/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:
            evenodd(x,0()) -> not(evenodd(x,s(0())))
            evenodd(0(),s(0())) -> false()
            evenodd(s(x),s(0())) -> evenodd(x,0())
            not(false()) -> true()
            not(true()) -> false()
        - Signature:
            {evenodd/2,not/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {evenodd,not} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  MAYBE
    + Considered Problem:
        - Strict TRS:
            evenodd(x,0()) -> not(evenodd(x,s(0())))
            evenodd(0(),s(0())) -> false()
            evenodd(s(x),s(0())) -> evenodd(x,0())
            not(false()) -> true()
            not(true()) -> false()
        - Signature:
            {evenodd/2,not/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {evenodd,not} and constructors {0,false,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            evenodd(x,0()) -> not(evenodd(x,s(0())))
            evenodd(0(),s(0())) -> false()
            evenodd(s(x),s(0())) -> evenodd(x,0())
            not(false()) -> true()
            not(true()) -> false()
        - Signature:
            {evenodd/2,not/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {evenodd,not} and constructors {0,false,s,true}
    + 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 "evenodd") :: ["A"(0, 0, 0) x "A"(0, 0, 0)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "false") :: [] -(0)-> "A"(1, 1, 1)
          F (TrsFun "false") :: [] -(0)-> "A"(0, 0, 0)
          F (TrsFun "main") :: ["A"(1, 1, 1)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "not") :: ["A"(1, 1, 1)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "s") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "true") :: [] -(0)-> "A"(1, 1, 1)
          F (TrsFun "true") :: [] -(0)-> "A"(0, 0, 0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          evenodd(x,0()) -> not(evenodd(x,s(0())))
          evenodd(0(),s(0())) -> false()
          evenodd(s(x),s(0())) -> evenodd(x,0())
          not(false()) -> true()
          not(true()) -> false()
          main(x1) -> not(x1)
        2. Weak:
          
        

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            evenodd(x,0()) -> not(evenodd(x,s(0())))
            evenodd(0(),s(0())) -> false()
            evenodd(s(x),s(0())) -> evenodd(x,0())
            not(false()) -> true()
            not(true()) -> false()
        - Signature:
            {evenodd/2,not/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {evenodd,not} and constructors {0,false,s,true}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 3.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 2
          0_1() -> 5
          0_2() -> 8
          evenodd_0(2,2) -> 1
          evenodd_1(2,4) -> 3
          evenodd_1(2,5) -> 1
          evenodd_1(2,5) -> 3
          evenodd_1(2,5) -> 6
          evenodd_2(2,7) -> 6
          false_0() -> 2
          false_1() -> 1
          false_1() -> 3
          false_1() -> 6
          false_2() -> 1
          false_3() -> 1
          false_3() -> 3
          false_3() -> 6
          not_0(2) -> 1
          not_1(3) -> 1
          not_2(6) -> 1
          not_2(6) -> 3
          not_2(6) -> 6
          s_0(2) -> 2
          s_1(5) -> 4
          s_2(8) -> 7
          true_0() -> 2
          true_1() -> 1
          true_2() -> 1
          true_2() -> 3
          true_2() -> 6
          true_3() -> 1
          true_3() -> 3
          true_3() -> 6
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            evenodd(x,0()) -> not(evenodd(x,s(0())))
            evenodd(0(),s(0())) -> false()
            evenodd(s(x),s(0())) -> evenodd(x,0())
            not(false()) -> true()
            not(true()) -> false()
        - Signature:
            {evenodd/2,not/1} / {0/0,false/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {evenodd,not} and constructors {0,false,s,true}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))