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


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WORST_CASE(?,O(n^1))
* Step 1: Sum.  WORST_CASE(?,O(n^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:
             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: ToInnermost.  WORST_CASE(?,O(n^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:
             runtime complexity wrt. defined symbols {a__c,a__f,mark} and constructors {c,f,g}
    + Applied Processor:
        ToInnermost
    + Details:
        switch to innermost, as the system is overlay and right linear and does not contain weak rules
* Step 3: Bounds.  WORST_CASE(?,O(n^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:
        Bounds {initialAutomaton = minimal, enrichment = match}
    + Details:
        The problem is match-bounded by 3.
        The enriched problem is compatible with follwoing automaton.
          a__c_0() -> 1
          a__c_1() -> 1
          a__f_0(2) -> 1
          a__f_1(2) -> 1
          a__f_1(3) -> 1
          a__f_2(5) -> 1
          c_0() -> 2
          c_1() -> 1
          c_1() -> 4
          c_2() -> 1
          c_2() -> 6
          f_0(2) -> 2
          f_1(2) -> 1
          f_2(2) -> 1
          f_2(3) -> 1
          f_3(5) -> 1
          g_0(2) -> 2
          g_1(2) -> 1
          g_1(4) -> 3
          g_2(4) -> 1
          g_2(6) -> 5
          g_3(6) -> 1
          mark_0(2) -> 1
* Step 4: 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} / {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:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))