        int(s(x),s(y)) -> int_list(int(x,y))
        int_list(nil()) -> nil()
        int_list(.(x,y)) -> .(s(x),int_list(y))
      Qed
    
    DPs:
     int_list#(.(x,y)) -> int_list#(y)
    TRS:
     int(0(),0()) -> .(0(),nil())
     int(0(),s(y)) -> .(0(),int(s(0()),s(y)))
     int(s(x),0()) -> nil()
     int(s(x),s(y)) -> int_list(int(x,y))
     int_list(nil()) -> nil()
     int_list(.(x,y)) -> .(s(x),int_list(y))
    Subterm Criterion Processor:
     simple projection:
      pi(int_list#) = 0
     problem:
      DPs:
       
      TRS:
       int(0(),0()) -> .(0(),nil())
       int(0(),s(y)) -> .(0(),int(s(0()),s(y)))
       int(s(x),0()) -> nil()
       int(s(x),s(y)) -> int_list(int(x,y))
       int_list(nil()) -> nil()
       int_list(.(x,y)) -> .(s(x),int_list(y))
     Qed