/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            even(Cons(x,xs)) -> odd(xs)
            even(Nil()) -> True()
            evenodd(x) -> even(x)
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
            odd(Cons(x,xs)) -> even(xs)
            odd(Nil()) -> False()
        - Signature:
            {even/1,evenodd/1,notEmpty/1,odd/1} / {Cons/2,False/0,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {even,evenodd,notEmpty,odd} and constructors {Cons,False
            ,Nil,True}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 1.
        The enriched problem is compatible with follwoing automaton.
          Cons_0(2,2) -> 2
          False_0() -> 2
          False_1() -> 1
          Nil_0() -> 2
          True_0() -> 2
          True_1() -> 1
          even_0(2) -> 1
          even_1(2) -> 1
          evenodd_0(2) -> 1
          notEmpty_0(2) -> 1
          odd_0(2) -> 1
          odd_1(2) -> 1
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            even(Cons(x,xs)) -> odd(xs)
            even(Nil()) -> True()
            evenodd(x) -> even(x)
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
            odd(Cons(x,xs)) -> even(xs)
            odd(Nil()) -> False()
        - Signature:
            {even/1,evenodd/1,notEmpty/1,odd/1} / {Cons/2,False/0,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {even,evenodd,notEmpty,odd} and constructors {Cons,False
            ,Nil,True}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))