YES(?,O(1)) * Step 1: ArgumentFilter WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f300(A,B,C,D,E) -> f300(1 + A,B,C,D,E) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 100 >= A && B >= 1] (?,1) 1. f300(A,B,C,D,E) -> f3(A,B,0,0,0) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 101] (?,1) 2. f2(A,B,C,D,E) -> f300(1,B,C,D,E) [B >= 1] (1,1) 3. f2(A,B,C,D,E) -> f3(0,B,0,0,0) [0 >= B] (1,1) Signature: {(f2,5);(f3,5);(f300,5)} Flow Graph: [0->{0,1},1->{},2->{0,1},3->{}] + Applied Processor: ArgumentFilter [2,3,4] + Details: We remove following argument positions: [2,3,4]. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(1 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 100 >= A && B >= 1] (?,1) 1. f300(A,B) -> f3(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 101] (?,1) 2. f2(A,B) -> f300(1,B) [B >= 1] (1,1) 3. f2(A,B) -> f3(0,B) [0 >= B] (1,1) Signature: {(f2,5);(f3,5);(f300,5)} Flow Graph: [0->{0,1},1->{},2->{0,1},3->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,1)] * Step 3: FromIts WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f300(A,B) -> f300(1 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 100 >= A && B >= 1] (?,1) 1. f300(A,B) -> f3(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 101] (?,1) 2. f2(A,B) -> f300(1,B) [B >= 1] (1,1) 3. f2(A,B) -> f3(0,B) [0 >= B] (1,1) Signature: {(f2,5);(f3,5);(f300,5)} Flow Graph: [0->{0,1},1->{},2->{0},3->{}] + Applied Processor: FromIts + Details: () * Step 4: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: f300(A,B) -> f300(1 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 100 >= A && B >= 1] f300(A,B) -> f3(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 101] f2(A,B) -> f300(1,B) [B >= 1] f2(A,B) -> f3(0,B) [0 >= B] Signature: {(f2,5);(f3,5);(f300,5)} Rule Graph: [0->{0,1},1->{},2->{0},3->{}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(1)) + Considered Problem: Rules: f300(A,B) -> f300(1 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 100 >= A && B >= 1] f300(A,B) -> f3(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 101] f2(A,B) -> f300(1,B) [B >= 1] f2(A,B) -> f3(0,B) [0 >= B] f3(A,B) -> exitus616(A,B) True f3(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f2,5);(f3,5);(f300,5)} Rule Graph: [0->{0,1},1->{5},2->{0},3->{4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[0] c: [0] * Step 6: AbstractSize WORST_CASE(?,O(1)) + Considered Problem: (Rules: f300(A,B) -> f300(1 + A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && 100 >= A && B >= 1] f300(A,B) -> f3(A,B) [-1 + B >= 0 && -2 + A + B >= 0 && -1 + A >= 0 && A >= 101] f2(A,B) -> f300(1,B) [B >= 1] f2(A,B) -> f3(0,B) [0 >= B] f3(A,B) -> exitus616(A,B) True f3(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f2,5);(f3,5);(f300,5)} Rule Graph: [0->{0,1},1->{5},2->{0},3->{4}] ,We construct a looptree: P: [0,1,2,3,4,5] | `- p:[0] c: [0]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,0.0] f300 ~> f300 [A <= 101*K, B <= B] f300 ~> f3 [A <= A, B <= B] f2 ~> f300 [A <= K, B <= B] f2 ~> f3 [A <= 0*K, B <= B] f3 ~> exitus616 [A <= A, B <= B] f3 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= 100*K + A] f300 ~> f300 [A <= 101*K, B <= B] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0] f300 ~> f300 [K ~=> A] f300 ~> f3 [] f2 ~> f300 [K ~=> A] f2 ~> f3 [K ~=> A] f3 ~> exitus616 [] f3 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~*> 0.0] f300 ~> f300 [K ~=> A] + Applied Processor: Lare + Details: f2 ~> exitus616 [K ~=> A,tick ~+> tick,K ~+> 0.0,K ~+> tick,K ~*> 0.0,K ~*> tick] + f300> [K ~=> A,A ~+> 0.0,A ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] YES(?,O(1))