/export/starexec/sandbox/solver/bin/starexec_run_tct_rc /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:
            a__c() -> c()
            a__c() -> d()
            a__g(X) -> a__h(X)
            a__g(X) -> g(X)
            a__h(X) -> h(X)
            a__h(d()) -> a__g(c())
            mark(c()) -> a__c()
            mark(d()) -> d()
            mark(g(X)) -> a__g(X)
            mark(h(X)) -> a__h(X)
        - Signature:
            {a__c/0,a__g/1,a__h/1,mark/1} / {c/0,d/0,g/1,h/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a__c,a__g,a__h,mark} and constructors {c,d,g,h}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: ToInnermost.  WORST_CASE(?,O(n^1))
    + Considered Problem:
        - Strict TRS:
            a__c() -> c()
            a__c() -> d()
            a__g(X) -> a__h(X)
            a__g(X) -> g(X)
            a__h(X) -> h(X)
            a__h(d()) -> a__g(c())
            mark(c()) -> a__c()
            mark(d()) -> d()
            mark(g(X)) -> a__g(X)
            mark(h(X)) -> a__h(X)
        - Signature:
            {a__c/0,a__g/1,a__h/1,mark/1} / {c/0,d/0,g/1,h/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a__c,a__g,a__h,mark} and constructors {c,d,g,h}
    + 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() -> c()
            a__c() -> d()
            a__g(X) -> a__h(X)
            a__g(X) -> g(X)
            a__h(X) -> h(X)
            a__h(d()) -> a__g(c())
            mark(c()) -> a__c()
            mark(d()) -> d()
            mark(g(X)) -> a__g(X)
            mark(h(X)) -> a__h(X)
        - Signature:
            {a__c/0,a__g/1,a__h/1,mark/1} / {c/0,d/0,g/1,h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__c,a__g,a__h,mark} and constructors {c,d,g,h}
    + Applied Processor:
        Bounds {initialAutomaton = perSymbol, enrichment = match}
    + Details:
        The problem is match-bounded by 5.
        The enriched problem is compatible with follwoing automaton.
          a__c_0() -> 1
          a__c_1() -> 8
          a__g_0(4) -> 2
          a__g_0(5) -> 2
          a__g_0(6) -> 2
          a__g_0(7) -> 2
          a__g_1(1) -> 2
          a__g_1(1) -> 3
          a__g_1(1) -> 8
          a__g_1(4) -> 8
          a__g_1(5) -> 8
          a__g_1(6) -> 8
          a__g_1(7) -> 8
          a__g_2(8) -> 2
          a__g_2(8) -> 3
          a__g_2(8) -> 8
          a__g_3(9) -> 2
          a__g_3(9) -> 3
          a__g_3(9) -> 8
          a__h_0(4) -> 3
          a__h_0(5) -> 3
          a__h_0(6) -> 3
          a__h_0(7) -> 3
          a__h_1(4) -> 2
          a__h_1(4) -> 8
          a__h_1(5) -> 2
          a__h_1(5) -> 8
          a__h_1(6) -> 2
          a__h_1(6) -> 8
          a__h_1(7) -> 2
          a__h_1(7) -> 8
          a__h_2(1) -> 2
          a__h_2(1) -> 3
          a__h_2(1) -> 8
          a__h_2(4) -> 8
          a__h_2(5) -> 8
          a__h_2(6) -> 8
          a__h_2(7) -> 8
          a__h_3(8) -> 2
          a__h_3(8) -> 3
          a__h_3(8) -> 8
          a__h_4(9) -> 2
          a__h_4(9) -> 3
          a__h_4(9) -> 8
          c_0() -> 4
          c_1() -> 1
          c_2() -> 8
          c_3() -> 9
          d_0() -> 5
          d_1() -> 1
          d_1() -> 8
          d_2() -> 8
          g_0(4) -> 6
          g_0(5) -> 6
          g_0(6) -> 6
          g_0(7) -> 6
          g_1(4) -> 2
          g_1(5) -> 2
          g_1(6) -> 2
          g_1(7) -> 2
          g_2(1) -> 2
          g_2(1) -> 3
          g_2(1) -> 8
          g_2(4) -> 8
          g_2(5) -> 8
          g_2(6) -> 8
          g_2(7) -> 8
          g_3(8) -> 2
          g_3(8) -> 3
          g_3(8) -> 8
          g_4(9) -> 2
          g_4(9) -> 3
          g_4(9) -> 8
          h_0(4) -> 7
          h_0(5) -> 7
          h_0(6) -> 7
          h_0(7) -> 7
          h_1(4) -> 3
          h_1(5) -> 3
          h_1(6) -> 3
          h_1(7) -> 3
          h_2(4) -> 2
          h_2(4) -> 8
          h_2(5) -> 2
          h_2(5) -> 8
          h_2(6) -> 2
          h_2(6) -> 8
          h_2(7) -> 2
          h_2(7) -> 8
          h_3(1) -> 2
          h_3(1) -> 3
          h_3(1) -> 8
          h_3(4) -> 8
          h_3(5) -> 8
          h_3(6) -> 8
          h_3(7) -> 8
          h_4(8) -> 2
          h_4(8) -> 3
          h_4(8) -> 8
          h_5(9) -> 2
          h_5(9) -> 3
          h_5(9) -> 8
          mark_0(4) -> 8
          mark_0(5) -> 8
          mark_0(6) -> 8
          mark_0(7) -> 8
* Step 4: EmptyProcessor.  WORST_CASE(?,O(1))
    + Considered Problem:
        - Weak TRS:
            a__c() -> c()
            a__c() -> d()
            a__g(X) -> a__h(X)
            a__g(X) -> g(X)
            a__h(X) -> h(X)
            a__h(d()) -> a__g(c())
            mark(c()) -> a__c()
            mark(d()) -> d()
            mark(g(X)) -> a__g(X)
            mark(h(X)) -> a__h(X)
        - Signature:
            {a__c/0,a__g/1,a__h/1,mark/1} / {c/0,d/0,g/1,h/1}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {a__c,a__g,a__h,mark} and constructors {c,d,g,h}
    + Applied Processor:
        EmptyProcessor
    + Details:
        The problem is already closed. The intended complexity is O(1).

WORST_CASE(?,O(n^1))