* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a(x,s(y),h()) -> a(x,y,s(h())) a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z)) a(h(),h(),x) -> s(x) a(s(x),h(),z) -> a(x,z,z) app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) app(nil(),k) -> k sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l)) sum(cons(x,nil())) -> cons(x,nil()) - Signature: {a/3,app/2,sum/1} / {cons/2,h/0,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {a,app,sum} and constructors {cons,h,nil,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: a(x,s(y),h()) -> a(x,y,s(h())) a(x,s(y),s(z)) -> a(x,y,a(x,s(y),z)) a(h(),h(),x) -> s(x) a(s(x),h(),z) -> a(x,z,z) app(l,nil()) -> l app(cons(x,l),k) -> cons(x,app(l,k)) app(nil(),k) -> k sum(cons(x,cons(y,l))) -> sum(cons(a(x,y,h()),l)) sum(cons(x,nil())) -> cons(x,nil()) - Signature: {a/3,app/2,sum/1} / {cons/2,h/0,nil/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {a,app,sum} and constructors {cons,h,nil,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: a(x,s(y),z){z -> s(z)} = a(x,s(y),s(z)) ->^+ a(x,y,a(x,s(y),z)) = C[a(x,s(y),z) = a(x,s(y),z){}] WORST_CASE(Omega(n^1),?)