MAYBE

Problem:
 fst(0(),Z) -> nil()
 fst(s(X),cons(Y,Z)) -> cons(Y,fst(X,Z))
 from(X) -> cons(X,from(s(X)))
 add(0(),X) -> X
 add(s(X),Y) -> s(add(X,Y))
 len(nil()) -> 0()
 len(cons(X,Z)) -> s(len(Z))

Proof:
 DP Processor:
  DPs:
   fst#(s(X),cons(Y,Z)) -> fst#(X,Z)
   from#(X) -> from#(s(X))
   add#(s(X),Y) -> add#(X,Y)
   len#(cons(X,Z)) -> len#(Z)
  TRS:
   fst(0(),Z) -> nil()
   fst(s(X),cons(Y,Z)) -> cons(Y,fst(X,Z))
   from(X) -> cons(X,from(s(X)))
   add(0(),X) -> X
   add(s(X),Y) -> s(add(X,Y))
   len(nil()) -> 0()
   len(cons(X,Z)) -> s(len(Z))
  CDG Processor:
   DPs:
    fst#(s(X),cons(Y,Z)) -> fst#(X,Z)
    from#(X) -> from#(s(X))
    add#(s(X),Y) -> add#(X,Y)
    len#(cons(X,Z)) -> len#(Z)
   TRS:
    fst(0(),Z) -> nil()
    fst(s(X),cons(Y,Z)) -> cons(Y,fst(X,Z))
    from(X) -> cons(X,from(s(X)))
    add(0(),X) -> X
    add(s(X),Y) -> s(add(X,Y))
    len(nil()) -> 0()
    len(cons(X,Z)) -> s(len(Z))
   graph:
    len#(cons(X,Z)) -> len#(Z) -> len#(cons(X,Z)) -> len#(Z)
    add#(s(X),Y) -> add#(X,Y) -> add#(s(X),Y) -> add#(X,Y)
    from#(X) -> from#(s(X)) -> from#(X) -> from#(s(X))
    fst#(s(X),cons(Y,Z)) -> fst#(X,Z) -> fst#(s(X),cons(Y,Z)) -> fst#(X,Z)
   SCC Processor:
    #sccs: 4
    #rules: 4
    #arcs: 4/16
    DPs:
     fst#(s(X),cons(Y,Z)) -> fst#(X,Z)
    TRS:
     fst(0(),Z) -> nil()
     fst(s(X),cons(Y,Z)) -> cons(Y,fst(X,Z))
     from(X) -> cons(X,from(s(X)))
     add(0(),X) -> X
     add(s(X),Y) -> s(add(X,Y))
     len(nil()) -> 0()
     len(cons(X,Z)) -> s(len(Z))
    Open
    
    DPs:
     from#(X) -> from#(s(X))
    TRS:
     fst(0(),Z) -> nil()
     fst(s(X),cons(Y,Z)) -> cons(Y,fst(X,Z))
     from(X) -> cons(X,from(s(X)))
     add(0(),X) -> X
     add(s(X),Y) -> s(add(X,Y))
     len(nil()) -> 0()
     len(cons(X,Z)) -> s(len(Z))
    Open
    
    DPs:
     add#(s(X),Y) -> add#(X,Y)
    TRS:
     fst(0(),Z) -> nil()
     fst(s(X),cons(Y,Z)) -> cons(Y,fst(X,Z))
     from(X) -> cons(X,from(s(X)))
     add(0(),X) -> X
     add(s(X),Y) -> s(add(X,Y))
     len(nil()) -> 0()
     len(cons(X,Z)) -> s(len(Z))
    Open
    
    DPs:
     len#(cons(X,Z)) -> len#(Z)
    TRS:
     fst(0(),Z) -> nil()
     fst(s(X),cons(Y,Z)) -> cons(Y,fst(X,Z))
     from(X) -> cons(X,from(s(X)))
     add(0(),X) -> X
     add(s(X),Y) -> s(add(X,Y))
     len(nil()) -> 0()
     len(cons(X,Z)) -> s(len(Z))
    Open