* Step 1: Sum WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: evenodd(x,0()) -> not(evenodd(x,s(0()))) evenodd(0(),s(0())) -> false() evenodd(s(x),s(0())) -> evenodd(x,0()) not(false()) -> true() not(true()) -> false() - Signature: {evenodd/2,not/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {evenodd,not} and constructors {0,false,s,true} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Bounds WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: evenodd(x,0()) -> not(evenodd(x,s(0()))) evenodd(0(),s(0())) -> false() evenodd(s(x),s(0())) -> evenodd(x,0()) not(false()) -> true() not(true()) -> false() - Signature: {evenodd/2,not/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {evenodd,not} and constructors {0,false,s,true} + Applied Processor: Bounds {initialAutomaton = minimal, enrichment = match} + Details: The problem is match-bounded by 3. The enriched problem is compatible with follwoing automaton. 0_0() -> 2 0_1() -> 5 0_2() -> 8 evenodd_0(2,2) -> 1 evenodd_1(2,4) -> 3 evenodd_1(2,5) -> 1 evenodd_1(2,5) -> 3 evenodd_1(2,5) -> 6 evenodd_2(2,7) -> 6 false_0() -> 2 false_1() -> 1 false_1() -> 3 false_1() -> 6 false_2() -> 1 false_3() -> 1 false_3() -> 3 false_3() -> 6 not_0(2) -> 1 not_1(3) -> 1 not_2(6) -> 1 not_2(6) -> 3 not_2(6) -> 6 s_0(2) -> 2 s_1(5) -> 4 s_2(8) -> 7 true_0() -> 2 true_1() -> 1 true_2() -> 1 true_2() -> 3 true_2() -> 6 true_3() -> 1 true_3() -> 3 true_3() -> 6 * Step 3: EmptyProcessor WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: evenodd(x,0()) -> not(evenodd(x,s(0()))) evenodd(0(),s(0())) -> false() evenodd(s(x),s(0())) -> evenodd(x,0()) not(false()) -> true() not(true()) -> false() - Signature: {evenodd/2,not/1} / {0/0,false/0,s/1,true/0} - Obligation: innermost runtime complexity wrt. defined symbols {evenodd,not} and constructors {0,false,s,true} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(n^1))