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