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


--------------------------------------------------------------------------------


WORST_CASE(Omega(n^1),?)
* Step 1: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__2nd(X) -> 2nd(X)
            a__2nd(cons(X,X1)) -> a__2nd(cons1(mark(X),mark(X1)))
            a__2nd(cons1(X,cons(Y,Z))) -> mark(Y)
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            mark(2nd(X)) -> a__2nd(mark(X))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(cons1(X1,X2)) -> cons1(mark(X1),mark(X2))
            mark(from(X)) -> a__from(mark(X))
            mark(s(X)) -> s(mark(X))
        - Signature:
            {a__2nd/1,a__from/1,mark/1} / {2nd/1,cons/2,cons1/2,from/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a__2nd,a__from,mark} and constructors {2nd,cons,cons1,from,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__2nd(X) -> 2nd(X)
            a__2nd(cons(X,X1)) -> a__2nd(cons1(mark(X),mark(X1)))
            a__2nd(cons1(X,cons(Y,Z))) -> mark(Y)
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            mark(2nd(X)) -> a__2nd(mark(X))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(cons1(X1,X2)) -> cons1(mark(X1),mark(X2))
            mark(from(X)) -> a__from(mark(X))
            mark(s(X)) -> s(mark(X))
        - Signature:
            {a__2nd/1,a__from/1,mark/1} / {2nd/1,cons/2,cons1/2,from/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a__2nd,a__from,mark} and constructors {2nd,cons,cons1,from,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            a__2nd(X) -> 2nd(X)
            a__2nd(cons(X,X1)) -> a__2nd(cons1(mark(X),mark(X1)))
            a__2nd(cons1(X,cons(Y,Z))) -> mark(Y)
            a__from(X) -> cons(mark(X),from(s(X)))
            a__from(X) -> from(X)
            mark(2nd(X)) -> a__2nd(mark(X))
            mark(cons(X1,X2)) -> cons(mark(X1),X2)
            mark(cons1(X1,X2)) -> cons1(mark(X1),mark(X2))
            mark(from(X)) -> a__from(mark(X))
            mark(s(X)) -> s(mark(X))
        - Signature:
            {a__2nd/1,a__from/1,mark/1} / {2nd/1,cons/2,cons1/2,from/1,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {a__2nd,a__from,mark} and constructors {2nd,cons,cons1,from,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mark(x){x -> 2nd(x)} =
            mark(2nd(x)) ->^+ a__2nd(mark(x))
              = C[mark(x) = mark(x){}]

WORST_CASE(Omega(n^1),?)