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