MAYBE

Problem:
 a__f(X) -> cons(mark(X),f(g(X)))
 a__g(0()) -> s(0())
 a__g(s(X)) -> s(s(a__g(mark(X))))
 a__sel(0(),cons(X,Y)) -> mark(X)
 a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z))
 mark(f(X)) -> a__f(mark(X))
 mark(g(X)) -> a__g(mark(X))
 mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(0()) -> 0()
 mark(s(X)) -> s(mark(X))
 a__f(X) -> f(X)
 a__g(X) -> g(X)
 a__sel(X1,X2) -> sel(X1,X2)

Proof:
 DP Processor:
  DPs:
   a__f#(X) -> mark#(X)
   a__g#(s(X)) -> mark#(X)
   a__g#(s(X)) -> a__g#(mark(X))
   a__sel#(0(),cons(X,Y)) -> mark#(X)
   a__sel#(s(X),cons(Y,Z)) -> mark#(Z)
   a__sel#(s(X),cons(Y,Z)) -> mark#(X)
   a__sel#(s(X),cons(Y,Z)) -> a__sel#(mark(X),mark(Z))
   mark#(f(X)) -> mark#(X)
   mark#(f(X)) -> a__f#(mark(X))
   mark#(g(X)) -> mark#(X)
   mark#(g(X)) -> a__g#(mark(X))
   mark#(sel(X1,X2)) -> mark#(X2)
   mark#(sel(X1,X2)) -> mark#(X1)
   mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(s(X)) -> mark#(X)
  TRS:
   a__f(X) -> cons(mark(X),f(g(X)))
   a__g(0()) -> s(0())
   a__g(s(X)) -> s(s(a__g(mark(X))))
   a__sel(0(),cons(X,Y)) -> mark(X)
   a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z))
   mark(f(X)) -> a__f(mark(X))
   mark(g(X)) -> a__g(mark(X))
   mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(0()) -> 0()
   mark(s(X)) -> s(mark(X))
   a__f(X) -> f(X)
   a__g(X) -> g(X)
   a__sel(X1,X2) -> sel(X1,X2)
  ADG Processor:
   DPs:
    a__f#(X) -> mark#(X)
    a__g#(s(X)) -> mark#(X)
    a__g#(s(X)) -> a__g#(mark(X))
    a__sel#(0(),cons(X,Y)) -> mark#(X)
    a__sel#(s(X),cons(Y,Z)) -> mark#(Z)
    a__sel#(s(X),cons(Y,Z)) -> mark#(X)
    a__sel#(s(X),cons(Y,Z)) -> a__sel#(mark(X),mark(Z))
    mark#(f(X)) -> mark#(X)
    mark#(f(X)) -> a__f#(mark(X))
    mark#(g(X)) -> mark#(X)
    mark#(g(X)) -> a__g#(mark(X))
    mark#(sel(X1,X2)) -> mark#(X2)
    mark#(sel(X1,X2)) -> mark#(X1)
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X)
   TRS:
    a__f(X) -> cons(mark(X),f(g(X)))
    a__g(0()) -> s(0())
    a__g(s(X)) -> s(s(a__g(mark(X))))
    a__sel(0(),cons(X,Y)) -> mark(X)
    a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z))
    mark(f(X)) -> a__f(mark(X))
    mark(g(X)) -> a__g(mark(X))
    mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
    mark(cons(X1,X2)) -> cons(mark(X1),X2)
    mark(0()) -> 0()
    mark(s(X)) -> s(mark(X))
    a__f(X) -> f(X)
    a__g(X) -> g(X)
    a__sel(X1,X2) -> sel(X1,X2)
   graph:
    a__sel#(s(X),cons(Y,Z)) -> a__sel#(mark(X),mark(Z)) ->
    a__sel#(0(),cons(X,Y)) -> mark#(X)
    a__sel#(s(X),cons(Y,Z)) -> a__sel#(mark(X),mark(Z)) ->
    a__sel#(s(X),cons(Y,Z)) -> mark#(Z)
    a__sel#(s(X),cons(Y,Z)) -> a__sel#(mark(X),mark(Z)) ->
    a__sel#(s(X),cons(Y,Z)) -> mark#(X)
    a__sel#(s(X),cons(Y,Z)) -> a__sel#(mark(X),mark(Z)) ->
    a__sel#(s(X),cons(Y,Z)) -> a__sel#(mark(X),mark(Z))
    a__sel#(s(X),cons(Y,Z)) -> mark#(Z) ->
    mark#(f(X)) -> mark#(X)
    a__sel#(s(X),cons(Y,Z)) -> mark#(Z) ->
    mark#(f(X)) -> a__f#(mark(X))
    a__sel#(s(X),cons(Y,Z)) -> mark#(Z) ->
    mark#(g(X)) -> mark#(X)
    a__sel#(s(X),cons(Y,Z)) -> mark#(Z) ->
    mark#(g(X)) -> a__g#(mark(X))
    a__sel#(s(X),cons(Y,Z)) -> mark#(Z) ->
    mark#(sel(X1,X2)) -> mark#(X2)
    a__sel#(s(X),cons(Y,Z)) -> mark#(Z) ->
    mark#(sel(X1,X2)) -> mark#(X1)
    a__sel#(s(X),cons(Y,Z)) -> mark#(Z) ->
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
    a__sel#(s(X),cons(Y,Z)) -> mark#(Z) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__sel#(s(X),cons(Y,Z)) -> mark#(Z) ->
    mark#(s(X)) -> mark#(X)
    a__sel#(s(X),cons(Y,Z)) -> mark#(X) ->
    mark#(f(X)) -> mark#(X)
    a__sel#(s(X),cons(Y,Z)) -> mark#(X) ->
    mark#(f(X)) -> a__f#(mark(X))
    a__sel#(s(X),cons(Y,Z)) -> mark#(X) ->
    mark#(g(X)) -> mark#(X)
    a__sel#(s(X),cons(Y,Z)) -> mark#(X) ->
    mark#(g(X)) -> a__g#(mark(X))
    a__sel#(s(X),cons(Y,Z)) -> mark#(X) ->
    mark#(sel(X1,X2)) -> mark#(X2)
    a__sel#(s(X),cons(Y,Z)) -> mark#(X) ->
    mark#(sel(X1,X2)) -> mark#(X1)
    a__sel#(s(X),cons(Y,Z)) -> mark#(X) ->
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
    a__sel#(s(X),cons(Y,Z)) -> mark#(X) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__sel#(s(X),cons(Y,Z)) -> mark#(X) ->
    mark#(s(X)) -> mark#(X)
    a__sel#(0(),cons(X,Y)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    a__sel#(0(),cons(X,Y)) -> mark#(X) ->
    mark#(f(X)) -> a__f#(mark(X))
    a__sel#(0(),cons(X,Y)) -> mark#(X) -> mark#(g(X)) -> mark#(X)
    a__sel#(0(),cons(X,Y)) -> mark#(X) ->
    mark#(g(X)) -> a__g#(mark(X))
    a__sel#(0(),cons(X,Y)) -> mark#(X) ->
    mark#(sel(X1,X2)) -> mark#(X2)
    a__sel#(0(),cons(X,Y)) -> mark#(X) ->
    mark#(sel(X1,X2)) -> mark#(X1)
    a__sel#(0(),cons(X,Y)) -> mark#(X) ->
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
    a__sel#(0(),cons(X,Y)) -> mark#(X) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    a__sel#(0(),cons(X,Y)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    a__g#(s(X)) -> a__g#(mark(X)) -> a__g#(s(X)) -> mark#(X)
    a__g#(s(X)) -> a__g#(mark(X)) -> a__g#(s(X)) -> a__g#(mark(X))
    a__g#(s(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    a__g#(s(X)) -> mark#(X) -> mark#(f(X)) -> a__f#(mark(X))
    a__g#(s(X)) -> mark#(X) -> mark#(g(X)) -> mark#(X)
    a__g#(s(X)) -> mark#(X) -> mark#(g(X)) -> a__g#(mark(X))
    a__g#(s(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X2)
    a__g#(s(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X1)
    a__g#(s(X)) -> mark#(X) ->
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
    a__g#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    a__g#(s(X)) -> mark#(X) ->
    mark#(s(X)) -> mark#(X)
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2)) ->
    a__sel#(0(),cons(X,Y)) -> mark#(X)
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2)) ->
    a__sel#(s(X),cons(Y,Z)) -> mark#(Z)
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2)) ->
    a__sel#(s(X),cons(Y,Z)) -> mark#(X)
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2)) ->
    a__sel#(s(X),cons(Y,Z)) -> a__sel#(mark(X),mark(Z))
    mark#(sel(X1,X2)) -> mark#(X2) -> mark#(f(X)) -> mark#(X)
    mark#(sel(X1,X2)) -> mark#(X2) -> mark#(f(X)) -> a__f#(mark(X))
    mark#(sel(X1,X2)) -> mark#(X2) -> mark#(g(X)) -> mark#(X)
    mark#(sel(X1,X2)) -> mark#(X2) -> mark#(g(X)) -> a__g#(mark(X))
    mark#(sel(X1,X2)) -> mark#(X2) -> mark#(sel(X1,X2)) -> mark#(X2)
    mark#(sel(X1,X2)) -> mark#(X2) -> mark#(sel(X1,X2)) -> mark#(X1)
    mark#(sel(X1,X2)) -> mark#(X2) ->
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
    mark#(sel(X1,X2)) -> mark#(X2) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(sel(X1,X2)) -> mark#(X2) -> mark#(s(X)) -> mark#(X)
    mark#(sel(X1,X2)) -> mark#(X1) -> mark#(f(X)) -> mark#(X)
    mark#(sel(X1,X2)) -> mark#(X1) -> mark#(f(X)) -> a__f#(mark(X))
    mark#(sel(X1,X2)) -> mark#(X1) -> mark#(g(X)) -> mark#(X)
    mark#(sel(X1,X2)) -> mark#(X1) -> mark#(g(X)) -> a__g#(mark(X))
    mark#(sel(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> mark#(X2)
    mark#(sel(X1,X2)) -> mark#(X1) -> mark#(sel(X1,X2)) -> mark#(X1)
    mark#(sel(X1,X2)) -> mark#(X1) ->
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
    mark#(sel(X1,X2)) -> mark#(X1) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(sel(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(f(X)) -> a__f#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(g(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(g(X)) -> a__g#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X2)
    mark#(s(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) ->
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
    mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(f(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(f(X)) -> a__f#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(g(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(g(X)) -> a__g#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(sel(X1,X2)) -> mark#(X2)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(sel(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> a__f#(mark(X))
    mark#(f(X)) -> mark#(X) -> mark#(g(X)) -> mark#(X)
    mark#(f(X)) -> mark#(X) -> mark#(g(X)) -> a__g#(mark(X))
    mark#(f(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X2)
    mark#(f(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X1)
    mark#(f(X)) -> mark#(X) ->
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
    mark#(f(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(f(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(f(X)) -> a__f#(mark(X)) -> a__f#(X) -> mark#(X)
    mark#(g(X)) -> a__g#(mark(X)) -> a__g#(s(X)) -> mark#(X)
    mark#(g(X)) -> a__g#(mark(X)) -> a__g#(s(X)) -> a__g#(mark(X))
    mark#(g(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    mark#(g(X)) -> mark#(X) -> mark#(f(X)) -> a__f#(mark(X))
    mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> mark#(X)
    mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> a__g#(mark(X))
    mark#(g(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X2)
    mark#(g(X)) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X1)
    mark#(g(X)) -> mark#(X) ->
    mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
    mark#(g(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(g(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    a__f#(X) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    a__f#(X) -> mark#(X) -> mark#(f(X)) -> a__f#(mark(X))
    a__f#(X) -> mark#(X) -> mark#(g(X)) -> mark#(X)
    a__f#(X) -> mark#(X) -> mark#(g(X)) -> a__g#(mark(X))
    a__f#(X) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X2)
    a__f#(X) -> mark#(X) -> mark#(sel(X1,X2)) -> mark#(X1)
    a__f#(X) -> mark#(X) -> mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
    a__f#(X) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    a__f#(X) -> mark#(X) -> mark#(s(X)) -> mark#(X)
   SCC Processor:
    #sccs: 1
    #rules: 16
    #arcs: 112/256
    DPs:
     a__sel#(s(X),cons(Y,Z)) -> a__sel#(mark(X),mark(Z))
     a__sel#(s(X),cons(Y,Z)) -> mark#(X)
     mark#(s(X)) -> mark#(X)
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(sel(X1,X2)) -> a__sel#(mark(X1),mark(X2))
     a__sel#(s(X),cons(Y,Z)) -> mark#(Z)
     mark#(sel(X1,X2)) -> mark#(X1)
     mark#(sel(X1,X2)) -> mark#(X2)
     mark#(g(X)) -> a__g#(mark(X))
     a__g#(s(X)) -> a__g#(mark(X))
     a__g#(s(X)) -> mark#(X)
     mark#(g(X)) -> mark#(X)
     mark#(f(X)) -> a__f#(mark(X))
     a__f#(X) -> mark#(X)
     mark#(f(X)) -> mark#(X)
     a__sel#(0(),cons(X,Y)) -> mark#(X)
    TRS:
     a__f(X) -> cons(mark(X),f(g(X)))
     a__g(0()) -> s(0())
     a__g(s(X)) -> s(s(a__g(mark(X))))
     a__sel(0(),cons(X,Y)) -> mark(X)
     a__sel(s(X),cons(Y,Z)) -> a__sel(mark(X),mark(Z))
     mark(f(X)) -> a__f(mark(X))
     mark(g(X)) -> a__g(mark(X))
     mark(sel(X1,X2)) -> a__sel(mark(X1),mark(X2))
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(0()) -> 0()
     mark(s(X)) -> s(mark(X))
     a__f(X) -> f(X)
     a__g(X) -> g(X)
     a__sel(X1,X2) -> sel(X1,X2)
    Open