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

WORST_CASE(Omega(n^1),?)