/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:
            f(s(s(s(s(s(s(s(s(x)))))))),y,y) -> f(id(s(s(s(s(s(s(s(s(x))))))))),y,y)
            id(0()) -> 0()
            id(s(x)) -> s(id(x))
        - Signature:
            {f/3,id/1} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,id} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(s(s(s(s(s(s(s(s(x)))))))),y,y) -> f(id(s(s(s(s(s(s(s(s(x))))))))),y,y)
            id(0()) -> 0()
            id(s(x)) -> s(id(x))
        - Signature:
            {f/3,id/1} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,id} and constructors {0,s}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            f(s(s(s(s(s(s(s(s(x)))))))),y,y) -> f(id(s(s(s(s(s(s(s(s(x))))))))),y,y)
            id(0()) -> 0()
            id(s(x)) -> s(id(x))
        - Signature:
            {f/3,id/1} / {0/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {f,id} and constructors {0,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          id(x){x -> s(x)} =
            id(s(x)) ->^+ s(id(x))
              = C[id(x) = id(x){}]

WORST_CASE(Omega(n^1),?)