/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:
            g(x,y) -> h(x,y)
            h(f(x),y) -> f(g(x,y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:1: Sum.  MAYBE
    + Considered Problem:
        - Strict TRS:
            g(x,y) -> h(x,y)
            h(f(x),y) -> f(g(x,y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 1.a:2: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            g(x,y) -> h(x,y)
            h(f(x),y) -> f(g(x,y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + Applied Processor:
        Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False}
    + Details:
        Signatures used:
        ----------------
          F (TrsFun "f") :: ["A"(0, 0, 0)] -(0)-> "A"(0, 0, 0)
          F (TrsFun "g") :: ["A"(0, 0, 0) x "A"(0, 0, 1)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "h") :: ["A"(0, 0, 0) x "A"(0, 0, 1)] -(1)-> "A"(0, 0, 0)
          F (TrsFun "main") :: ["A"(0, 0, 0) x "A"(0, 0, 1)] -(1)-> "A"(0, 0, 0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          g(x,y) -> h(x,y)
          h(f(x),y) -> f(g(x,y))
          main(x1,x2) -> h(x1,x2)
        2. Weak:
          
        

** Step 1.b:1: Bounds.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            g(x,y) -> h(x,y)
            h(f(x),y) -> f(g(x,y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + Applied Processor:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 2.
        The enriched problem is compatible with follwoing automaton.
          f_0(2) -> 2
          f_1(3) -> 1
          f_1(3) -> 3
          g_0(2,2) -> 1
          g_1(2,2) -> 3
          h_0(2,2) -> 1
          h_1(2,2) -> 1
          h_2(2,2) -> 3
** Step 1.b:2: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            g(x,y) -> h(x,y)
            h(f(x),y) -> f(g(x,y))
        - Signature:
            {g/2,h/2} / {f/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {g,h} and constructors {f}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))