YES(?,O(n^1)) * Step 1: ArgumentFilter WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B,C) -> f2(-1 + A,B,C) [-21 + B >= 0 && A >= 31] (?,1) 1. f2(A,B,C) -> f300(A,-1 + B,C) [-21 + B >= 0 && 30 >= A] (?,1) 2. f300(A,B,C) -> f2(A,B,C) [B >= 21] (?,1) 3. f300(A,B,C) -> f1(A,B,D) [20 >= B] (?,1) 4. f3(A,B,C) -> f300(A,B,C) True (1,1) Signature: {(f1,3);(f2,3);(f3,3);(f300,3)} Flow Graph: [0->{0,1},1->{2,3},2->{0,1},3->{},4->{2,3}] + Applied Processor: ArgumentFilter [2] + Details: We remove following argument positions: [2]. * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f2(A,B) -> f2(-1 + A,B) [-21 + B >= 0 && A >= 31] (?,1) 1. f2(A,B) -> f300(A,-1 + B) [-21 + B >= 0 && 30 >= A] (?,1) 2. f300(A,B) -> f2(A,B) [B >= 21] (?,1) 3. f300(A,B) -> f1(A,B) [20 >= B] (?,1) 4. f3(A,B) -> f300(A,B) True (1,1) Signature: {(f1,3);(f2,3);(f3,3);(f300,3)} Flow Graph: [0->{0,1},1->{2,3},2->{0,1},3->{},4->{2,3}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f2(A,B) -> f2(-1 + A,B) [-21 + B >= 0 && A >= 31] f2(A,B) -> f300(A,-1 + B) [-21 + B >= 0 && 30 >= A] f300(A,B) -> f2(A,B) [B >= 21] f300(A,B) -> f1(A,B) [20 >= B] f3(A,B) -> f300(A,B) True Signature: {(f1,3);(f2,3);(f3,3);(f300,3)} Rule Graph: [0->{0,1},1->{2,3},2->{0,1},3->{},4->{2,3}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f2(A,B) -> f2(-1 + A,B) [-21 + B >= 0 && A >= 31] f2(A,B) -> f300(A,-1 + B) [-21 + B >= 0 && 30 >= A] f300(A,B) -> f2(A,B) [B >= 21] f300(A,B) -> f1(A,B) [20 >= B] f3(A,B) -> f300(A,B) True f1(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f1,3);(f2,3);(f3,3);(f300,3)} Rule Graph: [0->{0,1},1->{2,3},2->{0,1},3->{5},4->{2,3}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5] | `- p:[0,2,1] c: [0,1,2] * Step 5: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: f2(A,B) -> f2(-1 + A,B) [-21 + B >= 0 && A >= 31] f2(A,B) -> f300(A,-1 + B) [-21 + B >= 0 && 30 >= A] f300(A,B) -> f2(A,B) [B >= 21] f300(A,B) -> f1(A,B) [20 >= B] f3(A,B) -> f300(A,B) True f1(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f1,3);(f2,3);(f3,3);(f300,3)} Rule Graph: [0->{0,1},1->{2,3},2->{0,1},3->{5},4->{2,3}] ,We construct a looptree: P: [0,1,2,3,4,5] | `- p:[0,2,1] c: [0,1,2]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,0.0] f2 ~> f2 [A <= A, B <= B] f2 ~> f300 [A <= A, B <= B] f300 ~> f2 [A <= A, B <= B] f300 ~> f1 [A <= A, B <= B] f3 ~> f300 [A <= A, B <= B] f1 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= 21*K + A + B] f2 ~> f2 [A <= A, B <= B] f300 ~> f2 [A <= A, B <= B] f2 ~> f300 [A <= A, 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] f2 ~> f2 [] f2 ~> f300 [] f300 ~> f2 [] f300 ~> f1 [] f3 ~> f300 [] f1 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0,K ~*> 0.0] f2 ~> f2 [] f300 ~> f2 [] f2 ~> f300 [] + Applied Processor: Lare + Details: f3 ~> exitus616 [A ~+> 0.0,A ~+> tick,B ~+> 0.0,B ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] + f300> [A ~+> 0.0,A ~+> tick,B ~+> 0.0,B ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] YES(?,O(n^1))