/export/starexec/sandbox/solver/bin/starexec_run_tct_rci /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:
            goal(xs) -> subsets(xs)
            mapconsapp(x,Nil(),rest) -> rest
            mapconsapp(x',Cons(x,xs),rest) -> Cons(Cons(x',x),mapconsapp(x',xs,rest))
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
            subsets(Cons(x,xs)) -> subsets[Ite][True][Let](Cons(x,xs),subsets(xs))
            subsets(Nil()) -> Cons(Nil(),Nil())
        - Weak TRS:
            subsets[Ite][True][Let](Cons(x,xs),subs) -> mapconsapp(x,subs,subs)
        - Signature:
            {goal/1,mapconsapp/3,notEmpty/1,subsets/1,subsets[Ite][True][Let]/2} / {Cons/2,False/0,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal,mapconsapp,notEmpty,subsets
            ,subsets[Ite][True][Let]} and constructors {Cons,False,Nil,True}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: Sum.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            goal(xs) -> subsets(xs)
            mapconsapp(x,Nil(),rest) -> rest
            mapconsapp(x',Cons(x,xs),rest) -> Cons(Cons(x',x),mapconsapp(x',xs,rest))
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
            subsets(Cons(x,xs)) -> subsets[Ite][True][Let](Cons(x,xs),subsets(xs))
            subsets(Nil()) -> Cons(Nil(),Nil())
        - Weak TRS:
            subsets[Ite][True][Let](Cons(x,xs),subs) -> mapconsapp(x,subs,subs)
        - Signature:
            {goal/1,mapconsapp/3,notEmpty/1,subsets/1,subsets[Ite][True][Let]/2} / {Cons/2,False/0,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal,mapconsapp,notEmpty,subsets
            ,subsets[Ite][True][Let]} and constructors {Cons,False,Nil,True}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 3: DecreasingLoops.  WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            goal(xs) -> subsets(xs)
            mapconsapp(x,Nil(),rest) -> rest
            mapconsapp(x',Cons(x,xs),rest) -> Cons(Cons(x',x),mapconsapp(x',xs,rest))
            notEmpty(Cons(x,xs)) -> True()
            notEmpty(Nil()) -> False()
            subsets(Cons(x,xs)) -> subsets[Ite][True][Let](Cons(x,xs),subsets(xs))
            subsets(Nil()) -> Cons(Nil(),Nil())
        - Weak TRS:
            subsets[Ite][True][Let](Cons(x,xs),subs) -> mapconsapp(x,subs,subs)
        - Signature:
            {goal/1,mapconsapp/3,notEmpty/1,subsets/1,subsets[Ite][True][Let]/2} / {Cons/2,False/0,Nil/0,True/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {goal,mapconsapp,notEmpty,subsets
            ,subsets[Ite][True][Let]} and constructors {Cons,False,Nil,True}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          mapconsapp(x,z,u){z -> Cons(y,z)} =
            mapconsapp(x,Cons(y,z),u) ->^+ Cons(Cons(x,y),mapconsapp(x,z,u))
              = C[mapconsapp(x,z,u) = mapconsapp(x,z,u){}]

WORST_CASE(Omega(n^1),?)