/export/starexec/sandbox2/solver/bin/starexec_run_tct_rc /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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

WORST_CASE(Omega(n^1),?)