WORST_CASE(?,O(n^1)) * Step 1: Sum. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: add0(0(),x2) -> x2 add0(S(x),x2) -> +(S(0()),add0(x2,x)) - Weak TRS: +(x,S(0())) -> S(x) +(S(0()),y) -> S(y) - Signature: {+/2,add0/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,add0} and constructors {0,S} + Applied Processor: Sum {left = someStrategy, right = someStrategy} + Details: () * Step 2: Ara. WORST_CASE(?,O(n^1)) + Considered Problem: - Strict TRS: add0(0(),x2) -> x2 add0(S(x),x2) -> +(S(0()),add0(x2,x)) - Weak TRS: +(x,S(0())) -> S(x) +(S(0()),y) -> S(y) - Signature: {+/2,add0/2} / {0/0,S/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,add0} and constructors {0,S} + Applied Processor: Ara {minDegree = 1, maxDegree = 1, araTimeout = 8, araRuleShifting = Just 1, isBestCase = False, mkCompletelyDefined = False, verboseOutput = False} + Details: Signatures used: ---------------- F (TrsFun "+") :: ["A"(0) x "A"(0)] -(0)-> "A"(0) F (TrsFun "0") :: [] -(0)-> "A"(1) F (TrsFun "0") :: [] -(0)-> "A"(0) F (TrsFun "S") :: ["A"(1)] -(1)-> "A"(1) F (TrsFun "S") :: ["A"(0)] -(0)-> "A"(0) F (TrsFun "add0") :: ["A"(1) x "A"(1)] -(1)-> "A"(0) Cost-free Signatures used: -------------------------- Base Constructor Signatures used: --------------------------------- Following Still Strict Rules were Typed as: ------------------------------------------- 1. Strict: add0(0(),x2) -> x2 add0(S(x),x2) -> +(S(0()),add0(x2,x)) 2. Weak: WORST_CASE(?,O(n^1))