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