/bin/sh: line 1: 58815 Quit (core dumped) z3 -T:7.6 -smt2 /tmp/SMTP58699-56 > /tmp/SMTS58699-57 WORST_CASE(Omega(n^1),O(n^2)) * Step 1: Sum. WORST_CASE(Omega(n^1),O(n^2)) + Considered Problem: - Strict TRS: f(x,c(y)) -> f(x,s(f(y,y))) f(s(x),y) -> f(x,s(c(y))) - Signature: {f/2} / {c/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} 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(x,c(y)) -> f(x,s(f(y,y))) f(s(x),y) -> f(x,s(c(y))) - Signature: {f/2} / {c/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} 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(x,c(y)) -> f(x,s(f(y,y))) f(s(x),y) -> f(x,s(c(y))) - Signature: {f/2} / {c/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} 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"(2, 1)] -(1)-> "A"(1, 1) F (TrsFun "f") :: ["A"(1, 0) x "A"(1, 1)] -(0)-> "A"(0, 0) F (TrsFun "main") :: ["A"(0, 0) x "A"(0, 1)] -(1)-> "A"(0, 0) F (TrsFun "s") :: ["A"(1, 0)] -(1)-> "A"(1, 0) F (TrsFun "s") :: ["A"(0, 0)] -(0)-> "A"(0, 0) F (TrsFun "s") :: ["A"(2, 1)] -(1)-> "A"(1, 1) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- Following Still Strict Rules were Typed as: ------------------------------------------- 1. Strict: f(x,c(y)) -> f(x,s(f(y,y))) f(s(x),y) -> f(x,s(c(y))) main(x1,x2) -> f(x1,x2) 2. Weak: *** Step 1.a:1.b:1: DecreasingLoops. WORST_CASE(Omega(n^1),?) + Considered Problem: - Strict TRS: f(x,c(y)) -> f(x,s(f(y,y))) f(s(x),y) -> f(x,s(c(y))) - Signature: {f/2} / {c/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {c,s} + Applied Processor: DecreasingLoops {bound = AnyLoop, narrow = 10} + Details: The system has following decreasing Loops: f(x,y){y -> c(y)} = f(x,c(y)) ->^+ f(x,s(f(y,y))) = C[f(y,y) = f(x,y){x -> y}] ** Step 1.b:1: Ara. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(x,c(y)) -> f(x,s(f(y,y))) f(s(x),y) -> f(x,s(c(y))) - Signature: {f/2} / {c/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {c,s} + Applied Processor: Ara {minDegree = 1, maxDegree = 1, araTimeout = 8, araRuleShifting = Just 1, isBestCase = False, mkCompletelyDefined = False, verboseOutput = False} + Details: Signatures used: ---------------- F (TrsFun "c") :: ["A"(14)] -(14)-> "A"(14) F (TrsFun "c") :: ["A"(0)] -(0)-> "A"(0) F (TrsFun "f") :: ["A"(0) x "A"(14)] -(13)-> "A"(12) F (TrsFun "s") :: ["A"(0)] -(0)-> "A"(0) F (TrsFun "s") :: ["A"(0)] -(0)-> "A"(15) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "F (TrsFun \"c\")_A" :: ["A"(1)] -(1)-> "A"(1) "F (TrsFun \"s\")_A" :: ["A"(0)] -(0)-> "A"(1) Following Still Strict Rules were Typed as: ------------------------------------------- 1. Strict: f(x,c(y)) -> f(x,s(f(y,y))) 2. Weak: f(s(x),y) -> f(x,s(c(y))) ** Step 1.b:2: Ara. WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: f(s(x),y) -> f(x,s(c(y))) - Weak TRS: f(x,c(y)) -> f(x,s(f(y,y))) - Signature: {f/2} / {c/1,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {f} and constructors {c,s} + Applied Processor: Ara {minDegree = 2, maxDegree = 2, araTimeout = 8, araRuleShifting = Just 1, isBestCase = False, mkCompletelyDefined = False, verboseOutput = False} + Details: Signatures used: ---------------- F (TrsFun "c") :: ["A"(5, 5)] -(5)-> "A"(0, 5) F (TrsFun "c") :: ["A"(0, 0)] -(0)-> "A"(10, 0) F (TrsFun "f") :: ["A"(4, 0) x "A"(0, 5)] -(4)-> "A"(14, 14) F (TrsFun "s") :: ["A"(4, 0)] -(4)-> "A"(4, 0) F (TrsFun "s") :: ["A"(10, 0)] -(0)-> "A"(0, 10) F (TrsFun "s") :: ["A"(8, 0)] -(1)-> "A"(1, 7) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- "F (TrsFun \"c\")_A" :: ["A"(0, 0)] -(0)-> "A"(1, 0) "F (TrsFun \"c\")_A" :: ["A"(1, 1)] -(1)-> "A"(0, 1) "F (TrsFun \"s\")_A" :: ["A"(1, 0)] -(1)-> "A"(1, 0) "F (TrsFun \"s\")_A" :: ["A"(1, 0)] -(0)-> "A"(0, 1) Following Still Strict Rules were Typed as: ------------------------------------------- 1. Strict: f(s(x),y) -> f(x,s(c(y))) 2. Weak: WORST_CASE(Omega(n^1),O(n^2))