WORST_CASE(Omega(n^1),?) * Step 1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: +'(z0,0()) -> c4() +'(z0,s(z1)) -> c5(+'(z0,z1)) FIB(0()) -> c() FIB(s(0())) -> c1() FIB(s(s(z0))) -> c2(+'(fib(s(z0)),fib(z0)),FIB(s(z0))) FIB(s(s(z0))) -> c3(+'(fib(s(z0)),fib(z0)),FIB(z0)) - Weak TRS: +(z0,0()) -> z0 +(z0,s(z1)) -> s(+(z0,z1)) fib(0()) -> 0() fib(s(0())) -> s(0()) fib(s(s(z0))) -> +(fib(s(z0)),fib(z0)) - Signature: {+/2,+'/2,FIB/1,fib/1} / {0/0,c/0,c1/0,c2/2,c3/2,c4/0,c5/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,+',FIB,fib} and constructors {0,c,c1,c2,c3,c4,c5,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: +'(z0,0()) -> c4() +'(z0,s(z1)) -> c5(+'(z0,z1)) FIB(0()) -> c() FIB(s(0())) -> c1() FIB(s(s(z0))) -> c2(+'(fib(s(z0)),fib(z0)),FIB(s(z0))) FIB(s(s(z0))) -> c3(+'(fib(s(z0)),fib(z0)),FIB(z0)) - Weak TRS: +(z0,0()) -> z0 +(z0,s(z1)) -> s(+(z0,z1)) fib(0()) -> 0() fib(s(0())) -> s(0()) fib(s(s(z0))) -> +(fib(s(z0)),fib(z0)) - Signature: {+/2,+'/2,FIB/1,fib/1} / {0/0,c/0,c1/0,c2/2,c3/2,c4/0,c5/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,+',FIB,fib} and constructors {0,c,c1,c2,c3,c4,c5,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: +'(z0,0()) -> c4() +'(z0,s(z1)) -> c5(+'(z0,z1)) FIB(0()) -> c() FIB(s(0())) -> c1() FIB(s(s(z0))) -> c2(+'(fib(s(z0)),fib(z0)),FIB(s(z0))) FIB(s(s(z0))) -> c3(+'(fib(s(z0)),fib(z0)),FIB(z0)) - Weak TRS: +(z0,0()) -> z0 +(z0,s(z1)) -> s(+(z0,z1)) fib(0()) -> 0() fib(s(0())) -> s(0()) fib(s(s(z0))) -> +(fib(s(z0)),fib(z0)) - Signature: {+/2,+'/2,FIB/1,fib/1} / {0/0,c/0,c1/0,c2/2,c3/2,c4/0,c5/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,+',FIB,fib} and constructors {0,c,c1,c2,c3,c4,c5,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: +'(x,y){y -> s(y)} = +'(x,s(y)) ->^+ c5(+'(x,y)) = C[+'(x,y) = +'(x,y){}] WORST_CASE(Omega(n^1),?)