WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: -(x,0()) -> x -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0()) -(0(),y) -> 0() p(0()) -> 0() p(s(x)) -> x - Signature: {-/2,p/1} / {0/0,greater/2,if/3,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {-,p} and constructors {0,greater,if,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- - :: [A(0, 0) x A(4, 4)] -(2)-> A(0, 0) 0 :: [] -(0)-> A(4, 4) 0 :: [] -(0)-> A(0, 0) 0 :: [] -(0)-> A(0, 4) 0 :: [] -(0)-> A(1, 1) 0 :: [] -(0)-> A(4, 3) greater :: [A(0, 0) x A(0, 0)] -(0)-> A(1, 5) if :: [A(0, 2) x A(0, 0) x A(0, 0)] -(0)-> A(0, 2) p :: [A(0, 4)] -(1)-> A(4, 4) s :: [A(4, 4)] -(4)-> A(4, 4) s :: [A(4, 4)] -(0)-> A(0, 4) s :: [A(0, 0)] -(0)-> A(0, 0) Cost-free Signatures used: -------------------------- - :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) 0 :: [] -(0)-> A_cf(0, 0) greater :: [A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) if :: [A_cf(0, 0) x A_cf(0, 0) x A_cf(0, 0)] -(0)-> A_cf(0, 0) p :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) s :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) Base Constructor Signatures used: --------------------------------- 0_A :: [] -(0)-> A(1, 0) 0_A :: [] -(0)-> A(0, 1) greater_A :: [A(0, 0) x A(0, 0)] -(0)-> A(1, 0) greater_A :: [A(0, 0) x A(0, 0)] -(0)-> A(0, 1) if_A :: [A(0, 0) x A(1, 0) x A(1, 0)] -(0)-> A(1, 0) if_A :: [A(0, 1) x A(0, 0) x A(0, 0)] -(0)-> A(0, 1) s_A :: [A(0, 0)] -(1)-> A(1, 0) s_A :: [A(1, 1)] -(0)-> A(0, 1) * Step 2: Open MAYBE - Strict TRS: -(x,0()) -> x -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0()) -(0(),y) -> 0() p(0()) -> 0() p(s(x)) -> x - Signature: {-/2,p/1} / {0/0,greater/2,if/3,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {-,p} and constructors {0,greater,if,s} Following problems could not be solved: - Strict TRS: -(x,0()) -> x -(x,s(y)) -> if(greater(x,s(y)),s(-(x,p(s(y)))),0()) -(0(),y) -> 0() p(0()) -> 0() p(s(x)) -> x - Signature: {-/2,p/1} / {0/0,greater/2,if/3,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {-,p} and constructors {0,greater,if,s} WORST_CASE(?,O(n^2))