/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:
            a__eq(X,Y) -> false()
            a__eq(X1,X2) -> eq(X1,X2)
            a__eq(0(),0()) -> true()
            a__eq(s(X),s(Y)) -> a__eq(X,Y)
            a__inf(X) -> cons(X,inf(s(X)))
            a__inf(X) -> inf(X)
            a__length(X) -> length(X)
            a__length(cons(X,L)) -> s(length(L))
            a__length(nil()) -> 0()
            a__take(X1,X2) -> take(X1,X2)
            a__take(0(),X) -> nil()
            a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(X1,X2)
            mark(eq(X1,X2)) -> a__eq(X1,X2)
            mark(false()) -> false()
            mark(inf(X)) -> a__inf(mark(X))
            mark(length(X)) -> a__length(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(X)
            mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
            mark(true()) -> true()
        - Signature:
            {a__eq/2,a__inf/1,a__length/1,a__take/2,mark/1} / {0/0,cons/2,eq/2,false/0,inf/1,length/1,nil/0,s/1,take/2
            ,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__eq,a__inf,a__length,a__take,mark} and constructors {0,cons,eq
            ,false,inf,length,nil,s,take,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__eq(X,Y) -> false()
            a__eq(X1,X2) -> eq(X1,X2)
            a__eq(0(),0()) -> true()
            a__eq(s(X),s(Y)) -> a__eq(X,Y)
            a__inf(X) -> cons(X,inf(s(X)))
            a__inf(X) -> inf(X)
            a__length(X) -> length(X)
            a__length(cons(X,L)) -> s(length(L))
            a__length(nil()) -> 0()
            a__take(X1,X2) -> take(X1,X2)
            a__take(0(),X) -> nil()
            a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(X1,X2)
            mark(eq(X1,X2)) -> a__eq(X1,X2)
            mark(false()) -> false()
            mark(inf(X)) -> a__inf(mark(X))
            mark(length(X)) -> a__length(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(X)
            mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
            mark(true()) -> true()
        - Signature:
            {a__eq/2,a__inf/1,a__length/1,a__take/2,mark/1} / {0/0,cons/2,eq/2,false/0,inf/1,length/1,nil/0,s/1,take/2
            ,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__eq,a__inf,a__length,a__take,mark} and constructors {0,cons,eq
            ,false,inf,length,nil,s,take,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__eq(X,Y) -> false()
            a__eq(X1,X2) -> eq(X1,X2)
            a__eq(0(),0()) -> true()
            a__eq(s(X),s(Y)) -> a__eq(X,Y)
            a__inf(X) -> cons(X,inf(s(X)))
            a__inf(X) -> inf(X)
            a__length(X) -> length(X)
            a__length(cons(X,L)) -> s(length(L))
            a__length(nil()) -> 0()
            a__take(X1,X2) -> take(X1,X2)
            a__take(0(),X) -> nil()
            a__take(s(X),cons(Y,L)) -> cons(Y,take(X,L))
            mark(0()) -> 0()
            mark(cons(X1,X2)) -> cons(X1,X2)
            mark(eq(X1,X2)) -> a__eq(X1,X2)
            mark(false()) -> false()
            mark(inf(X)) -> a__inf(mark(X))
            mark(length(X)) -> a__length(mark(X))
            mark(nil()) -> nil()
            mark(s(X)) -> s(X)
            mark(take(X1,X2)) -> a__take(mark(X1),mark(X2))
            mark(true()) -> true()
        - Signature:
            {a__eq/2,a__inf/1,a__length/1,a__take/2,mark/1} / {0/0,cons/2,eq/2,false/0,inf/1,length/1,nil/0,s/1,take/2
            ,true/0}
        - Obligation:
             runtime complexity wrt. defined symbols {a__eq,a__inf,a__length,a__take,mark} and constructors {0,cons,eq
            ,false,inf,length,nil,s,take,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          a__eq(x,y){x -> s(x),y -> s(y)} =
            a__eq(s(x),s(y)) ->^+ a__eq(x,y)
              = C[a__eq(x,y) = a__eq(x,y){}]

WORST_CASE(Omega(n^1),?)