WORST_CASE(Omega(n^1),?) * Step 1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: REV(++(z0,z1)) -> c1(REV1(z0,z1)) REV(++(z0,z1)) -> c2(REV2(z0,z1)) REV(nil()) -> c() REV1(z0,++(z1,z2)) -> c4(REV1(z1,z2)) REV1(z0,nil()) -> c3() REV2(z0,++(z1,z2)) -> c6(REV(++(z0,rev(rev2(z1,z2)))),REV(rev2(z1,z2)),REV2(z1,z2)) REV2(z0,nil()) -> c5() - Weak TRS: rev(++(z0,z1)) -> ++(rev1(z0,z1),rev2(z0,z1)) rev(nil()) -> nil() rev1(z0,++(z1,z2)) -> rev1(z1,z2) rev1(z0,nil()) -> z0 rev2(z0,++(z1,z2)) -> rev(++(z0,rev(rev2(z1,z2)))) rev2(z0,nil()) -> nil() - Signature: {REV/1,REV1/2,REV2/2,rev/1,rev1/2,rev2/2} / {++/2,c/0,c1/1,c2/1,c3/0,c4/1,c5/0,c6/3,nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {REV,REV1,REV2,rev,rev1,rev2} and constructors {++,c,c1,c2 ,c3,c4,c5,c6,nil} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: REV(++(z0,z1)) -> c1(REV1(z0,z1)) REV(++(z0,z1)) -> c2(REV2(z0,z1)) REV(nil()) -> c() REV1(z0,++(z1,z2)) -> c4(REV1(z1,z2)) REV1(z0,nil()) -> c3() REV2(z0,++(z1,z2)) -> c6(REV(++(z0,rev(rev2(z1,z2)))),REV(rev2(z1,z2)),REV2(z1,z2)) REV2(z0,nil()) -> c5() - Weak TRS: rev(++(z0,z1)) -> ++(rev1(z0,z1),rev2(z0,z1)) rev(nil()) -> nil() rev1(z0,++(z1,z2)) -> rev1(z1,z2) rev1(z0,nil()) -> z0 rev2(z0,++(z1,z2)) -> rev(++(z0,rev(rev2(z1,z2)))) rev2(z0,nil()) -> nil() - Signature: {REV/1,REV1/2,REV2/2,rev/1,rev1/2,rev2/2} / {++/2,c/0,c1/1,c2/1,c3/0,c4/1,c5/0,c6/3,nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {REV,REV1,REV2,rev,rev1,rev2} and constructors {++,c,c1,c2 ,c3,c4,c5,c6,nil} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 3: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: REV(++(z0,z1)) -> c1(REV1(z0,z1)) REV(++(z0,z1)) -> c2(REV2(z0,z1)) REV(nil()) -> c() REV1(z0,++(z1,z2)) -> c4(REV1(z1,z2)) REV1(z0,nil()) -> c3() REV2(z0,++(z1,z2)) -> c6(REV(++(z0,rev(rev2(z1,z2)))),REV(rev2(z1,z2)),REV2(z1,z2)) REV2(z0,nil()) -> c5() - Weak TRS: rev(++(z0,z1)) -> ++(rev1(z0,z1),rev2(z0,z1)) rev(nil()) -> nil() rev1(z0,++(z1,z2)) -> rev1(z1,z2) rev1(z0,nil()) -> z0 rev2(z0,++(z1,z2)) -> rev(++(z0,rev(rev2(z1,z2)))) rev2(z0,nil()) -> nil() - Signature: {REV/1,REV1/2,REV2/2,rev/1,rev1/2,rev2/2} / {++/2,c/0,c1/1,c2/1,c3/0,c4/1,c5/0,c6/3,nil/0} - Obligation: innermost runtime complexity wrt. defined symbols {REV,REV1,REV2,rev,rev1,rev2} and constructors {++,c,c1,c2 ,c3,c4,c5,c6,nil} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: REV1(x,z){z -> ++(y,z)} = REV1(x,++(y,z)) ->^+ c4(REV1(y,z)) = C[REV1(y,z) = REV1(x,z){x -> y}] WORST_CASE(Omega(n^1),?)