YES

Problem:
 app(app(plus(),0()),y) -> y
 app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
 app(inc(),xs) -> app(app(map(),app(plus(),app(s(),0()))),xs)
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))

Proof:
 DP Processor:
  DPs:
   app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
   app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
   app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
   app#(inc(),xs) -> app#(s(),0())
   app#(inc(),xs) -> app#(plus(),app(s(),0()))
   app#(inc(),xs) -> app#(map(),app(plus(),app(s(),0())))
   app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
   app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
  TRS:
   app(app(plus(),0()),y) -> y
   app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
   app(inc(),xs) -> app(app(map(),app(plus(),app(s(),0()))),xs)
   app(app(map(),f),nil()) -> nil()
   app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
  EDG Processor:
   DPs:
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    app#(inc(),xs) -> app#(s(),0())
    app#(inc(),xs) -> app#(plus(),app(s(),0()))
    app#(inc(),xs) -> app#(map(),app(plus(),app(s(),0())))
    app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
   TRS:
    app(app(plus(),0()),y) -> y
    app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
    app(inc(),xs) -> app(app(map(),app(plus(),app(s(),0()))),xs)
    app(app(map(),f),nil()) -> nil()
    app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
   graph:
    app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(inc(),xs) -> app#(s(),0())
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(inc(),xs) -> app#(plus(),app(s(),0()))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(inc(),xs) -> app#(map(),app(plus(),app(s(),0())))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(cons(),app(f,x))
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x) ->
    app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(cons(),app(f,x)),app(app(map(),f),xs))
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(plus(),app(s(),x)),y) -> app#(plus(),x)
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y) ->
    app#(app(plus(),app(s(),x)),y) -> app#(s(),app(app(plus(),x),y))
   SCC Processor:
    #sccs: 2
    #rules: 4
    #arcs: 22/121
    DPs:
     app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs)
     app#(app(map(),f),app(app(cons(),x),xs)) -> app#(f,x)
     app#(app(map(),f),app(app(cons(),x),xs)) -> app#(app(map(),f),xs)
    TRS:
     app(app(plus(),0()),y) -> y
     app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
     app(inc(),xs) -> app(app(map(),app(plus(),app(s(),0()))),xs)
     app(app(map(),f),nil()) -> nil()
     app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
    Subterm Criterion Processor:
     simple projection:
      pi(app#) = 1
     problem:
      DPs:
       app#(inc(),xs) -> app#(app(map(),app(plus(),app(s(),0()))),xs)
      TRS:
       app(app(plus(),0()),y) -> y
       app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
       app(inc(),xs) -> app(app(map(),app(plus(),app(s(),0()))),xs)
       app(app(map(),f),nil()) -> nil()
       app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
     Matrix Interpretation Processor:
      dimension: 1
      interpretation:
       [app#](x0, x1) = x0,
       
       [cons] = 0,
       
       [nil] = 0,
       
       [map] = 0,
       
       [inc] = 1,
       
       [s] = 0,
       
       [app](x0, x1) = x1,
       
       [0] = 0,
       
       [plus] = 0
      orientation:
       app#(inc(),xs) = 1 >= 0 = app#(app(map(),app(plus(),app(s(),0()))),xs)
       
       app(app(plus(),0()),y) = y >= y = y
       
       app(app(plus(),app(s(),x)),y) = y >= y = app(s(),app(app(plus(),x),y))
       
       app(inc(),xs) = xs >= xs = app(app(map(),app(plus(),app(s(),0()))),xs)
       
       app(app(map(),f),nil()) = 0 >= 0 = nil()
       
       app(app(map(),f),app(app(cons(),x),xs)) = xs >= xs = app(app(cons(),app(f,x)),app(app(map(),f),xs))
      problem:
       DPs:
        
       TRS:
        app(app(plus(),0()),y) -> y
        app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
        app(inc(),xs) -> app(app(map(),app(plus(),app(s(),0()))),xs)
        app(app(map(),f),nil()) -> nil()
        app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
      Qed
    
    DPs:
     app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
    TRS:
     app(app(plus(),0()),y) -> y
     app(app(plus(),app(s(),x)),y) -> app(s(),app(app(plus(),x),y))
     app(inc(),xs) -> app(app(map(),app(plus(),app(s(),0()))),xs)
     app(app(map(),f),nil()) -> nil()
     app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
    Usable Rule Processor:
     DPs:
      app#(app(plus(),app(s(),x)),y) -> app#(app(plus(),x),y)
     TRS:
      
     Bounds Processor:
      bound: 1
      enrichment: match
      automaton:
       final states: {7}
       transitions:
        app{#,0}(5,5) -> 7*
        app{#,0}(6,6) -> 7*
        app{#,0}(5,6) -> 7*
        app{#,0}(6,5) -> 7*
        app0(5,5) -> 5*
        app0(6,6) -> 5*
        app0(5,6) -> 5*
        app0(6,5) -> 5*
        plus0() -> 5*
        s0() -> 6*
        app{#,1}(11,6) -> 7*
        app{#,1}(11,5) -> 7*
        app1(10,5) -> 11*
        app1(10,6) -> 11*
        plus1() -> 10*
      problem:
       DPs:
        
       TRS:
        
      Qed