/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()
            *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
            +(x,0()) -> x
            +(0(),x) -> x
            +(s(x),s(y)) -> s(s(+(x,y)))
            prod(cons(x,l)) -> *(x,prod(l))
            prod(nil()) -> s(0())
            sum(cons(x,l)) -> +(x,sum(l))
            sum(nil()) -> 0()
        - Signature:
            {*/2,+/2,prod/1,sum/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {*,+,prod,sum} and constructors {0,cons,nil,s}
    + 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()
            *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
            +(x,0()) -> x
            +(0(),x) -> x
            +(s(x),s(y)) -> s(s(+(x,y)))
            prod(cons(x,l)) -> *(x,prod(l))
            prod(nil()) -> s(0())
            sum(cons(x,l)) -> +(x,sum(l))
            sum(nil()) -> 0()
        - Signature:
            {*/2,+/2,prod/1,sum/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {*,+,prod,sum} and constructors {0,cons,nil,s}
    + 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()
            *(s(x),s(y)) -> s(+(*(x,y),+(x,y)))
            +(x,0()) -> x
            +(0(),x) -> x
            +(s(x),s(y)) -> s(s(+(x,y)))
            prod(cons(x,l)) -> *(x,prod(l))
            prod(nil()) -> s(0())
            sum(cons(x,l)) -> +(x,sum(l))
            sum(nil()) -> 0()
        - Signature:
            {*/2,+/2,prod/1,sum/1} / {0/0,cons/2,nil/0,s/1}
        - Obligation:
             runtime complexity wrt. defined symbols {*,+,prod,sum} and constructors {0,cons,nil,s}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          *(x,y){x -> s(x),y -> s(y)} =
            *(s(x),s(y)) ->^+ s(+(*(x,y),+(x,y)))
              = C[*(x,y) = *(x,y){}]

WORST_CASE(Omega(n^1),?)