*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        addlist(Cons(x,xs'),Cons(S(0()),xs)) -> Cons(S(x),addlist(xs',xs))
        addlist(Cons(S(0()),xs'),Cons(x,xs)) -> Cons(S(x),addlist(xs',xs))
        addlist(Nil(),ys) -> Nil()
        goal(xs,ys) -> addlist(xs,ys)
        notEmpty(Cons(x,xs)) -> True()
        notEmpty(Nil()) -> False()
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {addlist/2,goal/2,notEmpty/1} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
      Obligation:
        Innermost
        basic terms: {addlist,goal,notEmpty}/{0,Cons,False,Nil,S,True}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 1.
      The enriched problem is compatible with follwoing automaton.
        0_0() -> 2
        Cons_0(2,2) -> 2
        Cons_1(3,4) -> 1
        Cons_1(3,4) -> 4
        False_0() -> 2
        False_1() -> 1
        Nil_0() -> 2
        Nil_1() -> 1
        Nil_1() -> 4
        S_0(2) -> 2
        S_1(2) -> 3
        True_0() -> 2
        True_1() -> 1
        addlist_0(2,2) -> 1
        addlist_1(2,2) -> 1
        addlist_1(2,2) -> 4
        goal_0(2,2) -> 1
        notEmpty_0(2) -> 1
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        addlist(Cons(x,xs'),Cons(S(0()),xs)) -> Cons(S(x),addlist(xs',xs))
        addlist(Cons(S(0()),xs'),Cons(x,xs)) -> Cons(S(x),addlist(xs',xs))
        addlist(Nil(),ys) -> Nil()
        goal(xs,ys) -> addlist(xs,ys)
        notEmpty(Cons(x,xs)) -> True()
        notEmpty(Nil()) -> False()
      Signature:
        {addlist/2,goal/2,notEmpty/1} / {0/0,Cons/2,False/0,Nil/0,S/1,True/0}
      Obligation:
        Innermost
        basic terms: {addlist,goal,notEmpty}/{0,Cons,False,Nil,S,True}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).