/bin/sh: line 1: 22095 Quit (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP21944-38 > /tmp/SMTS21944-39 /bin/sh: line 1: 22104 Quit (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP21944-56 > /tmp/SMTS21944-57 WORST_CASE(Omega(n^1),O(n^1)) * Step 1: Sum. WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: dbl(0(),y) -> y dbl(S(0()),S(0())) -> S(S(S(S(0())))) save(0()) -> 0() save(S(x)) -> dbl(0(),save(x)) - Signature: {dbl/2,save/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {dbl,save} and constructors {0,S} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: dbl(0(),y) -> y dbl(S(0()),S(0())) -> S(S(S(S(0())))) save(0()) -> 0() save(S(x)) -> dbl(0(),save(x)) - Signature: {dbl/2,save/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {dbl,save} and constructors {0,S} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () *** Step 1.a:1.a:1: Ara. MAYBE + Considered Problem: - Strict TRS: dbl(0(),y) -> y dbl(S(0()),S(0())) -> S(S(S(S(0())))) save(0()) -> 0() save(S(x)) -> dbl(0(),save(x)) - Signature: {dbl/2,save/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {dbl,save} and constructors {0,S} + Applied Processor: Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False} + Details: Signatures used: ---------------- F (TrsFun "0") :: [] -(0)-> "A"(0) F (TrsFun "0") :: [] -(0)-> "A"(1) F (TrsFun "S") :: ["A"(0)] -(0)-> "A"(0) F (TrsFun "S") :: ["A"(1)] -(1)-> "A"(1) F (TrsFun "dbl") :: ["A"(0) x "A"(0)] -(1)-> "A"(0) F (TrsFun "main") :: ["A"(1)] -(1)-> "A"(0) F (TrsFun "save") :: ["A"(1)] -(1)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- Following Still Strict Rules were Typed as: ------------------------------------------- 1. Strict: dbl(0(),y) -> y dbl(S(0()),S(0())) -> S(S(S(S(0())))) save(0()) -> 0() save(S(x)) -> dbl(0(),save(x)) main(x1) -> save(x1) 2. Weak: *** Step 1.a:1.b:1: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: dbl(0(),y) -> y dbl(S(0()),S(0())) -> S(S(S(S(0())))) save(0()) -> 0() save(S(x)) -> dbl(0(),save(x)) - Signature: {dbl/2,save/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {dbl,save} and constructors {0,S} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: save(x){x -> S(x)} = save(S(x)) ->^+ dbl(0(),save(x)) = C[save(x) = save(x){}] ** Step 1.b:1: Bounds. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: dbl(0(),y) -> y dbl(S(0()),S(0())) -> S(S(S(S(0())))) save(0()) -> 0() save(S(x)) -> dbl(0(),save(x)) - Signature: {dbl/2,save/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {dbl,save} and constructors {0,S} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 1. The enriched problem is compatible with follwoing automaton. 0_0() -> 1 0_0() -> 3 0_1() -> 4 0_1() -> 8 0_1() -> 9 S_0(1) -> 2 S_0(1) -> 3 S_0(2) -> 2 S_0(2) -> 3 S_1(5) -> 3 S_1(6) -> 5 S_1(7) -> 6 S_1(8) -> 7 dbl_0(1,1) -> 3 dbl_0(1,2) -> 3 dbl_0(2,1) -> 3 dbl_0(2,2) -> 3 dbl_1(8,9) -> 4 dbl_1(9,9) -> 4 dbl_1(9,9) -> 9 save_0(1) -> 4 save_0(2) -> 4 save_1(1) -> 4 save_1(1) -> 9 save_1(2) -> 4 save_1(2) -> 9 1 -> 3 2 -> 3 9 -> 4 ** Step 1.b:2: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: dbl(0(),y) -> y dbl(S(0()),S(0())) -> S(S(S(S(0())))) save(0()) -> 0() save(S(x)) -> dbl(0(),save(x)) - Signature: {dbl/2,save/1} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {dbl,save} and constructors {0,S} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))