*** 1 Progress [(O(1),O(n^1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        activate(X) -> X
        activate(n__f(X)) -> f(X)
        f(X) -> n__f(X)
        f(0()) -> cons(0(),n__f(s(0())))
        f(s(0())) -> f(p(s(0())))
        p(s(X)) -> X
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1}
      Obligation:
        Full
        basic terms: {activate,f,p}/{0,cons,n__f,s}
    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:
        activate(X) -> X
        activate(n__f(X)) -> f(X)
        f(X) -> n__f(X)
        f(0()) -> cons(0(),n__f(s(0())))
        f(s(0())) -> f(p(s(0())))
        p(s(X)) -> X
      Weak DP Rules:
        
      Weak TRS Rules:
        
      Signature:
        {activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1}
      Obligation:
        Innermost
        basic terms: {activate,f,p}/{0,cons,n__f,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_0() -> 2
        0_1() -> 1
        0_1() -> 2
        0_1() -> 3
        0_1() -> 6
        0_2() -> 7
        0_2() -> 10
        activate_0(2) -> 1
        cons_0(2,2) -> 1
        cons_0(2,2) -> 2
        cons_1(3,4) -> 1
        cons_2(7,8) -> 1
        f_0(2) -> 1
        f_1(2) -> 1
        n__f_0(2) -> 1
        n__f_0(2) -> 2
        n__f_1(2) -> 1
        n__f_1(5) -> 4
        n__f_2(2) -> 1
        n__f_2(9) -> 8
        p_0(2) -> 1
        p_1(5) -> 1
        p_1(5) -> 2
        s_0(2) -> 1
        s_0(2) -> 2
        s_1(6) -> 5
        s_2(10) -> 9
        2 -> 1
        6 -> 1
        6 -> 2
*** 1.1.1 Progress [(O(1),O(1))]  ***
    Considered Problem:
      Strict DP Rules:
        
      Strict TRS Rules:
        
      Weak DP Rules:
        
      Weak TRS Rules:
        activate(X) -> X
        activate(n__f(X)) -> f(X)
        f(X) -> n__f(X)
        f(0()) -> cons(0(),n__f(s(0())))
        f(s(0())) -> f(p(s(0())))
        p(s(X)) -> X
      Signature:
        {activate/1,f/1,p/1} / {0/0,cons/2,n__f/1,s/1}
      Obligation:
        Innermost
        basic terms: {activate,f,p}/{0,cons,n__f,s}
    Applied Processor:
      EmptyProcessor
    Proof:
      The problem is already closed. The intended complexity is O(1).