YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f1(A,B,2) [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1) 1. f1(A,B,C) -> f1(A,1 + B,C) [2 + -1*C >= 0 (?,1) && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && A + C >= 1 + 2*B] 2. f1(A,B,C) -> f1(A,-1 + B,C) [2 + -1*C >= 0 (?,1) && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && 2*B >= 2 + A + C] Signature: {(f0,3);(f1,3)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,2),(2,1)] * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. f0(A,B,C) -> f1(A,B,2) [A >= 0 && 3 >= A && 3 >= B && B >= 0] (1,1) 1. f1(A,B,C) -> f1(A,1 + B,C) [2 + -1*C >= 0 (?,1) && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && A + C >= 1 + 2*B] 2. f1(A,B,C) -> f1(A,-1 + B,C) [2 + -1*C >= 0 (?,1) && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && 2*B >= 2 + A + C] Signature: {(f0,3);(f1,3)} Flow Graph: [0->{1,2},1->{1},2->{2}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f0(A,B,C) -> f1(A,B,2) [A >= 0 && 3 >= A && 3 >= B && B >= 0] f1(A,B,C) -> f1(A,1 + B,C) [2 + -1*C >= 0 && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && A + C >= 1 + 2*B] f1(A,B,C) -> f1(A,-1 + B,C) [2 + -1*C >= 0 && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && 2*B >= 2 + A + C] Signature: {(f0,3);(f1,3)} Rule Graph: [0->{1,2},1->{1},2->{2}] + Applied Processor: AddSinks + Details: () * Step 4: Unfold WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f0(A,B,C) -> f1(A,B,2) [A >= 0 && 3 >= A && 3 >= B && B >= 0] f1(A,B,C) -> f1(A,1 + B,C) [2 + -1*C >= 0 && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && A + C >= 1 + 2*B] f1(A,B,C) -> f1(A,-1 + B,C) [2 + -1*C >= 0 && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && 2*B >= 2 + A + C] f1(A,B,C) -> exitus616(A,B,C) True f1(A,B,C) -> exitus616(A,B,C) True Signature: {(exitus616,3);(f0,3);(f1,3)} Rule Graph: [0->{1,2},1->{1,4},2->{2,3}] + Applied Processor: Unfold + Details: () * Step 5: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: f0.0(A,B,C) -> f1.1(A,B,2) [A >= 0 && 3 >= A && 3 >= B && B >= 0] f0.0(A,B,C) -> f1.2(A,B,2) [A >= 0 && 3 >= A && 3 >= B && B >= 0] f1.1(A,B,C) -> f1.1(A,1 + B,C) [2 + -1*C >= 0 && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && A + C >= 1 + 2*B] f1.1(A,B,C) -> f1.4(A,1 + B,C) [2 + -1*C >= 0 && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && A + C >= 1 + 2*B] f1.2(A,B,C) -> f1.2(A,-1 + B,C) [2 + -1*C >= 0 && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && 2*B >= 2 + A + C] f1.2(A,B,C) -> f1.3(A,-1 + B,C) [2 + -1*C >= 0 && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && 2*B >= 2 + A + C] f1.3(A,B,C) -> exitus616.5(A,B,C) True f1.4(A,B,C) -> exitus616.5(A,B,C) True Signature: {(exitus616.5,3);(f0.0,3);(f1.1,3);(f1.2,3);(f1.3,3);(f1.4,3)} Rule Graph: [0->{2,3},1->{4,5},2->{2,3},3->{7},4->{4,5},5->{6},6->{},7->{}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[4] c: [4] | `- p:[2] c: [2] * Step 6: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: f0.0(A,B,C) -> f1.1(A,B,2) [A >= 0 && 3 >= A && 3 >= B && B >= 0] f0.0(A,B,C) -> f1.2(A,B,2) [A >= 0 && 3 >= A && 3 >= B && B >= 0] f1.1(A,B,C) -> f1.1(A,1 + B,C) [2 + -1*C >= 0 && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && A + C >= 1 + 2*B] f1.1(A,B,C) -> f1.4(A,1 + B,C) [2 + -1*C >= 0 && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && A + C >= 1 + 2*B] f1.2(A,B,C) -> f1.2(A,-1 + B,C) [2 + -1*C >= 0 && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && 2*B >= 2 + A + C] f1.2(A,B,C) -> f1.3(A,-1 + B,C) [2 + -1*C >= 0 && 2 + B + -1*C >= 0 && 5 + -1*B + -1*C >= 0 && 2 + A + -1*C >= 0 && 5 + -1*A + -1*C >= 0 && -2 + C >= 0 && -2 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + A + C >= 0 && 1 + -1*A + C >= 0 && 3 + -1*B >= 0 && 3 + A + -1*B >= 0 && 6 + -1*A + -1*B >= 0 && B >= 0 && A + B >= 0 && 3 + -1*A + B >= 0 && 3 + -1*A >= 0 && A >= 0 && 2*B >= 2 + A + C] f1.3(A,B,C) -> exitus616.5(A,B,C) True f1.4(A,B,C) -> exitus616.5(A,B,C) True Signature: {(exitus616.5,3);(f0.0,3);(f1.1,3);(f1.2,3);(f1.3,3);(f1.4,3)} Rule Graph: [0->{2,3},1->{4,5},2->{2,3},3->{7},4->{4,5},5->{6},6->{},7->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7] | +- p:[4] c: [4] | `- p:[2] c: [2]) + Applied Processor: AbstractSize NoMinimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [A,B,C,0.0,0.1] f0.0 ~> f1.1 [A <= A, B <= B, C <= 2*K] f0.0 ~> f1.2 [A <= A, B <= B, C <= 2*K] f1.1 ~> f1.1 [A <= A, B <= 4*K, C <= C] f1.1 ~> f1.4 [A <= A, B <= 4*K, C <= C] f1.2 ~> f1.2 [A <= A, B <= 2*K, C <= C] f1.2 ~> f1.3 [A <= A, B <= 2*K, C <= C] f1.3 ~> exitus616.5 [A <= A, B <= B, C <= C] f1.4 ~> exitus616.5 [A <= A, B <= B, C <= C] + Loop: [0.0 <= 2*K + B + C] f1.2 ~> f1.2 [A <= A, B <= 2*K, C <= C] + Loop: [0.1 <= K + B + C] f1.1 ~> f1.1 [A <= A, B <= 4*K, C <= C] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,0.0,0.1] f0.0 ~> f1.1 [K ~=> C] f0.0 ~> f1.2 [K ~=> C] f1.1 ~> f1.1 [K ~=> B] f1.1 ~> f1.4 [K ~=> B] f1.2 ~> f1.2 [K ~=> B] f1.2 ~> f1.3 [K ~=> B] f1.3 ~> exitus616.5 [] f1.4 ~> exitus616.5 [] + Loop: [B ~+> 0.0,C ~+> 0.0,K ~*> 0.0] f1.2 ~> f1.2 [K ~=> B] + Loop: [B ~+> 0.1,C ~+> 0.1,K ~+> 0.1] f1.1 ~> f1.1 [K ~=> B] + Applied Processor: Lare + Details: f0.0 ~> exitus616.5 [K ~=> B ,K ~=> C ,B ~+> 0.0 ,B ~+> 0.1 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,K ~*> 0.0 ,K ~*> 0.1 ,K ~*> tick] + f1.2> [K ~=> B,B ~+> 0.0,B ~+> tick,C ~+> 0.0,C ~+> tick,tick ~+> tick,K ~*> 0.0,K ~*> tick] + f1.1> [K ~=> B,B ~+> 0.1,B ~+> tick,C ~+> 0.1,C ~+> tick,tick ~+> tick,K ~+> 0.1,K ~+> tick] YES(?,O(n^1))