* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            active(add(X1,X2)) -> add(X1,active(X2))
            active(add(X1,X2)) -> add(active(X1),X2)
            active(add(0(),X)) -> mark(X)
            active(add(s(X),Y)) -> mark(s(add(X,Y)))
            active(fact(X)) -> fact(active(X))
            active(fact(X)) -> mark(if(zero(X),s(0()),prod(X,fact(p(X)))))
            active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
            active(if(false(),X,Y)) -> mark(Y)
            active(if(true(),X,Y)) -> mark(X)
            active(p(X)) -> p(active(X))
            active(p(s(X))) -> mark(X)
            active(prod(X1,X2)) -> prod(X1,active(X2))
            active(prod(X1,X2)) -> prod(active(X1),X2)
            active(prod(0(),X)) -> mark(0())
            active(prod(s(X),Y)) -> mark(add(Y,prod(X,Y)))
            active(s(X)) -> s(active(X))
            active(zero(X)) -> zero(active(X))
            active(zero(0())) -> mark(true())
            active(zero(s(X))) -> mark(false())
            add(X1,mark(X2)) -> mark(add(X1,X2))
            add(mark(X1),X2) -> mark(add(X1,X2))
            add(ok(X1),ok(X2)) -> ok(add(X1,X2))
            fact(mark(X)) -> mark(fact(X))
            fact(ok(X)) -> ok(fact(X))
            if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
            if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
            p(mark(X)) -> mark(p(X))
            p(ok(X)) -> ok(p(X))
            prod(X1,mark(X2)) -> mark(prod(X1,X2))
            prod(mark(X1),X2) -> mark(prod(X1,X2))
            prod(ok(X1),ok(X2)) -> ok(prod(X1,X2))
            proper(0()) -> ok(0())
            proper(add(X1,X2)) -> add(proper(X1),proper(X2))
            proper(fact(X)) -> fact(proper(X))
            proper(false()) -> ok(false())
            proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
            proper(p(X)) -> p(proper(X))
            proper(prod(X1,X2)) -> prod(proper(X1),proper(X2))
            proper(s(X)) -> s(proper(X))
            proper(true()) -> ok(true())
            proper(zero(X)) -> zero(proper(X))
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
            zero(mark(X)) -> mark(zero(X))
            zero(ok(X)) -> ok(zero(X))
        - Signature:
            {active/1,add/2,fact/1,if/3,p/1,prod/2,proper/1,s/1,top/1,zero/1} / {0/0,false/0,mark/1,ok/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,add,fact,if,p,prod,proper,s,top
            ,zero} and constructors {0,false,mark,ok,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            active(add(X1,X2)) -> add(X1,active(X2))
            active(add(X1,X2)) -> add(active(X1),X2)
            active(add(0(),X)) -> mark(X)
            active(add(s(X),Y)) -> mark(s(add(X,Y)))
            active(fact(X)) -> fact(active(X))
            active(fact(X)) -> mark(if(zero(X),s(0()),prod(X,fact(p(X)))))
            active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
            active(if(false(),X,Y)) -> mark(Y)
            active(if(true(),X,Y)) -> mark(X)
            active(p(X)) -> p(active(X))
            active(p(s(X))) -> mark(X)
            active(prod(X1,X2)) -> prod(X1,active(X2))
            active(prod(X1,X2)) -> prod(active(X1),X2)
            active(prod(0(),X)) -> mark(0())
            active(prod(s(X),Y)) -> mark(add(Y,prod(X,Y)))
            active(s(X)) -> s(active(X))
            active(zero(X)) -> zero(active(X))
            active(zero(0())) -> mark(true())
            active(zero(s(X))) -> mark(false())
            add(X1,mark(X2)) -> mark(add(X1,X2))
            add(mark(X1),X2) -> mark(add(X1,X2))
            add(ok(X1),ok(X2)) -> ok(add(X1,X2))
            fact(mark(X)) -> mark(fact(X))
            fact(ok(X)) -> ok(fact(X))
            if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
            if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
            p(mark(X)) -> mark(p(X))
            p(ok(X)) -> ok(p(X))
            prod(X1,mark(X2)) -> mark(prod(X1,X2))
            prod(mark(X1),X2) -> mark(prod(X1,X2))
            prod(ok(X1),ok(X2)) -> ok(prod(X1,X2))
            proper(0()) -> ok(0())
            proper(add(X1,X2)) -> add(proper(X1),proper(X2))
            proper(fact(X)) -> fact(proper(X))
            proper(false()) -> ok(false())
            proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
            proper(p(X)) -> p(proper(X))
            proper(prod(X1,X2)) -> prod(proper(X1),proper(X2))
            proper(s(X)) -> s(proper(X))
            proper(true()) -> ok(true())
            proper(zero(X)) -> zero(proper(X))
            s(mark(X)) -> mark(s(X))
            s(ok(X)) -> ok(s(X))
            top(mark(X)) -> top(proper(X))
            top(ok(X)) -> top(active(X))
            zero(mark(X)) -> mark(zero(X))
            zero(ok(X)) -> ok(zero(X))
        - Signature:
            {active/1,add/2,fact/1,if/3,p/1,prod/2,proper/1,s/1,top/1,zero/1} / {0/0,false/0,mark/1,ok/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {active,add,fact,if,p,prod,proper,s,top
            ,zero} and constructors {0,false,mark,ok,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          add(x,y){y -> mark(y)} =
            add(x,mark(y)) ->^+ mark(add(x,y))
              = C[add(x,y) = add(x,y){}]

WORST_CASE(Omega(n^1),?)