/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:
            rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
            rev(nil()) -> nil()
            rev1(x,++(y,z)) -> rev1(y,z)
            rev1(x,nil()) -> x
            rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
            rev2(x,nil()) -> nil()
        - Signature:
            {rev/1,rev1/2,rev2/2} / {++/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {rev,rev1,rev2} and constructors {++,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
            rev(nil()) -> nil()
            rev1(x,++(y,z)) -> rev1(y,z)
            rev1(x,nil()) -> x
            rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
            rev2(x,nil()) -> nil()
        - Signature:
            {rev/1,rev1/2,rev2/2} / {++/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {rev,rev1,rev2} and constructors {++,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            rev(++(x,y)) -> ++(rev1(x,y),rev2(x,y))
            rev(nil()) -> nil()
            rev1(x,++(y,z)) -> rev1(y,z)
            rev1(x,nil()) -> x
            rev2(x,++(y,z)) -> rev(++(x,rev(rev2(y,z))))
            rev2(x,nil()) -> nil()
        - Signature:
            {rev/1,rev1/2,rev2/2} / {++/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {rev,rev1,rev2} and constructors {++,nil}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          rev1(x,z){z -> ++(y,z)} =
            rev1(x,++(y,z)) ->^+ rev1(y,z)
              = C[rev1(y,z) = rev1(x,z){x -> y}]

WORST_CASE(Omega(n^1),?)