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