*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        0() -> n__0()
        activate(X) -> X
        activate(n__0()) -> 0()
        activate(n__f(X)) -> f(activate(X))
        activate(n__s(X)) -> s(activate(X))
        f(X) -> n__f(X)
        f(0()) -> cons(0(),n__f(n__s(n__0())))
        f(s(0())) -> f(p(s(0())))
        p(s(X)) -> X
        s(X) -> n__s(X)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {0/0,activate/1,f/1,p/1,s/1} / {cons/2,n__0/0,n__f/1,n__s/1}
      Obligation:
        Innermost
        basic terms: {0,activate,f,p,s}/{cons,n__0,n__f,n__s}
    Applied Processor:
      InnermostRuleRemoval
    Proof:
      Arguments of following rules are not normal-forms.
        f(0()) -> cons(0(),n__f(n__s(n__0())))
        f(s(0())) -> f(p(s(0())))
        p(s(X)) -> X
      All above mentioned rules can be savely removed.
*** 1.1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        0() -> n__0()
        activate(X) -> X
        activate(n__0()) -> 0()
        activate(n__f(X)) -> f(activate(X))
        activate(n__s(X)) -> s(activate(X))
        f(X) -> n__f(X)
        s(X) -> n__s(X)
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {0/0,activate/1,f/1,p/1,s/1} / {cons/2,n__0/0,n__f/1,n__s/1}
      Obligation:
        Innermost
        basic terms: {0,activate,f,p,s}/{cons,n__0,n__f,n__s}
    Applied Processor:
      Bounds {initialAutomaton = minimal, enrichment = match}
    Proof:
      The problem is match-bounded by 2.
      The enriched problem is compatible with follwoing automaton.
        0_0() -> 1
        0_1() -> 1
        0_1() -> 3
        activate_0(2) -> 1
        activate_1(2) -> 3
        cons_0(2,2) -> 1
        cons_0(2,2) -> 2
        cons_0(2,2) -> 3
        f_0(2) -> 1
        f_1(3) -> 1
        f_1(3) -> 3
        n__0_0() -> 1
        n__0_0() -> 2
        n__0_0() -> 3
        n__0_1() -> 1
        n__0_2() -> 1
        n__0_2() -> 3
        n__f_0(2) -> 1
        n__f_0(2) -> 2
        n__f_0(2) -> 3
        n__f_1(2) -> 1
        n__f_2(3) -> 1
        n__f_2(3) -> 3
        n__s_0(2) -> 1
        n__s_0(2) -> 2
        n__s_0(2) -> 3
        n__s_1(2) -> 1
        n__s_2(3) -> 1
        n__s_2(3) -> 3
        p_0(2) -> 1
        s_0(2) -> 1
        s_1(3) -> 1
        s_1(3) -> 3
        2 -> 1
        2 -> 3
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        0() -> n__0()
        activate(X) -> X
        activate(n__0()) -> 0()
        activate(n__f(X)) -> f(activate(X))
        activate(n__s(X)) -> s(activate(X))
        f(X) -> n__f(X)
        s(X) -> n__s(X)
      Signature:
        {0/0,activate/1,f/1,p/1,s/1} / {cons/2,n__0/0,n__f/1,n__s/1}
      Obligation:
        Innermost
        basic terms: {0,activate,f,p,s}/{cons,n__0,n__f,n__s}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).