/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(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(first(X1,X2)) -> first(X1,active(X2))
            active(first(X1,X2)) -> first(active(X1),X2)
            active(first(0(),X)) -> mark(nil())
            active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
            active(from(X)) -> from(active(X))
            active(from(X)) -> mark(cons(X,from(s(X))))
            active(s(X)) -> s(active(X))
            cons(mark(X1),X2) -> mark(cons(X1,X2))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            first(X1,mark(X2)) -> mark(first(X1,X2))
            first(mark(X1),X2) -> mark(first(X1,X2))
            first(ok(X1),ok(X2)) -> ok(first(X1,X2))
            from(mark(X)) -> mark(from(X))
            from(ok(X)) -> ok(from(X))
            proper(0()) -> ok(0())
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(first(X1,X2)) -> first(proper(X1),proper(X2))
            proper(from(X)) -> from(proper(X))
            proper(nil()) -> ok(nil())
            proper(s(X)) -> s(proper(X))
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,cons/2,first/2,from/1,proper/1,s/1,top/1} / {0/0,mark/1,nil/0,ok/1}
        - Obligation:
             runtime complexity wrt. defined symbols {active,cons,first,from,proper,s,top} and constructors {0,mark,nil
            ,ok}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(first(X1,X2)) -> first(X1,active(X2))
            active(first(X1,X2)) -> first(active(X1),X2)
            active(first(0(),X)) -> mark(nil())
            active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
            active(from(X)) -> from(active(X))
            active(from(X)) -> mark(cons(X,from(s(X))))
            active(s(X)) -> s(active(X))
            cons(mark(X1),X2) -> mark(cons(X1,X2))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            first(X1,mark(X2)) -> mark(first(X1,X2))
            first(mark(X1),X2) -> mark(first(X1,X2))
            first(ok(X1),ok(X2)) -> ok(first(X1,X2))
            from(mark(X)) -> mark(from(X))
            from(ok(X)) -> ok(from(X))
            proper(0()) -> ok(0())
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(first(X1,X2)) -> first(proper(X1),proper(X2))
            proper(from(X)) -> from(proper(X))
            proper(nil()) -> ok(nil())
            proper(s(X)) -> s(proper(X))
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,cons/2,first/2,from/1,proper/1,s/1,top/1} / {0/0,mark/1,nil/0,ok/1}
        - Obligation:
             runtime complexity wrt. defined symbols {active,cons,first,from,proper,s,top} and constructors {0,mark,nil
            ,ok}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            active(cons(X1,X2)) -> cons(active(X1),X2)
            active(first(X1,X2)) -> first(X1,active(X2))
            active(first(X1,X2)) -> first(active(X1),X2)
            active(first(0(),X)) -> mark(nil())
            active(first(s(X),cons(Y,Z))) -> mark(cons(Y,first(X,Z)))
            active(from(X)) -> from(active(X))
            active(from(X)) -> mark(cons(X,from(s(X))))
            active(s(X)) -> s(active(X))
            cons(mark(X1),X2) -> mark(cons(X1,X2))
            cons(ok(X1),ok(X2)) -> ok(cons(X1,X2))
            first(X1,mark(X2)) -> mark(first(X1,X2))
            first(mark(X1),X2) -> mark(first(X1,X2))
            first(ok(X1),ok(X2)) -> ok(first(X1,X2))
            from(mark(X)) -> mark(from(X))
            from(ok(X)) -> ok(from(X))
            proper(0()) -> ok(0())
            proper(cons(X1,X2)) -> cons(proper(X1),proper(X2))
            proper(first(X1,X2)) -> first(proper(X1),proper(X2))
            proper(from(X)) -> from(proper(X))
            proper(nil()) -> ok(nil())
            proper(s(X)) -> s(proper(X))
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
        - Signature:
            {active/1,cons/2,first/2,from/1,proper/1,s/1,top/1} / {0/0,mark/1,nil/0,ok/1}
        - Obligation:
             runtime complexity wrt. defined symbols {active,cons,first,from,proper,s,top} and constructors {0,mark,nil
            ,ok}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          cons(x,y){x -> mark(x)} =
            cons(mark(x),y) ->^+ mark(cons(x,y))
              = C[cons(x,y) = cons(x,y){}]

WORST_CASE(Omega(n^1),?)