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

WORST_CASE(?,O(1))