/bin/sh: line 1: 3151 Quit (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP3063-28 > /tmp/SMTS3063-29 /bin/sh: line 1: 3156 Quit (core dumped) z3 -T:14.25 -smt2 /tmp/SMTP3063-18 > /tmp/SMTS3063-21 WORST_CASE(?,O(1)) * Step 1: Sum. WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: a(b(x)) -> a(c(b(x))) - Signature: {a/1} / {b/1,c/1} - Obligation: innermost runtime complexity wrt. defined symbols {a} and constructors {b,c} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:1: Sum. MAYBE + Considered Problem: - Strict TRS: a(b(x)) -> a(c(b(x))) - Signature: {a/1} / {b/1,c/1} - Obligation: innermost runtime complexity wrt. defined symbols {a} and constructors {b,c} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () ** Step 1.a:2: Ara. MAYBE + Considered Problem: - Strict TRS: a(b(x)) -> a(c(b(x))) - Signature: {a/1} / {b/1,c/1} - Obligation: innermost runtime complexity wrt. defined symbols {a} and constructors {b,c} + Applied Processor: Ara {minDegree = 1, maxDegree = 3, araTimeout = 15, araRuleShifting = Just 1, isBestCase = True, mkCompletelyDefined = False, verboseOutput = False} + Details: Signatures used: ---------------- F (TrsFun "a") :: ["A"(1, 1, 1)] -(0)-> "A"(0, 0, 0) F (TrsFun "b") :: ["A"(2, 2, 1)] -(1)-> "A"(1, 1, 1) F (TrsFun "c") :: ["A"(1, 1, 1)] -(1)-> "A"(1, 0, 1) F (TrsFun "main") :: ["A"(0, 0, 1)] -(1)-> "A"(0, 0, 0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- Following Still Strict Rules were Typed as: ------------------------------------------- 1. Strict: a(b(x)) -> a(c(b(x))) main(x1) -> a(x1) 2. Weak: ** Step 1.b:1: NaturalMI. WORST_CASE(?,O(1)) + Considered Problem: - Strict TRS: a(b(x)) -> a(c(b(x))) - Signature: {a/1} / {b/1,c/1} - Obligation: innermost runtime complexity wrt. defined symbols {a} and constructors {b,c} + Applied Processor: NaturalMI {miDimension = 1, miDegree = 1, miKind = Algebraic, uargs = UArgs, urules = URules, selector = Just any strict-rules} + Details: We apply a matrix interpretation of kind constructor based matrix interpretation: The following argument positions are considered usable: none Following symbols are considered usable: {a} TcT has computed the following interpretation: p(a) = [9] x1 + [3] p(b) = [3] p(c) = [2] Following rules are strictly oriented: a(b(x)) = [30] > [21] = a(c(b(x))) Following rules are (at-least) weakly oriented: ** Step 1.b:2: EmptyProcessor. WORST_CASE(?,O(1)) + Considered Problem: - Weak TRS: a(b(x)) -> a(c(b(x))) - Signature: {a/1} / {b/1,c/1} - Obligation: innermost runtime complexity wrt. defined symbols {a} and constructors {b,c} + Applied Processor: EmptyProcessor + Details: The problem is already closed. The intended complexity is O(1). WORST_CASE(?,O(1))