*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        fold#3(Cons(x4,x2)) -> plus#2(x4,fold#3(x2))
        fold#3(Nil()) -> 0()
        main(x1) -> fold#3(x1)
        plus#2(0(),x12) -> x12
        plus#2(S(x4),x2) -> S(plus#2(x4,x2))
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {fold#3/1,main/1,plus#2/2} / {0/0,Cons/2,Nil/0,S/1}
      Obligation:
        Innermost
        basic terms: {fold#3,main,plus#2}/{0,Cons,Nil,S}
    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() -> 1
        0_0() -> 2
        0_0() -> 4
        0_1() -> 1
        0_1() -> 3
        Cons_0(2,2) -> 1
        Cons_0(2,2) -> 2
        Cons_0(2,2) -> 4
        Nil_0() -> 1
        Nil_0() -> 2
        Nil_0() -> 4
        S_0(2) -> 1
        S_0(2) -> 2
        S_0(2) -> 4
        S_1(1) -> 1
        S_1(3) -> 1
        S_1(3) -> 3
        S_1(4) -> 1
        S_1(4) -> 4
        fold#3_0(2) -> 1
        fold#3_1(2) -> 1
        fold#3_1(2) -> 3
        main_0(2) -> 1
        plus#2_0(2,2) -> 1
        plus#2_1(2,2) -> 4
        plus#2_1(2,3) -> 1
        plus#2_1(2,3) -> 3
        2 -> 1
        2 -> 4
        3 -> 1
*** 1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        fold#3(Cons(x4,x2)) -> plus#2(x4,fold#3(x2))
        fold#3(Nil()) -> 0()
        main(x1) -> fold#3(x1)
        plus#2(0(),x12) -> x12
        plus#2(S(x4),x2) -> S(plus#2(x4,x2))
      Signature:
        {fold#3/1,main/1,plus#2/2} / {0/0,Cons/2,Nil/0,S/1}
      Obligation:
        Innermost
        basic terms: {fold#3,main,plus#2}/{0,Cons,Nil,S}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).