YES(?,O(n^1)) * Step 1: ArgumentFilter WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C,D,E) -> f1(A,F,C,D,E) [1 >= A] (1,1) 1. f2(A,B,C,D,E) -> f300(A,B,C,D,E) [A >= 2 && C >= 2] (1,1) 2. f300(A,B,C,D,E) -> f1(A,F,C,D,E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && 1 + D >= 0] (?,1) 3. f300(A,B,C,D,E) -> f300(A,B,C,1 + D,1 + E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && E >= 0 && 0 >= 2 + D] (?,1) 4. f300(A,B,C,D,E) -> f300(A,B,C,1 + D,1 + E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && 0 >= 2 + E && 0 >= 2 + D] (?,1) Signature: {(f1,5);(f2,5);(f300,5)} Flow Graph: [0->{},1->{2,3,4},2->{},3->{2,3,4},4->{2,3,4}] + Applied Processor: ArgumentFilter [1] + Details: We remove following argument positions: [1]. * Step 2: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,C,D,E) -> f1(A,C,D,E) [1 >= A] (1,1) 1. f2(A,C,D,E) -> f300(A,C,D,E) [A >= 2 && C >= 2] (1,1) 2. f300(A,C,D,E) -> f1(A,C,D,E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && 1 + D >= 0] (?,1) 3. f300(A,C,D,E) -> f300(A,C,1 + D,1 + E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && E >= 0 && 0 >= 2 + D] (?,1) 4. f300(A,C,D,E) -> f300(A,C,1 + D,1 + E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && 0 >= 2 + E && 0 >= 2 + D] (?,1) Signature: {(f1,5);(f2,5);(f300,5)} Flow Graph: [0->{},1->{2,3,4},2->{},3->{2,3,4},4->{2,3,4}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,4),(4,3)] * Step 3: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,C,D,E) -> f1(A,C,D,E) [1 >= A] (1,1) 1. f2(A,C,D,E) -> f300(A,C,D,E) [A >= 2 && C >= 2] (1,1) 2. f300(A,C,D,E) -> f1(A,C,D,E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && 1 + D >= 0] (?,1) 3. f300(A,C,D,E) -> f300(A,C,1 + D,1 + E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && E >= 0 && 0 >= 2 + D] (?,1) 4. f300(A,C,D,E) -> f300(A,C,1 + D,1 + E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && 0 >= 2 + E && 0 >= 2 + D] (?,1) Signature: {(f1,5);(f2,5);(f300,5)} Flow Graph: [0->{},1->{2,3,4},2->{},3->{2,3},4->{2,4}] + Applied Processor: FromIts + Details: () * Step 4: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f2(A,C,D,E) -> f1(A,C,D,E) [1 >= A] f2(A,C,D,E) -> f300(A,C,D,E) [A >= 2 && C >= 2] f300(A,C,D,E) -> f1(A,C,D,E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && 1 + D >= 0] f300(A,C,D,E) -> f300(A,C,1 + D,1 + E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && E >= 0 && 0 >= 2 + D] f300(A,C,D,E) -> f300(A,C,1 + D,1 + E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && 0 >= 2 + E && 0 >= 2 + D] Signature: {(f1,5);(f2,5);(f300,5)} Rule Graph: [0->{},1->{2,3,4},2->{},3->{2,3},4->{2,4}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f2(A,C,D,E) -> f1(A,C,D,E) [1 >= A] f2(A,C,D,E) -> f300(A,C,D,E) [A >= 2 && C >= 2] f300(A,C,D,E) -> f1(A,C,D,E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && 1 + D >= 0] f300(A,C,D,E) -> f300(A,C,1 + D,1 + E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && E >= 0 && 0 >= 2 + D] f300(A,C,D,E) -> f300(A,C,1 + D,1 + E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && 0 >= 2 + E && 0 >= 2 + D] f1(A,C,D,E) -> exitus616(A,C,D,E) True f1(A,C,D,E) -> exitus616(A,C,D,E) True f1(A,C,D,E) -> exitus616(A,C,D,E) True Signature: {(exitus616,4);(f1,5);(f2,5);(f300,5)} Rule Graph: [0->{7},1->{2,3,4},2->{5,6},3->{2,3},4->{2,4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[4] c: [4] | `- p:[3] c: [3] * Step 6: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: f2(A,C,D,E) -> f1(A,C,D,E) [1 >= A] f2(A,C,D,E) -> f300(A,C,D,E) [A >= 2 && C >= 2] f300(A,C,D,E) -> f1(A,C,D,E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && 1 + D >= 0] f300(A,C,D,E) -> f300(A,C,1 + D,1 + E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && E >= 0 && 0 >= 2 + D] f300(A,C,D,E) -> f300(A,C,1 + D,1 + E) [-2 + C >= 0 && -4 + A + C >= 0 && -2 + A >= 0 && 0 >= 2 + E && 0 >= 2 + D] f1(A,C,D,E) -> exitus616(A,C,D,E) True f1(A,C,D,E) -> exitus616(A,C,D,E) True f1(A,C,D,E) -> exitus616(A,C,D,E) True Signature: {(exitus616,4);(f1,5);(f2,5);(f300,5)} Rule Graph: [0->{7},1->{2,3,4},2->{5,6},3->{2,3},4->{2,4}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[4] c: [4] | `- p:[3] c: [3]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,C,D,E,0.0,0.1] f2 ~> f1 [A <= A, C <= C, D <= D, E <= E] f2 ~> f300 [A <= A, C <= C, D <= D, E <= E] f300 ~> f1 [A <= A, C <= C, D <= D, E <= E] f300 ~> f300 [A <= A, C <= C, D <= D, E <= K + E] f300 ~> f300 [A <= A, C <= C, D <= D, E <= E] f1 ~> exitus616 [A <= A, C <= C, D <= D, E <= E] f1 ~> exitus616 [A <= A, C <= C, D <= D, E <= E] f1 ~> exitus616 [A <= A, C <= C, D <= D, E <= E] + Loop: [0.0 <= 2*K + E] f300 ~> f300 [A <= A, C <= C, D <= D, E <= E] + Loop: [0.1 <= 2*K + D] f300 ~> f300 [A <= A, C <= C, D <= D, E <= K + E] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,C,D,E,0.0,0.1] f2 ~> f1 [] f2 ~> f300 [] f300 ~> f1 [] f300 ~> f300 [E ~+> E,K ~+> E] f300 ~> f300 [] f1 ~> exitus616 [] f1 ~> exitus616 [] f1 ~> exitus616 [] + Loop: [E ~+> 0.0,K ~*> 0.0] f300 ~> f300 [] + Loop: [D ~+> 0.1,K ~*> 0.1] f300 ~> f300 [E ~+> E,K ~+> E] + Applied Processor: Lare + Details: f2 ~> exitus616 [D ~+> 0.1 ,D ~+> tick ,E ~+> E ,E ~+> 0.0 ,E ~+> tick ,tick ~+> tick ,K ~+> E ,D ~*> E ,K ~*> E ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] + f300> [E ~+> 0.0,E ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] + f300> [D ~+> 0.1 ,D ~+> tick ,E ~+> E ,tick ~+> tick ,K ~+> E ,D ~*> E ,K ~*> E ,K ~*> 0.1 ,K ~*> tick] YES(?,O(n^1))