* Step 1: Sum WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(add(n,x),y) -> add(n,app(x,y))
            app(nil(),y) -> y
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            head(add(n,x)) -> n
            if(false(),x,y,z) -> if2(eq(head(x),min(x)),x,y,z)
            if(true(),x,y,z) -> z
            if2(false(),x,y,z) -> mins(tail(x),add(head(x),y),z)
            if2(true(),x,y,z) -> mins(app(rm(head(x),tail(x)),y),nil(),app(z,add(head(x),nil())))
            if_min(false(),add(n,add(m,x))) -> min(add(m,x))
            if_min(true(),add(n,add(m,x))) -> min(add(n,x))
            if_rm(false(),n,add(m,x)) -> add(m,rm(n,x))
            if_rm(true(),n,add(m,x)) -> rm(n,x)
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            min(add(n,add(m,x))) -> if_min(le(n,m),add(n,add(m,x)))
            min(add(n,nil())) -> n
            mins(x,y,z) -> if(null(x),x,y,z)
            minsort(x) -> mins(x,nil(),nil())
            null(add(n,x)) -> false()
            null(nil()) -> true()
            rm(n,add(m,x)) -> if_rm(eq(n,m),n,add(m,x))
            rm(n,nil()) -> nil()
            tail(add(n,x)) -> x
            tail(nil()) -> nil()
        - Signature:
            {app/2,eq/2,head/1,if/4,if2/4,if_min/2,if_rm/3,le/2,min/1,mins/3,minsort/1,null/1,rm/2,tail/1} / {0/0,add/2
            ,false/0,nil/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app,eq,head,if,if2,if_min,if_rm,le,min,mins,minsort,null
            ,rm,tail} and constructors {0,add,false,nil,s,true}
    + Applied Processor:
        Sum {left = someStrategy, right = someStrategy}
    + Details:
        ()
* Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?)
    + Considered Problem:
        - Strict TRS:
            app(add(n,x),y) -> add(n,app(x,y))
            app(nil(),y) -> y
            eq(0(),0()) -> true()
            eq(0(),s(x)) -> false()
            eq(s(x),0()) -> false()
            eq(s(x),s(y)) -> eq(x,y)
            head(add(n,x)) -> n
            if(false(),x,y,z) -> if2(eq(head(x),min(x)),x,y,z)
            if(true(),x,y,z) -> z
            if2(false(),x,y,z) -> mins(tail(x),add(head(x),y),z)
            if2(true(),x,y,z) -> mins(app(rm(head(x),tail(x)),y),nil(),app(z,add(head(x),nil())))
            if_min(false(),add(n,add(m,x))) -> min(add(m,x))
            if_min(true(),add(n,add(m,x))) -> min(add(n,x))
            if_rm(false(),n,add(m,x)) -> add(m,rm(n,x))
            if_rm(true(),n,add(m,x)) -> rm(n,x)
            le(0(),y) -> true()
            le(s(x),0()) -> false()
            le(s(x),s(y)) -> le(x,y)
            min(add(n,add(m,x))) -> if_min(le(n,m),add(n,add(m,x)))
            min(add(n,nil())) -> n
            mins(x,y,z) -> if(null(x),x,y,z)
            minsort(x) -> mins(x,nil(),nil())
            null(add(n,x)) -> false()
            null(nil()) -> true()
            rm(n,add(m,x)) -> if_rm(eq(n,m),n,add(m,x))
            rm(n,nil()) -> nil()
            tail(add(n,x)) -> x
            tail(nil()) -> nil()
        - Signature:
            {app/2,eq/2,head/1,if/4,if2/4,if_min/2,if_rm/3,le/2,min/1,mins/3,minsort/1,null/1,rm/2,tail/1} / {0/0,add/2
            ,false/0,nil/0,s/1,true/0}
        - Obligation:
            innermost runtime complexity wrt. defined symbols {app,eq,head,if,if2,if_min,if_rm,le,min,mins,minsort,null
            ,rm,tail} and constructors {0,add,false,nil,s,true}
    + Applied Processor:
        DecreasingLoops {bound = AnyLoop, narrow = 10}
    + Details:
        The system has following decreasing Loops:
          app(y,z){y -> add(x,y)} =
            app(add(x,y),z) ->^+ add(x,app(y,z))
              = C[app(y,z) = app(y,z){}]

WORST_CASE(Omega(n^1),?)