*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        add0(x,Nil()) -> x
        add0(x',Cons(x,xs)) -> add0(Cons(Cons(Nil(),Nil()),x'),xs)
        goal(x,y) -> add0(x,y)
        notEmpty(Cons(x,xs)) -> True()
        notEmpty(Nil()) -> False()
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {add0/2,goal/2,notEmpty/1} / {Cons/2,False/0,Nil/0,True/0}
      Obligation:
        Innermost
        basic terms: {add0,goal,notEmpty}/{Cons,False,Nil,True}
    Applied Processor:
      Bounds {initialAutomaton = perSymbol, enrichment = match}
    Proof:
      The problem is match-bounded by 1.
      The enriched problem is compatible with follwoing automaton.
        Cons_0(1,1) -> 1
        Cons_0(1,1) -> 5
        Cons_0(1,1) -> 6
        Cons_0(1,2) -> 1
        Cons_0(1,2) -> 5
        Cons_0(1,2) -> 6
        Cons_0(1,3) -> 1
        Cons_0(1,3) -> 5
        Cons_0(1,3) -> 6
        Cons_0(1,4) -> 1
        Cons_0(1,4) -> 5
        Cons_0(1,4) -> 6
        Cons_0(2,1) -> 1
        Cons_0(2,1) -> 5
        Cons_0(2,1) -> 6
        Cons_0(2,2) -> 1
        Cons_0(2,2) -> 5
        Cons_0(2,2) -> 6
        Cons_0(2,3) -> 1
        Cons_0(2,3) -> 5
        Cons_0(2,3) -> 6
        Cons_0(2,4) -> 1
        Cons_0(2,4) -> 5
        Cons_0(2,4) -> 6
        Cons_0(3,1) -> 1
        Cons_0(3,1) -> 5
        Cons_0(3,1) -> 6
        Cons_0(3,2) -> 1
        Cons_0(3,2) -> 5
        Cons_0(3,2) -> 6
        Cons_0(3,3) -> 1
        Cons_0(3,3) -> 5
        Cons_0(3,3) -> 6
        Cons_0(3,4) -> 1
        Cons_0(3,4) -> 5
        Cons_0(3,4) -> 6
        Cons_0(4,1) -> 1
        Cons_0(4,1) -> 5
        Cons_0(4,1) -> 6
        Cons_0(4,2) -> 1
        Cons_0(4,2) -> 5
        Cons_0(4,2) -> 6
        Cons_0(4,3) -> 1
        Cons_0(4,3) -> 5
        Cons_0(4,3) -> 6
        Cons_0(4,4) -> 1
        Cons_0(4,4) -> 5
        Cons_0(4,4) -> 6
        Cons_1(9,1) -> 5
        Cons_1(9,1) -> 6
        Cons_1(9,1) -> 8
        Cons_1(9,2) -> 5
        Cons_1(9,2) -> 6
        Cons_1(9,2) -> 8
        Cons_1(9,3) -> 5
        Cons_1(9,3) -> 6
        Cons_1(9,3) -> 8
        Cons_1(9,4) -> 5
        Cons_1(9,4) -> 6
        Cons_1(9,4) -> 8
        Cons_1(9,8) -> 5
        Cons_1(9,8) -> 6
        Cons_1(9,8) -> 8
        Cons_1(10,11) -> 9
        False_0() -> 2
        False_0() -> 5
        False_0() -> 6
        False_1() -> 7
        Nil_0() -> 3
        Nil_0() -> 5
        Nil_0() -> 6
        Nil_1() -> 10
        Nil_1() -> 11
        True_0() -> 4
        True_0() -> 5
        True_0() -> 6
        True_1() -> 7
        add0_0(1,1) -> 5
        add0_0(1,2) -> 5
        add0_0(1,3) -> 5
        add0_0(1,4) -> 5
        add0_0(2,1) -> 5
        add0_0(2,2) -> 5
        add0_0(2,3) -> 5
        add0_0(2,4) -> 5
        add0_0(3,1) -> 5
        add0_0(3,2) -> 5
        add0_0(3,3) -> 5
        add0_0(3,4) -> 5
        add0_0(4,1) -> 5
        add0_0(4,2) -> 5
        add0_0(4,3) -> 5
        add0_0(4,4) -> 5
        add0_1(1,1) -> 6
        add0_1(1,2) -> 6
        add0_1(1,3) -> 6
        add0_1(1,4) -> 6
        add0_1(2,1) -> 6
        add0_1(2,2) -> 6
        add0_1(2,3) -> 6
        add0_1(2,4) -> 6
        add0_1(3,1) -> 6
        add0_1(3,2) -> 6
        add0_1(3,3) -> 6
        add0_1(3,4) -> 6
        add0_1(4,1) -> 6
        add0_1(4,2) -> 6
        add0_1(4,3) -> 6
        add0_1(4,4) -> 6
        add0_1(8,1) -> 5
        add0_1(8,1) -> 6
        add0_1(8,2) -> 5
        add0_1(8,2) -> 6
        add0_1(8,3) -> 5
        add0_1(8,3) -> 6
        add0_1(8,4) -> 5
        add0_1(8,4) -> 6
        goal_0(1,1) -> 6
        goal_0(1,2) -> 6
        goal_0(1,3) -> 6
        goal_0(1,4) -> 6
        goal_0(2,1) -> 6
        goal_0(2,2) -> 6
        goal_0(2,3) -> 6
        goal_0(2,4) -> 6
        goal_0(3,1) -> 6
        goal_0(3,2) -> 6
        goal_0(3,3) -> 6
        goal_0(3,4) -> 6
        goal_0(4,1) -> 6
        goal_0(4,2) -> 6
        goal_0(4,3) -> 6
        goal_0(4,4) -> 6
        notEmpty_0(1) -> 7
        notEmpty_0(2) -> 7
        notEmpty_0(3) -> 7
        notEmpty_0(4) -> 7
        1 -> 5
        1 -> 6
        2 -> 5
        2 -> 6
        3 -> 5
        3 -> 6
        4 -> 5
        4 -> 6
        8 -> 5
        8 -> 6
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        add0(x,Nil()) -> x
        add0(x',Cons(x,xs)) -> add0(Cons(Cons(Nil(),Nil()),x'),xs)
        goal(x,y) -> add0(x,y)
        notEmpty(Cons(x,xs)) -> True()
        notEmpty(Nil()) -> False()
      Signature:
        {add0/2,goal/2,notEmpty/1} / {Cons/2,False/0,Nil/0,True/0}
      Obligation:
        Innermost
        basic terms: {add0,goal,notEmpty}/{Cons,False,Nil,True}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).