/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),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(a(),g(y)) -> g(g(y))
            f(g(x),a()) -> f(x,g(a()))
            f(g(x),g(y)) -> h(g(y),x,g(y))
            h(a(),y,z) -> z
            h(g(x),y,z) -> f(y,h(x,y,z))
        - Signature:
            {f/2,h/3} / {a/0,g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,h} and constructors {a,g}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(a(),g(y)) -> g(g(y))
            f(g(x),a()) -> f(x,g(a()))
            f(g(x),g(y)) -> h(g(y),x,g(y))
            h(a(),y,z) -> z
            h(g(x),y,z) -> f(y,h(x,y,z))
        - Signature:
            {f/2,h/3} / {a/0,g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,h} and constructors {a,g}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
** Step 2.a:1: Ara.  MAYBE
    + Considered Problem:
        - Strict TRS:
            f(a(),g(y)) -> g(g(y))
            f(g(x),a()) -> f(x,g(a()))
            f(g(x),g(y)) -> h(g(y),x,g(y))
            h(a(),y,z) -> z
            h(g(x),y,z) -> f(y,h(x,y,z))
        - Signature:
            {f/2,h/3} / {a/0,g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,h} and constructors {a,g}
    + 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 "a") :: [] -(0)-> "A"(1)
          F (TrsFun "f") :: ["A"(0) x "A"(0)] -(1)-> "A"(0)
          F (TrsFun "g") :: ["A"(0)] -(0)-> "A"(0)
          F (TrsFun "g") :: ["A"(1)] -(1)-> "A"(1)
          F (TrsFun "h") :: ["A"(1) x "A"(0) x "A"(0)] -(1)-> "A"(0)
          F (TrsFun "main") :: ["A"(1) x "A"(0) x "A"(0)] -(1)-> "A"(0)
        
        
        Cost-free Signatures used:
        --------------------------
        
        
        
        Base Constructor Signatures used:
        ---------------------------------
        
        
        
        Following Still Strict Rules were Typed as:
        -------------------------------------------
        1. Strict:
          f(a(),g(y)) -> g(g(y))
          f(g(x),a()) -> f(x,g(a()))
          f(g(x),g(y)) -> h(g(y),x,g(y))
          h(a(),y,z) -> z
          h(g(x),y,z) -> f(y,h(x,y,z))
          main(x1,x2,x3) -> h(x1,x2,x3)
        2. Weak:
          
        

** Step 2.b:1: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(a(),g(y)) -> g(g(y))
            f(g(x),a()) -> f(x,g(a()))
            f(g(x),g(y)) -> h(g(y),x,g(y))
            h(a(),y,z) -> z
            h(g(x),y,z) -> f(y,h(x,y,z))
        - Signature:
            {f/2,h/3} / {a/0,g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {f,h} and constructors {a,g}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          h(x,y,z){x -> g(x)} =
            h(g(x),y,z) ->^+ f(y,h(x,y,z))
              = C[h(x,y,z) = h(x,y,z){}]

WORST_CASE(Omega(n^1),?)