* 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(#())))
            -(x,#()) -> x
            -(#(),x) -> #()
            -(0(x),0(y)) -> 0(-(x,y))
            -(0(x),1(y)) -> 1(-(-(x,y),1(#())))
            -(1(x),0(y)) -> 1(-(x,y))
            -(1(x),1(y)) -> 0(-(x,y))
            0(#()) -> #()
            app(cons(x,l1),l2) -> cons(x,app(l1,l2))
            app(nil(),l) -> l
            eq(#(),#()) -> true()
            eq(#(),0(y)) -> eq(#(),y)
            eq(#(),1(y)) -> false()
            eq(0(x),#()) -> eq(x,#())
            eq(0(x),0(y)) -> eq(x,y)
            eq(0(x),1(y)) -> false()
            eq(1(x),#()) -> false()
            eq(1(x),0(y)) -> false()
            eq(1(x),1(y)) -> eq(x,y)
            ge(x,#()) -> true()
            ge(#(),0(x)) -> ge(#(),x)
            ge(#(),1(x)) -> false()
            ge(0(x),0(y)) -> ge(x,y)
            ge(0(x),1(y)) -> not(ge(y,x))
            ge(1(x),0(y)) -> ge(x,y)
            ge(1(x),1(y)) -> ge(x,y)
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            ifinter(false(),x,l1,l2) -> inter(l1,l2)
            ifinter(true(),x,l1,l2) -> cons(x,inter(l1,l2))
            inter(l1,app(l2,l3)) -> app(inter(l1,l2),inter(l1,l3))
            inter(l1,cons(x,l2)) -> ifinter(mem(x,l1),x,l2,l1)
            inter(x,nil()) -> nil()
            inter(app(l1,l2),l3) -> app(inter(l1,l3),inter(l2,l3))
            inter(cons(x,l1),l2) -> ifinter(mem(x,l2),x,l1,l2)
            inter(nil(),x) -> nil()
            log(x) -> -(log'(x),1(#()))
            log'(#()) -> #()
            log'(0(x)) -> if(ge(x,1(#())),+(log'(x),1(#())),#())
            log'(1(x)) -> +(log'(x),1(#()))
            mem(x,cons(y,l)) -> if(eq(x,y),true(),mem(x,l))
            mem(x,nil()) -> false()
            not(false()) -> true()
            not(true()) -> false()
            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,-/2,0/1,app/2,eq/2,ge/2,if/3,ifinter/4,inter/2,log/1,log'/1,mem/2,not/1,prod/1,sum/1} / {#/0,1/1
            ,cons/2,false/0,nil/0,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*,+,-,0,app,eq,ge,if,ifinter,inter,log,log',mem,not,prod
            ,sum} and constructors {#,1,cons,false,nil,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: 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(#())))
            -(x,#()) -> x
            -(#(),x) -> #()
            -(0(x),0(y)) -> 0(-(x,y))
            -(0(x),1(y)) -> 1(-(-(x,y),1(#())))
            -(1(x),0(y)) -> 1(-(x,y))
            -(1(x),1(y)) -> 0(-(x,y))
            0(#()) -> #()
            app(cons(x,l1),l2) -> cons(x,app(l1,l2))
            app(nil(),l) -> l
            eq(#(),#()) -> true()
            eq(#(),0(y)) -> eq(#(),y)
            eq(#(),1(y)) -> false()
            eq(0(x),#()) -> eq(x,#())
            eq(0(x),0(y)) -> eq(x,y)
            eq(0(x),1(y)) -> false()
            eq(1(x),#()) -> false()
            eq(1(x),0(y)) -> false()
            eq(1(x),1(y)) -> eq(x,y)
            ge(x,#()) -> true()
            ge(#(),0(x)) -> ge(#(),x)
            ge(#(),1(x)) -> false()
            ge(0(x),0(y)) -> ge(x,y)
            ge(0(x),1(y)) -> not(ge(y,x))
            ge(1(x),0(y)) -> ge(x,y)
            ge(1(x),1(y)) -> ge(x,y)
            if(false(),x,y) -> y
            if(true(),x,y) -> x
            ifinter(false(),x,l1,l2) -> inter(l1,l2)
            ifinter(true(),x,l1,l2) -> cons(x,inter(l1,l2))
            inter(l1,app(l2,l3)) -> app(inter(l1,l2),inter(l1,l3))
            inter(l1,cons(x,l2)) -> ifinter(mem(x,l1),x,l2,l1)
            inter(x,nil()) -> nil()
            inter(app(l1,l2),l3) -> app(inter(l1,l3),inter(l2,l3))
            inter(cons(x,l1),l2) -> ifinter(mem(x,l2),x,l1,l2)
            inter(nil(),x) -> nil()
            log(x) -> -(log'(x),1(#()))
            log'(#()) -> #()
            log'(0(x)) -> if(ge(x,1(#())),+(log'(x),1(#())),#())
            log'(1(x)) -> +(log'(x),1(#()))
            mem(x,cons(y,l)) -> if(eq(x,y),true(),mem(x,l))
            mem(x,nil()) -> false()
            not(false()) -> true()
            not(true()) -> false()
            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,-/2,0/1,app/2,eq/2,ge/2,if/3,ifinter/4,inter/2,log/1,log'/1,mem/2,not/1,prod/1,sum/1} / {#/0,1/1
            ,cons/2,false/0,nil/0,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {*,+,-,0,app,eq,ge,if,ifinter,inter,log,log',mem,not,prod
            ,sum} and constructors {#,1,cons,false,nil,true}
    + 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),?)