YES(?,O(n^1)) * Step 1: ArgumentFilter WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f4(A,B,C,D,E,F,G) -> f4(A + B,B,C,D,E,F,G) [-1 + -1*B >= 0 && A >= 0] (?,1) 1. f4(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [-1 + -1*B >= 0 && 0 >= 1 + A] (?,1) 2. f5(A,B,C,D,E,F,G) -> f4(A,B,C,D,E,F,G) [0 >= 1 + B] (1,1) 3. f5(A,B,C,D,E,F,G) -> f6(A,B,0,0,0,0,0) [B >= 0] (1,1) Signature: {(f4,7);(f5,7);(f6,7)} Flow Graph: [0->{0,1},1->{},2->{0,1},3->{}] + Applied Processor: ArgumentFilter [2,3,4,5,6] + Details: We remove following argument positions: [2,3,4,5,6]. * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f4(A,B) -> f4(A + B,B) [-1 + -1*B >= 0 && A >= 0] (?,1) 1. f4(A,B) -> f6(A,B) [-1 + -1*B >= 0 && 0 >= 1 + A] (?,1) 2. f5(A,B) -> f4(A,B) [0 >= 1 + B] (1,1) 3. f5(A,B) -> f6(A,B) [B >= 0] (1,1) Signature: {(f4,7);(f5,7);(f6,7)} Flow Graph: [0->{0,1},1->{},2->{0,1},3->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f4(A,B) -> f4(A + B,B) [-1 + -1*B >= 0 && A >= 0] f4(A,B) -> f6(A,B) [-1 + -1*B >= 0 && 0 >= 1 + A] f5(A,B) -> f4(A,B) [0 >= 1 + B] f5(A,B) -> f6(A,B) [B >= 0] Signature: {(f4,7);(f5,7);(f6,7)} Rule Graph: [0->{0,1},1->{},2->{0,1},3->{}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f4(A,B) -> f4(A + B,B) [-1 + -1*B >= 0 && A >= 0] f4(A,B) -> f6(A,B) [-1 + -1*B >= 0 && 0 >= 1 + A] f5(A,B) -> f4(A,B) [0 >= 1 + B] f5(A,B) -> f6(A,B) [B >= 0] f6(A,B) -> exitus616(A,B) True f6(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f4,7);(f5,7);(f6,7)} Rule Graph: [0->{0,1},1->{5},2->{0,1},3->{4}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[0] c: [0] * Step 5: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: f4(A,B) -> f4(A + B,B) [-1 + -1*B >= 0 && A >= 0] f4(A,B) -> f6(A,B) [-1 + -1*B >= 0 && 0 >= 1 + A] f5(A,B) -> f4(A,B) [0 >= 1 + B] f5(A,B) -> f6(A,B) [B >= 0] f6(A,B) -> exitus616(A,B) True f6(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f4,7);(f5,7);(f6,7)} Rule Graph: [0->{0,1},1->{5},2->{0,1},3->{4}] ,We construct a looptree: P: [0,1,2,3,4,5] | `- p:[0] c: [0]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,0.0] f4 ~> f4 [A <= A + B, B <= B] f4 ~> f6 [A <= A, B <= B] f5 ~> f4 [A <= A, B <= B] f5 ~> f6 [A <= A, B <= B] f6 ~> exitus616 [A <= A, B <= B] f6 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= A] f4 ~> f4 [A <= A + B, B <= B] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0] f4 ~> f4 [A ~+> A,B ~+> A] f4 ~> f6 [] f5 ~> f4 [] f5 ~> f6 [] f6 ~> exitus616 [] f6 ~> exitus616 [] + Loop: [A ~=> 0.0] f4 ~> f4 [A ~+> A,B ~+> A] + Applied Processor: Lare + Details: f5 ~> exitus616 [A ~=> 0.0,A ~+> A,A ~+> tick,B ~+> A,tick ~+> tick,A ~*> A,B ~*> A] + f4> [A ~=> 0.0,A ~+> A,A ~+> tick,B ~+> A,tick ~+> tick,A ~*> A,B ~*> A] YES(?,O(n^1))