WORST_CASE(?,O(n^2)) * Step 1: Ara WORST_CASE(?,O(n^2)) + Considered Problem: - Strict TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) double(0()) -> 0() double(s(x)) -> s(s(double(x))) sqr(0()) -> 0() sqr(s(x)) -> +(sqr(x),s(double(x))) sqr(s(x)) -> s(+(sqr(x),double(x))) - Signature: {+/2,double/1,sqr/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,double,sqr} and constructors {0,s} + Applied Processor: Ara {heuristics_ = NoHeuristics, minDegree = 1, maxDegree = 3, araTimeout = 60, araFindStrictRules = Nothing, araSmtSolver = MiniSMT} + Details: Signatures used: ---------------- + :: [A(0, 0) x A(1, 0)] -(1)-> A(0, 0) 0 :: [] -(0)-> A(1, 0) 0 :: [] -(0)-> A(3, 0) 0 :: [] -(0)-> A(4, 3) double :: [A(3, 0)] -(1)-> A(1, 0) s :: [A(1, 0)] -(1)-> A(1, 0) s :: [A(3, 0)] -(3)-> A(3, 0) s :: [A(7, 3)] -(4)-> A(4, 3) s :: [A(0, 0)] -(0)-> A(0, 0) sqr :: [A(4, 3)] -(2)-> 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) double :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) s :: [A_cf(0, 0)] -(0)-> A_cf(0, 0) sqr :: [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) s_A :: [A(1, 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)) -> s(+(x,y)) double(0()) -> 0() double(s(x)) -> s(s(double(x))) sqr(0()) -> 0() sqr(s(x)) -> +(sqr(x),s(double(x))) sqr(s(x)) -> s(+(sqr(x),double(x))) - Signature: {+/2,double/1,sqr/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,double,sqr} and constructors {0,s} Following problems could not be solved: - Strict TRS: +(x,0()) -> x +(x,s(y)) -> s(+(x,y)) double(0()) -> 0() double(s(x)) -> s(s(double(x))) sqr(0()) -> 0() sqr(s(x)) -> +(sqr(x),s(double(x))) sqr(s(x)) -> s(+(sqr(x),double(x))) - Signature: {+/2,double/1,sqr/1} / {0/0,s/1} - Obligation: innermost runtime complexity wrt. defined symbols {+,double,sqr} and constructors {0,s} WORST_CASE(?,O(n^2))