* Step 1: Sum WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: fib(x) -> fibiter(x,0(),0(),s(0())) fibiter(b,c,x,y) -> if(lt(c,b),b,c,x,y) if(false(),b,c,x,y) -> x if(true(),b,c,x,y) -> fibiter(b,s(c),y,plus(x,y)) lt(x,0()) -> false() lt(0(),s(y)) -> true() lt(s(x),s(y)) -> lt(x,y) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) - Signature: {fib/1,fibiter/4,if/5,lt/2,plus/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {fib,fibiter,if,lt,plus} and constructors {0,false,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: DecreasingLoops WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: fib(x) -> fibiter(x,0(),0(),s(0())) fibiter(b,c,x,y) -> if(lt(c,b),b,c,x,y) if(false(),b,c,x,y) -> x if(true(),b,c,x,y) -> fibiter(b,s(c),y,plus(x,y)) lt(x,0()) -> false() lt(0(),s(y)) -> true() lt(s(x),s(y)) -> lt(x,y) plus(0(),y) -> y plus(s(x),y) -> s(plus(x,y)) - Signature: {fib/1,fibiter/4,if/5,lt/2,plus/2} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {fib,fibiter,if,lt,plus} and constructors {0,false,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: lt(x,y){x -> s(x),y -> s(y)} = lt(s(x),s(y)) ->^+ lt(x,y) = C[lt(x,y) = lt(x,y){}] WORST_CASE(Omega(n^1),?)