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