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

WORST_CASE(Omega(n^1),?)