* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: app(x,y) -> helpa(0(),plus(length(x),length(y)),x,y) ge(x,0()) -> true() ge(0(),s(x)) -> false() ge(s(x),s(y)) -> ge(x,y) helpa(c,l,ys,zs) -> if(ge(c,l),c,l,ys,zs) helpb(c,l,ys,zs) -> cons(take(c,ys,zs),helpa(s(c),l,ys,zs)) if(false(),c,l,ys,zs) -> helpb(c,l,ys,zs) if(true(),c,l,ys,zs) -> nil() length(cons(x,y)) -> s(length(y)) length(nil()) -> 0() plus(x,0()) -> x plus(x,s(y)) -> s(plus(x,y)) take(0(),cons(x,xs()),ys) -> x take(0(),nil(),cons(y,ys)) -> y take(s(c),cons(x,xs()),ys) -> take(c,xs(),ys) take(s(c),nil(),cons(y,ys)) -> take(c,nil(),ys) - Signature: {app/2,ge/2,helpa/4,helpb/4,if/5,length/1,plus/2,take/3} / {0/0,cons/2,false/0,nil/0,s/1,true/0,xs/0} - Obligation: innermost runtime complexity wrt. defined symbols {app,ge,helpa,helpb,if,length,plus ,take} and constructors {0,cons,false,nil,s,true,xs} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: app(x,y) -> helpa(0(),plus(length(x),length(y)),x,y) ge(x,0()) -> true() ge(0(),s(x)) -> false() ge(s(x),s(y)) -> ge(x,y) helpa(c,l,ys,zs) -> if(ge(c,l),c,l,ys,zs) helpb(c,l,ys,zs) -> cons(take(c,ys,zs),helpa(s(c),l,ys,zs)) if(false(),c,l,ys,zs) -> helpb(c,l,ys,zs) if(true(),c,l,ys,zs) -> nil() length(cons(x,y)) -> s(length(y)) length(nil()) -> 0() plus(x,0()) -> x plus(x,s(y)) -> s(plus(x,y)) take(0(),cons(x,xs()),ys) -> x take(0(),nil(),cons(y,ys)) -> y take(s(c),cons(x,xs()),ys) -> take(c,xs(),ys) take(s(c),nil(),cons(y,ys)) -> take(c,nil(),ys) - Signature: {app/2,ge/2,helpa/4,helpb/4,if/5,length/1,plus/2,take/3} / {0/0,cons/2,false/0,nil/0,s/1,true/0,xs/0} - Obligation: innermost runtime complexity wrt. defined symbols {app,ge,helpa,helpb,if,length,plus ,take} and constructors {0,cons,false,nil,s,true,xs} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: ge(x,y){x -> s(x),y -> s(y)} = ge(s(x),s(y)) ->^+ ge(x,y) = C[ge(x,y) = ge(x,y){}] WORST_CASE(Omega(n^1),?)