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

WORST_CASE(Omega(n^1),?)