/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:
            f(0()) -> s(0())
            f(s(x)) -> s(s(g(x)))
            g(0()) -> 0()
            g(s(x)) -> f(x)
        - Signature:
            {f/1,g/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  MAYBE
    + Considered Problem:
        - Strict TRS:
            f(0()) -> s(0())
            f(s(x)) -> s(s(g(x)))
            g(0()) -> 0()
            g(s(x)) -> f(x)
        - Signature:
            {f/1,g/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            f(0()) -> s(0())
            f(s(x)) -> s(s(g(x)))
            g(0()) -> 0()
            g(s(x)) -> f(x)
        - Signature:
            {f/1,g/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,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"(1)
          F (TrsFun "0") :: [] -(0)-> "A"(0)
          F (TrsFun "f") :: ["A"(1)] -(1)-> "A"(0)
          F (TrsFun "g") :: ["A"(1)] -(1)-> "A"(0)
          F (TrsFun "main") :: ["A"(1)] -(1)-> "A"(0)
          F (TrsFun "s") :: ["A"(1)] -(1)-> "A"(1)
          F (TrsFun "s") :: ["A"(0)] -(0)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          f(0()) -> s(0())
          f(s(x)) -> s(s(g(x)))
          g(0()) -> 0()
          g(s(x)) -> f(x)
          main(x1) -> g(x1)
        2. Weak:
          
        

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            f(0()) -> s(0())
            f(s(x)) -> s(s(g(x)))
            g(0()) -> 0()
            g(s(x)) -> f(x)
        - Signature:
            {f/1,g/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 1.
        The enriched problem is compatible with follwoing automaton.
          0_0() -> 2
          0_1() -> 1
          0_1() -> 3
          0_1() -> 4
          f_0(2) -> 1
          f_1(2) -> 1
          f_1(2) -> 4
          g_0(2) -> 1
          g_1(2) -> 4
          s_0(2) -> 2
          s_1(3) -> 1
          s_1(4) -> 3
          s_1(4) -> 4
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            f(0()) -> s(0())
            f(s(x)) -> s(s(g(x)))
            g(0()) -> 0()
            g(s(x)) -> f(x)
        - Signature:
            {f/1,g/1} / {0/0,s/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,g} and constructors {0,s}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))