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