/bin/sh: line 1: 990 Quit (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-30 > /tmp/SMTS809-31 /bin/sh: line 1: 1055 Quit (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-78 > /tmp/SMTS809-79 /bin/sh: line 1: 1074 Quit (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-74 > /tmp/SMTS809-75 /bin/sh: line 1: 1051 Quit (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-50 > /tmp/SMTS809-51 /bin/sh: line 1: 1076 Quit (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-28 > /tmp/SMTS809-29 /bin/sh: line 1: 1067 Quit (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-76 > /tmp/SMTS809-77 /bin/sh: line 1: 1061 Quit (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-43 > /tmp/SMTS809-45 /bin/sh: line 1: 1026 Quit (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP809-53 > /tmp/SMTS809-54 WORST_CASE(Omega(n^1),O(n^1)) * Step 1: Sum. WORST_CASE(Omega(n^1),O(n^1)) + Considered Problem: - Strict TRS: f(c(X,s(Y))) -> f(c(s(X),Y)) g(c(s(X),Y)) -> f(c(X,s(Y))) - Signature: {f/1,g/1} / {c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: Sum. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(c(X,s(Y))) -> f(c(s(X),Y)) g(c(s(X),Y)) -> f(c(X,s(Y))) - Signature: {f/1,g/1} / {c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () *** Step 1.a:1.a:1: Ara. MAYBE + Considered Problem: - Strict TRS: f(c(X,s(Y))) -> f(c(s(X),Y)) g(c(s(X),Y)) -> f(c(X,s(Y))) - Signature: {f/1,g/1} / {c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False} + Details: Signatures used: ---------------- F (TrsFun "c") :: ["A"(0) x "A"(1)] -(1)-> "A"(1) F (TrsFun "f") :: ["A"(1)] -(0)-> "A"(0) F (TrsFun "g") :: ["A"(1)] -(0)-> "A"(0) F (TrsFun "main") :: ["A"(1)] -(1)-> "A"(0) F (TrsFun "s") :: ["A"(1)] -(1)-> "A"(1) F (TrsFun "s") :: ["A"(0)] -(0)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- Following Still Strict Rules were Typed as: ------------------------------------------- 1. Strict: f(c(X,s(Y))) -> f(c(s(X),Y)) g(c(s(X),Y)) -> f(c(X,s(Y))) main(x1) -> g(x1) 2. Weak: *** Step 1.a:1.b:1: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(c(X,s(Y))) -> f(c(s(X),Y)) g(c(s(X),Y)) -> f(c(X,s(Y))) - Signature: {f/1,g/1} / {c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(c(x,y)){y -> s(y)} = f(c(x,s(y))) ->^+ f(c(s(x),y)) = C[f(c(s(x),y)) = f(c(x,y)){x -> s(x)}] ** Step 1.b:1: Bounds. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: f(c(X,s(Y))) -> f(c(s(X),Y)) g(c(s(X),Y)) -> f(c(X,s(Y))) - Signature: {f/1,g/1} / {c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: Bounds {initialAutomaton = perSymbol, enrichment = match} + Details: The problem is match-bounded by 2. The enriched problem is compatible with follwoing automaton. c_0(1,1) -> 1 c_0(1,4) -> 1 c_0(4,1) -> 1 c_0(4,4) -> 1 c_1(1,6) -> 7 c_1(4,6) -> 7 c_1(6,1) -> 5 c_1(6,4) -> 5 c_1(10,1) -> 7 c_1(10,4) -> 7 c_2(9,1) -> 8 c_2(9,4) -> 8 c_2(9,6) -> 8 f_0(1) -> 2 f_0(4) -> 2 f_1(5) -> 2 f_1(7) -> 3 f_2(8) -> 3 g_0(1) -> 3 g_0(4) -> 3 s_0(1) -> 4 s_0(4) -> 4 s_1(1) -> 6 s_1(4) -> 6 s_1(6) -> 6 s_1(9) -> 10 s_1(10) -> 10 s_2(1) -> 9 s_2(4) -> 9 s_2(9) -> 9 ** Step 1.b:2: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: f(c(X,s(Y))) -> f(c(s(X),Y)) g(c(s(X),Y)) -> f(c(X,s(Y))) - Signature: {f/1,g/1} / {c/2,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f,g} and constructors {c,s} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(Omega(n^1),O(n^1))