YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f1(A,B,C,D,E) True (1,1) 1. f1(A,B,C,D,E) -> f1(A,1 + B,C,D,E) [A >= 1 + B] (?,1) 2. f1(A,B,C,D,E) -> f2(A,B,B,D,E) [B >= A] (?,1) 3. f2(A,B,C,D,E) -> f2(A,B,-1 + C,D,E) [B + -1*C >= 0 && -1*A + B >= 0 && C >= 1] (?,1) 4. f2(A,B,C,D,E) -> f3(A,B,C,C,E) [B + -1*C >= 0 && -1*A + B >= 0 && 0 >= C] (?,1) 5. f3(A,B,C,D,E) -> f3(A,B,C,1 + D,E) [B + -1*D >= 0 && -1*C + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && A >= 1 + D] (?,1) 6. f3(A,B,C,D,E) -> f4(A,B,C,D,D) [B + -1*D >= 0 && -1*C + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && D >= A] (?,1) 7. f4(A,B,C,D,E) -> f4(A,B,C,D,-1 + E) [D + -1*E >= 0 (?,1) && B + -1*E >= 0 && -1*C + E >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && -1*A + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && E >= 1] Signature: {(f0,5);(f1,5);(f2,5);(f3,5);(f4,5)} Flow Graph: [0->{1,2},1->{1,2},2->{3,4},3->{3,4},4->{5,6},5->{5,6},6->{7},7->{7}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f1(A,B,C,D,E) True (1,1) 1. f1(A,B,C,D,E) -> f1(A,1 + B,C,D,E) [A >= 1 + B] (?,1) 2. f1(A,B,C,D,E) -> f2(A,B,B,D,E) [B >= A] (1,1) 3. f2(A,B,C,D,E) -> f2(A,B,-1 + C,D,E) [B + -1*C >= 0 && -1*A + B >= 0 && C >= 1] (?,1) 4. f2(A,B,C,D,E) -> f3(A,B,C,C,E) [B + -1*C >= 0 && -1*A + B >= 0 && 0 >= C] (1,1) 5. f3(A,B,C,D,E) -> f3(A,B,C,1 + D,E) [B + -1*D >= 0 && -1*C + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && A >= 1 + D] (?,1) 6. f3(A,B,C,D,E) -> f4(A,B,C,D,D) [B + -1*D >= 0 && -1*C + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && D >= A] (1,1) 7. f4(A,B,C,D,E) -> f4(A,B,C,D,-1 + E) [D + -1*E >= 0 (?,1) && B + -1*E >= 0 && -1*C + E >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && -1*A + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && E >= 1] Signature: {(f0,5);(f1,5);(f2,5);(f3,5);(f4,5)} Flow Graph: [0->{1,2},1->{1,2},2->{3,4},3->{3,4},4->{5,6},5->{5,6},6->{7},7->{7}] + Applied Processor: AddSinks + Details: () * Step 3: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f1(A,B,C,D,E) True (1,1) 1. f1(A,B,C,D,E) -> f1(A,1 + B,C,D,E) [A >= 1 + B] (?,1) 2. f1(A,B,C,D,E) -> f2(A,B,B,D,E) [B >= A] (?,1) 3. f2(A,B,C,D,E) -> f2(A,B,-1 + C,D,E) [B + -1*C >= 0 && -1*A + B >= 0 && C >= 1] (?,1) 4. f2(A,B,C,D,E) -> f3(A,B,C,C,E) [B + -1*C >= 0 && -1*A + B >= 0 && 0 >= C] (?,1) 5. f3(A,B,C,D,E) -> f3(A,B,C,1 + D,E) [B + -1*D >= 0 && -1*C + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && A >= 1 + D] (?,1) 6. f3(A,B,C,D,E) -> f4(A,B,C,D,D) [B + -1*D >= 0 && -1*C + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && D >= A] (?,1) 7. f4(A,B,C,D,E) -> f4(A,B,C,D,-1 + E) [D + -1*E >= 0 (?,1) && B + -1*E >= 0 && -1*C + E >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && -1*A + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && E >= 1] 8. f4(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f0,5);(f1,5);(f2,5);(f3,5);(f4,5)} Flow Graph: [0->{1,2},1->{1,2},2->{3,4},3->{3,4},4->{5,6},5->{5,6},6->{7,8},7->{7,8},8->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | +- p:[1] c: [1] | +- p:[3] c: [3] | +- p:[5] c: [5] | `- p:[7] c: [7] * Step 4: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. f0(A,B,C,D,E) -> f1(A,B,C,D,E) True (1,1) 1. f1(A,B,C,D,E) -> f1(A,1 + B,C,D,E) [A >= 1 + B] (?,1) 2. f1(A,B,C,D,E) -> f2(A,B,B,D,E) [B >= A] (?,1) 3. f2(A,B,C,D,E) -> f2(A,B,-1 + C,D,E) [B + -1*C >= 0 && -1*A + B >= 0 && C >= 1] (?,1) 4. f2(A,B,C,D,E) -> f3(A,B,C,C,E) [B + -1*C >= 0 && -1*A + B >= 0 && 0 >= C] (?,1) 5. f3(A,B,C,D,E) -> f3(A,B,C,1 + D,E) [B + -1*D >= 0 && -1*C + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && A >= 1 + D] (?,1) 6. f3(A,B,C,D,E) -> f4(A,B,C,D,D) [B + -1*D >= 0 && -1*C + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && D >= A] (?,1) 7. f4(A,B,C,D,E) -> f4(A,B,C,D,-1 + E) [D + -1*E >= 0 (?,1) && B + -1*E >= 0 && -1*C + E >= 0 && B + -1*D >= 0 && -1*C + D >= 0 && -1*A + D >= 0 && -1*C >= 0 && B + -1*C >= 0 && -1*A + B >= 0 && E >= 1] 8. f4(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f0,5);(f1,5);(f2,5);(f3,5);(f4,5)} Flow Graph: [0->{1,2},1->{1,2},2->{3,4},3->{3,4},4->{5,6},5->{5,6},6->{7,8},7->{7,8},8->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8] | +- p:[1] c: [1] | +- p:[3] c: [3] | +- p:[5] c: [5] | `- p:[7] c: [7]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 5: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,0.0,0.1,0.2,0.3] f0 ~> f1 [A <= A, B <= B, C <= C, D <= D, E <= E] f1 ~> f1 [A <= A, B <= A + B, C <= C, D <= D, E <= E] f1 ~> f2 [A <= A, B <= B, C <= B, D <= D, E <= E] f2 ~> f2 [A <= A, B <= B, C <= C, D <= D, E <= E] f2 ~> f3 [A <= A, B <= B, C <= C, D <= C, E <= E] f3 ~> f3 [A <= A, B <= B, C <= C, D <= B + D, E <= E] f3 ~> f4 [A <= A, B <= B, C <= C, D <= D, E <= D] f4 ~> f4 [A <= A, B <= B, C <= C, D <= D, E <= D] f4 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E] + Loop: [0.0 <= A + B] f1 ~> f1 [A <= A, B <= A + B, C <= C, D <= D, E <= E] + Loop: [0.1 <= C] f2 ~> f2 [A <= A, B <= B, C <= C, D <= D, E <= E] + Loop: [0.2 <= A + D] f3 ~> f3 [A <= A, B <= B, C <= C, D <= B + D, E <= E] + Loop: [0.3 <= E] f4 ~> f4 [A <= A, B <= B, C <= C, D <= D, E <= D] + Applied Processor: FlowAbstraction + Details: () * Step 6: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,0.0,0.1,0.2,0.3] f0 ~> f1 [] f1 ~> f1 [A ~+> B,B ~+> B] f1 ~> f2 [B ~=> C] f2 ~> f2 [] f2 ~> f3 [C ~=> D] f3 ~> f3 [B ~+> D,D ~+> D] f3 ~> f4 [D ~=> E] f4 ~> f4 [D ~=> E] f4 ~> exitus616 [] + Loop: [A ~+> 0.0,B ~+> 0.0] f1 ~> f1 [A ~+> B,B ~+> B] + Loop: [C ~=> 0.1] f2 ~> f2 [] + Loop: [A ~+> 0.2,D ~+> 0.2] f3 ~> f3 [B ~+> D,D ~+> D] + Loop: [E ~=> 0.3] f4 ~> f4 [D ~=> E] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [B ~=> C ,B ~=> D ,B ~=> E ,B ~=> 0.1 ,B ~=> 0.3 ,A ~+> B ,A ~+> C ,A ~+> D ,A ~+> E ,A ~+> 0.0 ,A ~+> 0.1 ,A ~+> 0.2 ,A ~+> 0.3 ,A ~+> tick ,B ~+> B ,B ~+> C ,B ~+> D ,B ~+> E ,B ~+> 0.0 ,B ~+> 0.1 ,B ~+> 0.2 ,B ~+> 0.3 ,B ~+> tick ,tick ~+> tick ,A ~*> B ,A ~*> C ,A ~*> D ,A ~*> E ,A ~*> 0.1 ,A ~*> 0.2 ,A ~*> 0.3 ,A ~*> tick ,B ~*> B ,B ~*> C ,B ~*> D ,B ~*> E ,B ~*> 0.1 ,B ~*> 0.2 ,B ~*> 0.3 ,B ~*> tick] + f1> [A ~+> B,A ~+> 0.0,A ~+> tick,B ~+> B,B ~+> 0.0,B ~+> tick,tick ~+> tick,A ~*> B,B ~*> B] + f2> [C ~=> 0.1,C ~+> tick,tick ~+> tick] + f3> [A ~+> 0.2 ,A ~+> tick ,B ~+> D ,D ~+> D ,D ~+> 0.2 ,D ~+> tick ,tick ~+> tick ,A ~*> D ,B ~*> D ,D ~*> D] + f4> [D ~=> E,E ~=> 0.3,E ~+> tick,tick ~+> tick] YES(?,POLY)