* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__add(X1,X2)) -> add(activate(X1),activate(X2)) activate(n__fib1(X1,X2)) -> fib1(activate(X1),activate(X2)) add(X1,X2) -> n__add(X1,X2) add(0(),X) -> X add(s(X),Y) -> s(add(X,Y)) fib(N) -> sel(N,fib1(s(0()),s(0()))) fib1(X,Y) -> cons(X,n__fib1(Y,n__add(X,Y))) fib1(X1,X2) -> n__fib1(X1,X2) sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) - Signature: {activate/1,add/2,fib/1,fib1/2,sel/2} / {0/0,cons/2,n__add/2,n__fib1/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,add,fib,fib1,sel} and constructors {0,cons ,n__add,n__fib1,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: activate(X) -> X activate(n__add(X1,X2)) -> add(activate(X1),activate(X2)) activate(n__fib1(X1,X2)) -> fib1(activate(X1),activate(X2)) add(X1,X2) -> n__add(X1,X2) add(0(),X) -> X add(s(X),Y) -> s(add(X,Y)) fib(N) -> sel(N,fib1(s(0()),s(0()))) fib1(X,Y) -> cons(X,n__fib1(Y,n__add(X,Y))) fib1(X1,X2) -> n__fib1(X1,X2) sel(0(),cons(X,XS)) -> X sel(s(N),cons(X,XS)) -> sel(N,activate(XS)) - Signature: {activate/1,add/2,fib/1,fib1/2,sel/2} / {0/0,cons/2,n__add/2,n__fib1/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {activate,add,fib,fib1,sel} and constructors {0,cons ,n__add,n__fib1,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: activate(x){x -> n__add(x,y)} = activate(n__add(x,y)) ->^+ add(activate(x),activate(y)) = C[activate(x) = activate(x){}] WORST_CASE(Omega(n^1),?)