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