WORST_CASE(Omega(n^1),?) * Step 1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: COND(true(),z0) -> c(COND(odd(z0),p(z0)),ODD(z0)) COND(true(),z0) -> c1(COND(odd(z0),p(z0)),P(z0)) ODD(0()) -> c2() ODD(s(0())) -> c3() ODD(s(s(z0))) -> c4(ODD(z0)) P(0()) -> c5() P(s(z0)) -> c6() - Weak TRS: cond(true(),z0) -> cond(odd(z0),p(z0)) odd(0()) -> false() odd(s(0())) -> true() odd(s(s(z0))) -> odd(z0) p(0()) -> 0() p(s(z0)) -> z0 - Signature: {COND/2,ODD/1,P/1,cond/2,odd/1,p/1} / {0/0,c/2,c1/2,c2/0,c3/0,c4/1,c5/0,c6/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {COND,ODD,P,cond,odd,p} and constructors {0,c,c1,c2,c3,c4 ,c5,c6,false,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: COND(true(),z0) -> c(COND(odd(z0),p(z0)),ODD(z0)) COND(true(),z0) -> c1(COND(odd(z0),p(z0)),P(z0)) ODD(0()) -> c2() ODD(s(0())) -> c3() ODD(s(s(z0))) -> c4(ODD(z0)) P(0()) -> c5() P(s(z0)) -> c6() - Weak TRS: cond(true(),z0) -> cond(odd(z0),p(z0)) odd(0()) -> false() odd(s(0())) -> true() odd(s(s(z0))) -> odd(z0) p(0()) -> 0() p(s(z0)) -> z0 - Signature: {COND/2,ODD/1,P/1,cond/2,odd/1,p/1} / {0/0,c/2,c1/2,c2/0,c3/0,c4/1,c5/0,c6/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {COND,ODD,P,cond,odd,p} and constructors {0,c,c1,c2,c3,c4 ,c5,c6,false,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: COND(true(),z0) -> c(COND(odd(z0),p(z0)),ODD(z0)) COND(true(),z0) -> c1(COND(odd(z0),p(z0)),P(z0)) ODD(0()) -> c2() ODD(s(0())) -> c3() ODD(s(s(z0))) -> c4(ODD(z0)) P(0()) -> c5() P(s(z0)) -> c6() - Weak TRS: cond(true(),z0) -> cond(odd(z0),p(z0)) odd(0()) -> false() odd(s(0())) -> true() odd(s(s(z0))) -> odd(z0) p(0()) -> 0() p(s(z0)) -> z0 - Signature: {COND/2,ODD/1,P/1,cond/2,odd/1,p/1} / {0/0,c/2,c1/2,c2/0,c3/0,c4/1,c5/0,c6/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {COND,ODD,P,cond,odd,p} and constructors {0,c,c1,c2,c3,c4 ,c5,c6,false,s,true} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: ODD(x){x -> s(s(x))} = ODD(s(s(x))) ->^+ c4(ODD(x)) = C[ODD(x) = ODD(x){}] WORST_CASE(Omega(n^1),?)