MAYBE

Problem:
 a__from(X) -> cons(mark(X),from(s(X)))
 a__length(nil()) -> 0()
 a__length(cons(X,Y)) -> s(a__length1(Y))
 a__length1(X) -> a__length(X)
 mark(from(X)) -> a__from(mark(X))
 mark(length(X)) -> a__length(X)
 mark(length1(X)) -> a__length1(X)
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(s(X)) -> s(mark(X))
 mark(nil()) -> nil()
 mark(0()) -> 0()
 a__from(X) -> from(X)
 a__length(X) -> length(X)
 a__length1(X) -> length1(X)

Proof:
 DP Processor:
  DPs:
   a__from#(X) -> mark#(X)
   a__length#(cons(X,Y)) -> a__length1#(Y)
   a__length1#(X) -> a__length#(X)
   mark#(from(X)) -> mark#(X)
   mark#(from(X)) -> a__from#(mark(X))
   mark#(length(X)) -> a__length#(X)
   mark#(length1(X)) -> a__length1#(X)
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(s(X)) -> mark#(X)
  TRS:
   a__from(X) -> cons(mark(X),from(s(X)))
   a__length(nil()) -> 0()
   a__length(cons(X,Y)) -> s(a__length1(Y))
   a__length1(X) -> a__length(X)
   mark(from(X)) -> a__from(mark(X))
   mark(length(X)) -> a__length(X)
   mark(length1(X)) -> a__length1(X)
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(s(X)) -> s(mark(X))
   mark(nil()) -> nil()
   mark(0()) -> 0()
   a__from(X) -> from(X)
   a__length(X) -> length(X)
   a__length1(X) -> length1(X)
  TDG Processor:
   DPs:
    a__from#(X) -> mark#(X)
    a__length#(cons(X,Y)) -> a__length1#(Y)
    a__length1#(X) -> a__length#(X)
    mark#(from(X)) -> mark#(X)
    mark#(from(X)) -> a__from#(mark(X))
    mark#(length(X)) -> a__length#(X)
    mark#(length1(X)) -> a__length1#(X)
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X)
   TRS:
    a__from(X) -> cons(mark(X),from(s(X)))
    a__length(nil()) -> 0()
    a__length(cons(X,Y)) -> s(a__length1(Y))
    a__length1(X) -> a__length(X)
    mark(from(X)) -> a__from(mark(X))
    mark(length(X)) -> a__length(X)
    mark(length1(X)) -> a__length1(X)
    mark(cons(X1,X2)) -> cons(mark(X1),X2)
    mark(s(X)) -> s(mark(X))
    mark(nil()) -> nil()
    mark(0()) -> 0()
    a__from(X) -> from(X)
    a__length(X) -> length(X)
    a__length1(X) -> length1(X)
   graph:
    a__length1#(X) -> a__length#(X) ->
    a__length#(cons(X,Y)) -> a__length1#(Y)
    a__length#(cons(X,Y)) -> a__length1#(Y) ->
    a__length1#(X) -> a__length#(X)
    mark#(length1(X)) -> a__length1#(X) ->
    a__length1#(X) -> a__length#(X)
    mark#(length(X)) -> a__length#(X) ->
    a__length#(cons(X,Y)) -> a__length1#(Y)
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(s(X)) -> mark#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(length1(X)) -> a__length1#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(length(X)) -> a__length#(X)
    mark#(cons(X1,X2)) -> mark#(X1) ->
    mark#(from(X)) -> a__from#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1) -> mark#(from(X)) -> mark#(X)
    mark#(from(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(from(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(from(X)) -> mark#(X) -> mark#(length1(X)) -> a__length1#(X)
    mark#(from(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(X)
    mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    mark#(from(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    mark#(from(X)) -> a__from#(mark(X)) -> a__from#(X) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    mark#(s(X)) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X) -> mark#(length1(X)) -> a__length1#(X)
    mark#(s(X)) -> mark#(X) -> mark#(length(X)) -> a__length#(X)
    mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    mark#(s(X)) -> mark#(X) -> mark#(from(X)) -> mark#(X)
    a__from#(X) -> mark#(X) -> mark#(s(X)) -> mark#(X)
    a__from#(X) -> mark#(X) -> mark#(cons(X1,X2)) -> mark#(X1)
    a__from#(X) -> mark#(X) -> mark#(length1(X)) -> a__length1#(X)
    a__from#(X) -> mark#(X) -> mark#(length(X)) -> a__length#(X)
    a__from#(X) -> mark#(X) -> mark#(from(X)) -> a__from#(mark(X))
    a__from#(X) -> mark#(X) -> mark#(from(X)) -> mark#(X)
   SCC Processor:
    #sccs: 2
    #rules: 7
    #arcs: 29/81
    DPs:
     mark#(cons(X1,X2)) -> mark#(X1)
     mark#(from(X)) -> mark#(X)
     mark#(from(X)) -> a__from#(mark(X))
     a__from#(X) -> mark#(X)
     mark#(s(X)) -> mark#(X)
    TRS:
     a__from(X) -> cons(mark(X),from(s(X)))
     a__length(nil()) -> 0()
     a__length(cons(X,Y)) -> s(a__length1(Y))
     a__length1(X) -> a__length(X)
     mark(from(X)) -> a__from(mark(X))
     mark(length(X)) -> a__length(X)
     mark(length1(X)) -> a__length1(X)
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(s(X)) -> s(mark(X))
     mark(nil()) -> nil()
     mark(0()) -> 0()
     a__from(X) -> from(X)
     a__length(X) -> length(X)
     a__length1(X) -> length1(X)
    Open
    
    DPs:
     a__length1#(X) -> a__length#(X)
     a__length#(cons(X,Y)) -> a__length1#(Y)
    TRS:
     a__from(X) -> cons(mark(X),from(s(X)))
     a__length(nil()) -> 0()
     a__length(cons(X,Y)) -> s(a__length1(Y))
     a__length1(X) -> a__length(X)
     mark(from(X)) -> a__from(mark(X))
     mark(length(X)) -> a__length(X)
     mark(length1(X)) -> a__length1(X)
     mark(cons(X1,X2)) -> cons(mark(X1),X2)
     mark(s(X)) -> s(mark(X))
     mark(nil()) -> nil()
     mark(0()) -> 0()
     a__from(X) -> from(X)
     a__length(X) -> length(X)
     a__length1(X) -> length1(X)
    Open