/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,+(y,z)) -> +(*(x,y),*(x,z))
            *(#(),x) -> #()
            *(*(x,y),z) -> *(x,*(y,z))
            *(0(x),y) -> 0(*(x,y))
            *(1(x),y) -> +(0(*(x,y)),y)
            +(x,#()) -> x
            +(#(),x) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(0(x),0(y)) -> 0(+(x,y))
            +(0(x),1(y)) -> 1(+(x,y))
            +(1(x),0(y)) -> 1(+(x,y))
            +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
            0(#()) -> #()
            app(cons(x,l1),l2) -> cons(x,app(l1,l2))
            app(nil(),l) -> l
            prod(app(l1,l2)) -> *(prod(l1),prod(l2))
            prod(cons(x,l)) -> *(x,prod(l))
            prod(nil()) -> 1(#())
            sum(app(l1,l2)) -> +(sum(l1),sum(l2))
            sum(cons(x,l)) -> +(x,sum(l))
            sum(nil()) -> 0(#())
        - Signature:
            {*/2,+/2,0/1,app/2,prod/1,sum/1} / {#/0,1/1,cons/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {*,+,0,app,prod,sum} and constructors {#,1,cons,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            *(x,+(y,z)) -> +(*(x,y),*(x,z))
            *(#(),x) -> #()
            *(*(x,y),z) -> *(x,*(y,z))
            *(0(x),y) -> 0(*(x,y))
            *(1(x),y) -> +(0(*(x,y)),y)
            +(x,#()) -> x
            +(#(),x) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(0(x),0(y)) -> 0(+(x,y))
            +(0(x),1(y)) -> 1(+(x,y))
            +(1(x),0(y)) -> 1(+(x,y))
            +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
            0(#()) -> #()
            app(cons(x,l1),l2) -> cons(x,app(l1,l2))
            app(nil(),l) -> l
            prod(app(l1,l2)) -> *(prod(l1),prod(l2))
            prod(cons(x,l)) -> *(x,prod(l))
            prod(nil()) -> 1(#())
            sum(app(l1,l2)) -> +(sum(l1),sum(l2))
            sum(cons(x,l)) -> +(x,sum(l))
            sum(nil()) -> 0(#())
        - Signature:
            {*/2,+/2,0/1,app/2,prod/1,sum/1} / {#/0,1/1,cons/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {*,+,0,app,prod,sum} and constructors {#,1,cons,nil}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            *(x,+(y,z)) -> +(*(x,y),*(x,z))
            *(#(),x) -> #()
            *(*(x,y),z) -> *(x,*(y,z))
            *(0(x),y) -> 0(*(x,y))
            *(1(x),y) -> +(0(*(x,y)),y)
            +(x,#()) -> x
            +(#(),x) -> x
            +(+(x,y),z) -> +(x,+(y,z))
            +(0(x),0(y)) -> 0(+(x,y))
            +(0(x),1(y)) -> 1(+(x,y))
            +(1(x),0(y)) -> 1(+(x,y))
            +(1(x),1(y)) -> 0(+(+(x,y),1(#())))
            0(#()) -> #()
            app(cons(x,l1),l2) -> cons(x,app(l1,l2))
            app(nil(),l) -> l
            prod(app(l1,l2)) -> *(prod(l1),prod(l2))
            prod(cons(x,l)) -> *(x,prod(l))
            prod(nil()) -> 1(#())
            sum(app(l1,l2)) -> +(sum(l1),sum(l2))
            sum(cons(x,l)) -> +(x,sum(l))
            sum(nil()) -> 0(#())
        - Signature:
            {*/2,+/2,0/1,app/2,prod/1,sum/1} / {#/0,1/1,cons/2,nil/0}
        - Obligation:
             runtime complexity wrt. defined symbols {*,+,0,app,prod,sum} and constructors {#,1,cons,nil}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          *(x,y){x -> 1(x)} =
            *(1(x),y) ->^+ +(0(*(x,y)),y)
              = C[*(x,y) = *(x,y){}]

WORST_CASE(Omega(n^1),?)