* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: ge(x,0()) -> true() ge(0(),s(y)) -> false() ge(s(x),s(y)) -> ge(x,y) gen(x,y,z) -> if(ge(z,x),x,y,z) generate(x,y) -> gen(x,y,0()) if(false(),x,y,z) -> cons(y,gen(x,y,s(z))) if(true(),x,y,z) -> nil() sum(cons(0(),xs)) -> sum(xs) sum(cons(s(x),xs)) -> s(sum(cons(x,xs))) sum(nil()) -> 0() times(x,y) -> sum(generate(x,y)) - Signature: {ge/2,gen/3,generate/2,if/4,sum/1,times/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {ge,gen,generate,if,sum,times} and constructors {0,cons ,false,nil,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: ge(x,0()) -> true() ge(0(),s(y)) -> false() ge(s(x),s(y)) -> ge(x,y) gen(x,y,z) -> if(ge(z,x),x,y,z) generate(x,y) -> gen(x,y,0()) if(false(),x,y,z) -> cons(y,gen(x,y,s(z))) if(true(),x,y,z) -> nil() sum(cons(0(),xs)) -> sum(xs) sum(cons(s(x),xs)) -> s(sum(cons(x,xs))) sum(nil()) -> 0() times(x,y) -> sum(generate(x,y)) - Signature: {ge/2,gen/3,generate/2,if/4,sum/1,times/2} / {0/0,cons/2,false/0,nil/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {ge,gen,generate,if,sum,times} and constructors {0,cons ,false,nil,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: ge(x,y){x -> s(x),y -> s(y)} = ge(s(x),s(y)) ->^+ ge(x,y) = C[ge(x,y) = ge(x,y){}] WORST_CASE(Omega(n^1),?)