/export/starexec/sandbox2/solver/bin/starexec_run_tct_rci /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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

*** Step 1.a:1.b:1: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            h(f(x,y)) -> f(f(a(),h(h(y))),x)
        - Signature:
            {h/1} / {a/0,f/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h} and constructors {a,f}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          h(y){y -> f(x,y)} =
            h(f(x,y)) ->^+ f(f(a(),h(h(y))),x)
              = C[h(y) = h(y){}]

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            h(f(x,y)) -> f(f(a(),h(h(y))),x)
        - Signature:
            {h/1} / {a/0,f/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h} and constructors {a,f}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          a_0() -> 2
          a_1() -> 4
          a_2() -> 8
          f_0(2,2) -> 2
          f_1(3,2) -> 1
          f_1(3,2) -> 6
          f_1(3,2) -> 10
          f_1(4,5) -> 3
          f_2(7,3) -> 5
          f_2(7,3) -> 9
          f_2(8,9) -> 7
          h_0(2) -> 1
          h_1(2) -> 6
          h_1(6) -> 5
          h_2(2) -> 10
          h_2(10) -> 9
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            h(f(x,y)) -> f(f(a(),h(h(y))),x)
        - Signature:
            {h/1} / {a/0,f/2}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {h} and constructors {a,f}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(Omega(n^1),O(n^1))