*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        f(a,cons(x,k)) -> f(cons(x,a),k)
        f(a,empty()) -> g(a,empty())
        g(cons(x,k),d) -> g(k,cons(x,d))
        g(empty(),d) -> d
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/2,g/2} / {cons/2,empty/0}
      Obligation:
        Full
        basic terms: {f,g}/{cons,empty}
    Applied Processor:
      ToInnermost
    Proof:
      switch to innermost, as the system is overlay and right linear and does not contain weak rules
*** 1.1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        f(a,cons(x,k)) -> f(cons(x,a),k)
        f(a,empty()) -> g(a,empty())
        g(cons(x,k),d) -> g(k,cons(x,d))
        g(empty(),d) -> d
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {f/2,g/2} / {cons/2,empty/0}
      Obligation:
        Innermost
        basic terms: {f,g}/{cons,empty}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 3.
      The enriched problem is compatible with follwoing automaton.
        cons_0(2,2) -> 1
        cons_0(2,2) -> 2
        cons_1(2,2) -> 1
        cons_1(2,2) -> 3
        cons_1(2,3) -> 1
        cons_1(2,3) -> 3
        cons_1(2,4) -> 1
        cons_1(2,4) -> 3
        cons_1(2,5) -> 1
        cons_1(2,5) -> 3
        cons_2(2,4) -> 1
        cons_2(2,4) -> 5
        cons_2(2,5) -> 1
        cons_2(2,5) -> 5
        cons_3(2,5) -> 1
        cons_3(2,5) -> 6
        cons_3(2,6) -> 1
        cons_3(2,6) -> 6
        empty_0() -> 1
        empty_0() -> 2
        empty_1() -> 1
        empty_1() -> 4
        f_0(2,2) -> 1
        f_1(3,2) -> 1
        g_0(2,2) -> 1
        g_1(2,3) -> 1
        g_1(2,4) -> 1
        g_1(3,4) -> 1
        g_2(2,5) -> 1
        g_2(3,5) -> 1
        g_2(4,5) -> 1
        g_2(5,5) -> 1
        g_3(4,6) -> 1
        g_3(5,6) -> 1
        2 -> 1
        3 -> 1
        4 -> 1
        5 -> 1
        6 -> 1
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        f(a,cons(x,k)) -> f(cons(x,a),k)
        f(a,empty()) -> g(a,empty())
        g(cons(x,k),d) -> g(k,cons(x,d))
        g(empty(),d) -> d
      Signature:
        {f/2,g/2} / {cons/2,empty/0}
      Obligation:
        Innermost
        basic terms: {f,g}/{cons,empty}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).