YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f1(A,B) -> f3(A,A) [A >= 1] (1,1) 1. f3(A,B) -> f3(A,-1 + B) [A + -1*B >= 0 && -1 + A >= 0 && B >= 1] (?,1) 2. f3(A,B) -> f3(-1 + A,-1 + A) [A + -1*B >= 0 && -1 + A >= 0 && 0 >= B && A >= 2] (?,1) Signature: {(f1,2);(f3,2)} Flow Graph: [0->{1,2},1->{1,2},2->{1,2}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,2),(2,2)] * Step 2: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f1(A,B) -> f3(A,A) [A >= 1] (1,1) 1. f3(A,B) -> f3(A,-1 + B) [A + -1*B >= 0 && -1 + A >= 0 && B >= 1] (?,1) 2. f3(A,B) -> f3(-1 + A,-1 + A) [A + -1*B >= 0 && -1 + A >= 0 && 0 >= B && A >= 2] (?,1) Signature: {(f1,2);(f3,2)} Flow Graph: [0->{1},1->{1,2},2->{1}] + Applied Processor: FromIts + Details: () * Step 3: Unfold WORST_CASE(?,POLY) + Considered Problem: Rules: f1(A,B) -> f3(A,A) [A >= 1] f3(A,B) -> f3(A,-1 + B) [A + -1*B >= 0 && -1 + A >= 0 && B >= 1] f3(A,B) -> f3(-1 + A,-1 + A) [A + -1*B >= 0 && -1 + A >= 0 && 0 >= B && A >= 2] Signature: {(f1,2);(f3,2)} Rule Graph: [0->{1},1->{1,2},2->{1}] + Applied Processor: Unfold + Details: () * Step 4: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: f1.0(A,B) -> f3.1(A,A) [A >= 1] f3.1(A,B) -> f3.1(A,-1 + B) [A + -1*B >= 0 && -1 + A >= 0 && B >= 1] f3.1(A,B) -> f3.2(A,-1 + B) [A + -1*B >= 0 && -1 + A >= 0 && B >= 1] f3.2(A,B) -> f3.1(-1 + A,-1 + A) [A + -1*B >= 0 && -1 + A >= 0 && 0 >= B && A >= 2] Signature: {(f1.0,2);(f3.1,2);(f3.2,2)} Rule Graph: [0->{1,2},1->{1,2},2->{3},3->{1,2}] + Applied Processor: AddSinks + Details: () * Step 5: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: f1.0(A,B) -> f3.1(A,A) [A >= 1] f3.1(A,B) -> f3.1(A,-1 + B) [A + -1*B >= 0 && -1 + A >= 0 && B >= 1] f3.1(A,B) -> f3.2(A,-1 + B) [A + -1*B >= 0 && -1 + A >= 0 && B >= 1] f3.2(A,B) -> f3.1(-1 + A,-1 + A) [A + -1*B >= 0 && -1 + A >= 0 && 0 >= B && A >= 2] f3.1(A,B) -> exitus616(A,B) True f3.1(A,B) -> exitus616(A,B) True f3.2(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f1.0,2);(f3.1,2);(f3.2,2)} Rule Graph: [0->{1,2},1->{1,2,4},2->{3,6},3->{1,2,5}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[1,3,2] c: [2,3] | `- p:[1] c: [1] * Step 6: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: f1.0(A,B) -> f3.1(A,A) [A >= 1] f3.1(A,B) -> f3.1(A,-1 + B) [A + -1*B >= 0 && -1 + A >= 0 && B >= 1] f3.1(A,B) -> f3.2(A,-1 + B) [A + -1*B >= 0 && -1 + A >= 0 && B >= 1] f3.2(A,B) -> f3.1(-1 + A,-1 + A) [A + -1*B >= 0 && -1 + A >= 0 && 0 >= B && A >= 2] f3.1(A,B) -> exitus616(A,B) True f3.1(A,B) -> exitus616(A,B) True f3.2(A,B) -> exitus616(A,B) True Signature: {(exitus616,2);(f1.0,2);(f3.1,2);(f3.2,2)} Rule Graph: [0->{1,2},1->{1,2,4},2->{3,6},3->{1,2,5}] ,We construct a looptree: P: [0,1,2,3,4,5,6] | `- p:[1,3,2] c: [2,3] | `- p:[1] c: [1]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,0.0,0.0.0] f1.0 ~> f3.1 [A <= A, B <= A] f3.1 ~> f3.1 [A <= A, B <= B] f3.1 ~> f3.2 [A <= A, B <= B] f3.2 ~> f3.1 [A <= A, B <= A] f3.1 ~> exitus616 [A <= A, B <= B] f3.1 ~> exitus616 [A <= A, B <= B] f3.2 ~> exitus616 [A <= A, B <= B] + Loop: [0.0 <= K + A] f3.1 ~> f3.1 [A <= A, B <= B] f3.2 ~> f3.1 [A <= A, B <= A] f3.1 ~> f3.2 [A <= A, B <= B] + Loop: [0.0.0 <= K + B] f3.1 ~> f3.1 [A <= A, B <= B] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,0.0,0.0.0] f1.0 ~> f3.1 [A ~=> B] f3.1 ~> f3.1 [] f3.1 ~> f3.2 [] f3.2 ~> f3.1 [A ~=> B] f3.1 ~> exitus616 [] f3.1 ~> exitus616 [] f3.2 ~> exitus616 [] + Loop: [A ~+> 0.0,K ~+> 0.0] f3.1 ~> f3.1 [] f3.2 ~> f3.1 [A ~=> B] f3.1 ~> f3.2 [] + Loop: [B ~+> 0.0.0,K ~+> 0.0.0] f3.1 ~> f3.1 [] + Applied Processor: Lare + Details: f1.0 ~> exitus616 [A ~=> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,K ~*> tick] + f3.1> [A ~=> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,B ~*> tick ,K ~*> tick] f3.2> [A ~=> B ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,B ~*> tick ,K ~*> tick] + f3.1> [B ~+> 0.0.0,B ~+> tick,tick ~+> tick,K ~+> 0.0.0,K ~+> tick] YES(?,POLY)