/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(?,O(1))
* Step 1: Sum.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__f(X)) -> f(X)
            activate(n__g(X)) -> g(X)
            f(X) -> n__f(X)
            f(n__f(n__a())) -> f(n__g(f(n__a())))
            g(X) -> n__g(X)
        - Signature:
            {a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {n__a,n__f,n__g}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DependencyPairs.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__f(X)) -> f(X)
            activate(n__g(X)) -> g(X)
            f(X) -> n__f(X)
            f(n__f(n__a())) -> f(n__g(f(n__a())))
            g(X) -> n__g(X)
        - Signature:
            {a/0,activate/1,f/1,g/1} / {n__a/0,n__f/1,n__g/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a,activate,f,g} and constructors {n__a,n__f,n__g}
    + Applied Processor:
        DependencyPairs {dpKind_ = DT}
    + Details:
        We add the following dependency tuples:
        
        Strict DPs
          a#() -> c_1()
          activate#(X) -> c_2()
          activate#(n__a()) -> c_3(a#())
          activate#(n__f(X)) -> c_4(f#(X))
          activate#(n__g(X)) -> c_5(g#(X))
          f#(X) -> c_6()
          f#(n__f(n__a())) -> c_7(f#(n__g(f(n__a()))),f#(n__a()))
          g#(X) -> c_8()
        Weak DPs
          
        
        and mark the set of starting terms.
* Step 3: PredecessorEstimation.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            a#() -> c_1()
            activate#(X) -> c_2()
            activate#(n__a()) -> c_3(a#())
            activate#(n__f(X)) -> c_4(f#(X))
            activate#(n__g(X)) -> c_5(g#(X))
            f#(X) -> c_6()
            f#(n__f(n__a())) -> c_7(f#(n__g(f(n__a()))),f#(n__a()))
            g#(X) -> c_8()
        - Weak TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__f(X)) -> f(X)
            activate(n__g(X)) -> g(X)
            f(X) -> n__f(X)
            f(n__f(n__a())) -> f(n__g(f(n__a())))
            g(X) -> n__g(X)
        - Signature:
            {a/0,activate/1,f/1,g/1,a#/0,activate#/1,f#/1,g#/1} / {n__a/0,n__f/1,n__g/1,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1
            ,c_6/0,c_7/2,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,activate#,f#,g#} and constructors {n__a,n__f,n__g}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,2,6,8}
        by application of
          Pre({1,2,6,8}) = {3,4,5,7}.
        Here rules are labelled as follows:
          1: a#() -> c_1()
          2: activate#(X) -> c_2()
          3: activate#(n__a()) -> c_3(a#())
          4: activate#(n__f(X)) -> c_4(f#(X))
          5: activate#(n__g(X)) -> c_5(g#(X))
          6: f#(X) -> c_6()
          7: f#(n__f(n__a())) -> c_7(f#(n__g(f(n__a()))),f#(n__a()))
          8: g#(X) -> c_8()
* Step 4: PredecessorEstimation.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            activate#(n__a()) -> c_3(a#())
            activate#(n__f(X)) -> c_4(f#(X))
            activate#(n__g(X)) -> c_5(g#(X))
            f#(n__f(n__a())) -> c_7(f#(n__g(f(n__a()))),f#(n__a()))
        - Weak DPs:
            a#() -> c_1()
            activate#(X) -> c_2()
            f#(X) -> c_6()
            g#(X) -> c_8()
        - Weak TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__f(X)) -> f(X)
            activate(n__g(X)) -> g(X)
            f(X) -> n__f(X)
            f(n__f(n__a())) -> f(n__g(f(n__a())))
            g(X) -> n__g(X)
        - Signature:
            {a/0,activate/1,f/1,g/1,a#/0,activate#/1,f#/1,g#/1} / {n__a/0,n__f/1,n__g/1,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1
            ,c_6/0,c_7/2,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,activate#,f#,g#} and constructors {n__a,n__f,n__g}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1,3,4}
        by application of
          Pre({1,3,4}) = {2}.
        Here rules are labelled as follows:
          1: activate#(n__a()) -> c_3(a#())
          2: activate#(n__f(X)) -> c_4(f#(X))
          3: activate#(n__g(X)) -> c_5(g#(X))
          4: f#(n__f(n__a())) -> c_7(f#(n__g(f(n__a()))),f#(n__a()))
          5: a#() -> c_1()
          6: activate#(X) -> c_2()
          7: f#(X) -> c_6()
          8: g#(X) -> c_8()
* Step 5: PredecessorEstimation.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Strict DPs:
            activate#(n__f(X)) -> c_4(f#(X))
        - Weak DPs:
            a#() -> c_1()
            activate#(X) -> c_2()
            activate#(n__a()) -> c_3(a#())
            activate#(n__g(X)) -> c_5(g#(X))
            f#(X) -> c_6()
            f#(n__f(n__a())) -> c_7(f#(n__g(f(n__a()))),f#(n__a()))
            g#(X) -> c_8()
        - Weak TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__f(X)) -> f(X)
            activate(n__g(X)) -> g(X)
            f(X) -> n__f(X)
            f(n__f(n__a())) -> f(n__g(f(n__a())))
            g(X) -> n__g(X)
        - Signature:
            {a/0,activate/1,f/1,g/1,a#/0,activate#/1,f#/1,g#/1} / {n__a/0,n__f/1,n__g/1,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1
            ,c_6/0,c_7/2,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,activate#,f#,g#} and constructors {n__a,n__f,n__g}
    + Applied Processor:
        PredecessorEstimation {onSelection = all simple predecessor estimation selector}
    + Details:
        We estimate the number of application of
          {1}
        by application of
          Pre({1}) = {}.
        Here rules are labelled as follows:
          1: activate#(n__f(X)) -> c_4(f#(X))
          2: a#() -> c_1()
          3: activate#(X) -> c_2()
          4: activate#(n__a()) -> c_3(a#())
          5: activate#(n__g(X)) -> c_5(g#(X))
          6: f#(X) -> c_6()
          7: f#(n__f(n__a())) -> c_7(f#(n__g(f(n__a()))),f#(n__a()))
          8: g#(X) -> c_8()
* Step 6: RemoveWeakSuffixes.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak DPs:
            a#() -> c_1()
            activate#(X) -> c_2()
            activate#(n__a()) -> c_3(a#())
            activate#(n__f(X)) -> c_4(f#(X))
            activate#(n__g(X)) -> c_5(g#(X))
            f#(X) -> c_6()
            f#(n__f(n__a())) -> c_7(f#(n__g(f(n__a()))),f#(n__a()))
            g#(X) -> c_8()
        - Weak TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__f(X)) -> f(X)
            activate(n__g(X)) -> g(X)
            f(X) -> n__f(X)
            f(n__f(n__a())) -> f(n__g(f(n__a())))
            g(X) -> n__g(X)
        - Signature:
            {a/0,activate/1,f/1,g/1,a#/0,activate#/1,f#/1,g#/1} / {n__a/0,n__f/1,n__g/1,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1
            ,c_6/0,c_7/2,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,activate#,f#,g#} and constructors {n__a,n__f,n__g}
    + Applied Processor:
        RemoveWeakSuffixes
    + Details:
        Consider the dependency graph
          1:W:a#() -> c_1()
             
          
          2:W:activate#(X) -> c_2()
             
          
          3:W:activate#(n__a()) -> c_3(a#())
             -->_1 a#() -> c_1():1
          
          4:W:activate#(n__f(X)) -> c_4(f#(X))
             -->_1 f#(n__f(n__a())) -> c_7(f#(n__g(f(n__a()))),f#(n__a())):7
             -->_1 f#(X) -> c_6():6
          
          5:W:activate#(n__g(X)) -> c_5(g#(X))
             -->_1 g#(X) -> c_8():8
          
          6:W:f#(X) -> c_6()
             
          
          7:W:f#(n__f(n__a())) -> c_7(f#(n__g(f(n__a()))),f#(n__a()))
             -->_2 f#(X) -> c_6():6
             -->_1 f#(X) -> c_6():6
          
          8:W:g#(X) -> c_8()
             
          
        The following weak DPs constitute a sub-graph of the DG that is closed under successors. The DPs are removed.
          5: activate#(n__g(X)) -> c_5(g#(X))
          8: g#(X) -> c_8()
          4: activate#(n__f(X)) -> c_4(f#(X))
          7: f#(n__f(n__a())) -> c_7(f#(n__g(f(n__a()))),f#(n__a()))
          6: f#(X) -> c_6()
          3: activate#(n__a()) -> c_3(a#())
          2: activate#(X) -> c_2()
          1: a#() -> c_1()
* Step 7: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a() -> n__a()
            activate(X) -> X
            activate(n__a()) -> a()
            activate(n__f(X)) -> f(X)
            activate(n__g(X)) -> g(X)
            f(X) -> n__f(X)
            f(n__f(n__a())) -> f(n__g(f(n__a())))
            g(X) -> n__g(X)
        - Signature:
            {a/0,activate/1,f/1,g/1,a#/0,activate#/1,f#/1,g#/1} / {n__a/0,n__f/1,n__g/1,c_1/0,c_2/0,c_3/1,c_4/1,c_5/1
            ,c_6/0,c_7/2,c_8/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a#,activate#,f#,g#} and constructors {n__a,n__f,n__g}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(1))