WORST_CASE(?,O(n^1))
* Step 1: Sum.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(0()) -> cons(0())
            f(s(0())) -> f(p(s(0())))
            p(s(0())) -> 0()
        - Signature:
            {f/1,p/1} / {0/0,cons/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  MAYBE
    + Considered Problem:
        - Strict TRS:
            f(0()) -> cons(0())
            f(s(0())) -> f(p(s(0())))
            p(s(0())) -> 0()
        - Signature:
            {f/1,p/1} / {0/0,cons/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            f(0()) -> cons(0())
            f(s(0())) -> f(p(s(0())))
            p(s(0())) -> 0()
        - Signature:
            {f/1,p/1} / {0/0,cons/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,s}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "0") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "0") :: [] -(0)-> "A"(2, 2, 1)
          F (TrsFun "cons") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "f") :: ["A"(0, 0, 0)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "main") :: ["A"(0, 0, 1)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "p") :: ["A"(1, 1, 1)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "s") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "s") :: ["A"(2, 2, 1)] -(1)-> "A"(1, 1, 1)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          f(0()) -> cons(0())
          f(s(0())) -> f(p(s(0())))
          p(s(0())) -> 0()
          main(x1) -> p(x1)
        2. Weak:
          
        

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(0()) -> cons(0())
            f(s(0())) -> f(p(s(0())))
            p(s(0())) -> 0()
        - Signature:
            {f/1,p/1} / {0/0,cons/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,s}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 2
          0_1() -> 1
          0_1() -> 3
          0_2() -> 4
          cons_0(2) -> 2
          cons_1(3) -> 1
          cons_2(4) -> 1
          f_0(2) -> 1
          f_1(4) -> 1
          p_0(2) -> 1
          p_1(5) -> 4
          s_0(2) -> 2
          s_1(3) -> 5
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(0()) -> cons(0())
            f(s(0())) -> f(p(s(0())))
            p(s(0())) -> 0()
        - Signature:
            {f/1,p/1} / {0/0,cons/1,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,p} and constructors {0,cons,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))