YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalspeedpldi3start(A,B,C,D) -> evalspeedpldi3entryin(A,B,C,D) True (1,1) 1. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [0 >= A] (?,1) 2. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [A >= B] (?,1) 3. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3bb5in(A,B,0,0) [A >= 1 && B >= 1 + A] (?,1) 4. evalspeedpldi3bb5in(A,B,C,D) -> evalspeedpldi3bb2in(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] 5. evalspeedpldi3bb5in(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= B] 6. evalspeedpldi3bb2in(A,B,C,D) -> evalspeedpldi3bb3in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + C] 7. evalspeedpldi3bb2in(A,B,C,D) -> evalspeedpldi3bb4in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= A] 8. evalspeedpldi3bb3in(A,B,C,D) -> evalspeedpldi3bb5in(A,B,1 + C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 9. evalspeedpldi3bb4in(A,B,C,D) -> evalspeedpldi3bb5in(A,B,0,1 + D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 10. evalspeedpldi3returnin(A,B,C,D) -> evalspeedpldi3stop(A,B,C,D) True (?,1) Signature: {(evalspeedpldi3bb2in,4) ;(evalspeedpldi3bb3in,4) ;(evalspeedpldi3bb4in,4) ;(evalspeedpldi3bb5in,4) ;(evalspeedpldi3entryin,4) ;(evalspeedpldi3returnin,4) ;(evalspeedpldi3start,4) ;(evalspeedpldi3stop,4)} Flow Graph: [0->{1,2,3},1->{10},2->{10},3->{4,5},4->{6,7},5->{10},6->{8},7->{9},8->{4,5},9->{4,5},10->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalspeedpldi3start(A,B,C,D) -> evalspeedpldi3entryin(A,B,C,D) True (1,1) 1. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [0 >= A] (1,1) 2. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [A >= B] (1,1) 3. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3bb5in(A,B,0,0) [A >= 1 && B >= 1 + A] (1,1) 4. evalspeedpldi3bb5in(A,B,C,D) -> evalspeedpldi3bb2in(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] 5. evalspeedpldi3bb5in(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [D >= 0 (1,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= B] 6. evalspeedpldi3bb2in(A,B,C,D) -> evalspeedpldi3bb3in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + C] 7. evalspeedpldi3bb2in(A,B,C,D) -> evalspeedpldi3bb4in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= A] 8. evalspeedpldi3bb3in(A,B,C,D) -> evalspeedpldi3bb5in(A,B,1 + C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 9. evalspeedpldi3bb4in(A,B,C,D) -> evalspeedpldi3bb5in(A,B,0,1 + D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 10. evalspeedpldi3returnin(A,B,C,D) -> evalspeedpldi3stop(A,B,C,D) True (1,1) Signature: {(evalspeedpldi3bb2in,4) ;(evalspeedpldi3bb3in,4) ;(evalspeedpldi3bb4in,4) ;(evalspeedpldi3bb5in,4) ;(evalspeedpldi3entryin,4) ;(evalspeedpldi3returnin,4) ;(evalspeedpldi3start,4) ;(evalspeedpldi3stop,4)} Flow Graph: [0->{1,2,3},1->{10},2->{10},3->{4,5},4->{6,7},5->{10},6->{8},7->{9},8->{4,5},9->{4,5},10->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,5),(8,5)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalspeedpldi3start(A,B,C,D) -> evalspeedpldi3entryin(A,B,C,D) True (1,1) 1. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [0 >= A] (1,1) 2. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [A >= B] (1,1) 3. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3bb5in(A,B,0,0) [A >= 1 && B >= 1 + A] (1,1) 4. evalspeedpldi3bb5in(A,B,C,D) -> evalspeedpldi3bb2in(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] 5. evalspeedpldi3bb5in(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [D >= 0 (1,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= B] 6. evalspeedpldi3bb2in(A,B,C,D) -> evalspeedpldi3bb3in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + C] 7. evalspeedpldi3bb2in(A,B,C,D) -> evalspeedpldi3bb4in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= A] 8. evalspeedpldi3bb3in(A,B,C,D) -> evalspeedpldi3bb5in(A,B,1 + C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 9. evalspeedpldi3bb4in(A,B,C,D) -> evalspeedpldi3bb5in(A,B,0,1 + D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 10. evalspeedpldi3returnin(A,B,C,D) -> evalspeedpldi3stop(A,B,C,D) True (1,1) Signature: {(evalspeedpldi3bb2in,4) ;(evalspeedpldi3bb3in,4) ;(evalspeedpldi3bb4in,4) ;(evalspeedpldi3bb5in,4) ;(evalspeedpldi3entryin,4) ;(evalspeedpldi3returnin,4) ;(evalspeedpldi3start,4) ;(evalspeedpldi3stop,4)} Flow Graph: [0->{1,2,3},1->{10},2->{10},3->{4},4->{6,7},5->{10},6->{8},7->{9},8->{4},9->{4,5},10->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalspeedpldi3start(A,B,C,D) -> evalspeedpldi3entryin(A,B,C,D) True (1,1) 1. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [0 >= A] (?,1) 2. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [A >= B] (?,1) 3. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3bb5in(A,B,0,0) [A >= 1 && B >= 1 + A] (?,1) 4. evalspeedpldi3bb5in(A,B,C,D) -> evalspeedpldi3bb2in(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] 5. evalspeedpldi3bb5in(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= B] 6. evalspeedpldi3bb2in(A,B,C,D) -> evalspeedpldi3bb3in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + C] 7. evalspeedpldi3bb2in(A,B,C,D) -> evalspeedpldi3bb4in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= A] 8. evalspeedpldi3bb3in(A,B,C,D) -> evalspeedpldi3bb5in(A,B,1 + C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 9. evalspeedpldi3bb4in(A,B,C,D) -> evalspeedpldi3bb5in(A,B,0,1 + D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 10. evalspeedpldi3returnin(A,B,C,D) -> evalspeedpldi3stop(A,B,C,D) True (?,1) 11. evalspeedpldi3returnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalspeedpldi3bb2in,4) ;(evalspeedpldi3bb3in,4) ;(evalspeedpldi3bb4in,4) ;(evalspeedpldi3bb5in,4) ;(evalspeedpldi3entryin,4) ;(evalspeedpldi3returnin,4) ;(evalspeedpldi3start,4) ;(evalspeedpldi3stop,4) ;(exitus616,4)} Flow Graph: [0->{1,2,3},1->{10,11},2->{10,11},3->{4,5},4->{6,7},5->{10,11},6->{8},7->{9},8->{4,5},9->{4,5},10->{} ,11->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,5),(8,5)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalspeedpldi3start(A,B,C,D) -> evalspeedpldi3entryin(A,B,C,D) True (1,1) 1. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [0 >= A] (?,1) 2. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [A >= B] (?,1) 3. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3bb5in(A,B,0,0) [A >= 1 && B >= 1 + A] (?,1) 4. evalspeedpldi3bb5in(A,B,C,D) -> evalspeedpldi3bb2in(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] 5. evalspeedpldi3bb5in(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= B] 6. evalspeedpldi3bb2in(A,B,C,D) -> evalspeedpldi3bb3in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + C] 7. evalspeedpldi3bb2in(A,B,C,D) -> evalspeedpldi3bb4in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= A] 8. evalspeedpldi3bb3in(A,B,C,D) -> evalspeedpldi3bb5in(A,B,1 + C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 9. evalspeedpldi3bb4in(A,B,C,D) -> evalspeedpldi3bb5in(A,B,0,1 + D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 10. evalspeedpldi3returnin(A,B,C,D) -> evalspeedpldi3stop(A,B,C,D) True (?,1) 11. evalspeedpldi3returnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalspeedpldi3bb2in,4) ;(evalspeedpldi3bb3in,4) ;(evalspeedpldi3bb4in,4) ;(evalspeedpldi3bb5in,4) ;(evalspeedpldi3entryin,4) ;(evalspeedpldi3returnin,4) ;(evalspeedpldi3start,4) ;(evalspeedpldi3stop,4) ;(exitus616,4)} Flow Graph: [0->{1,2,3},1->{10,11},2->{10,11},3->{4},4->{6,7},5->{10,11},6->{8},7->{9},8->{4},9->{4,5},10->{},11->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[4,8,6,9,7] c: [9] | `- p:[4,8,6] c: [8] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. evalspeedpldi3start(A,B,C,D) -> evalspeedpldi3entryin(A,B,C,D) True (1,1) 1. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [0 >= A] (?,1) 2. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [A >= B] (?,1) 3. evalspeedpldi3entryin(A,B,C,D) -> evalspeedpldi3bb5in(A,B,0,0) [A >= 1 && B >= 1 + A] (?,1) 4. evalspeedpldi3bb5in(A,B,C,D) -> evalspeedpldi3bb2in(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] 5. evalspeedpldi3bb5in(A,B,C,D) -> evalspeedpldi3returnin(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= B] 6. evalspeedpldi3bb2in(A,B,C,D) -> evalspeedpldi3bb3in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + C] 7. evalspeedpldi3bb2in(A,B,C,D) -> evalspeedpldi3bb4in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= A] 8. evalspeedpldi3bb3in(A,B,C,D) -> evalspeedpldi3bb5in(A,B,1 + C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 9. evalspeedpldi3bb4in(A,B,C,D) -> evalspeedpldi3bb5in(A,B,0,1 + D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 10. evalspeedpldi3returnin(A,B,C,D) -> evalspeedpldi3stop(A,B,C,D) True (?,1) 11. evalspeedpldi3returnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalspeedpldi3bb2in,4) ;(evalspeedpldi3bb3in,4) ;(evalspeedpldi3bb4in,4) ;(evalspeedpldi3bb5in,4) ;(evalspeedpldi3entryin,4) ;(evalspeedpldi3returnin,4) ;(evalspeedpldi3start,4) ;(evalspeedpldi3stop,4) ;(exitus616,4)} Flow Graph: [0->{1,2,3},1->{10,11},2->{10,11},3->{4},4->{6,7},5->{10,11},6->{8},7->{9},8->{4},9->{4,5},10->{},11->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11] | `- p:[4,8,6,9,7] c: [9] | `- p:[4,8,6] c: [8]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,0.0,0.0.0] evalspeedpldi3start ~> evalspeedpldi3entryin [A <= A, B <= B, C <= C, D <= D] evalspeedpldi3entryin ~> evalspeedpldi3returnin [A <= A, B <= B, C <= C, D <= D] evalspeedpldi3entryin ~> evalspeedpldi3returnin [A <= A, B <= B, C <= C, D <= D] evalspeedpldi3entryin ~> evalspeedpldi3bb5in [A <= A, B <= B, C <= 0*K, D <= 0*K] evalspeedpldi3bb5in ~> evalspeedpldi3bb2in [A <= A, B <= B, C <= C, D <= D] evalspeedpldi3bb5in ~> evalspeedpldi3returnin [A <= A, B <= B, C <= C, D <= D] evalspeedpldi3bb2in ~> evalspeedpldi3bb3in [A <= A, B <= B, C <= C, D <= D] evalspeedpldi3bb2in ~> evalspeedpldi3bb4in [A <= A, B <= B, C <= C, D <= D] evalspeedpldi3bb3in ~> evalspeedpldi3bb5in [A <= A, B <= B, C <= B, D <= D] evalspeedpldi3bb4in ~> evalspeedpldi3bb5in [A <= A, B <= B, C <= 0*K, D <= B] evalspeedpldi3returnin ~> evalspeedpldi3stop [A <= A, B <= B, C <= C, D <= D] evalspeedpldi3returnin ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= B + D] evalspeedpldi3bb5in ~> evalspeedpldi3bb2in [A <= A, B <= B, C <= C, D <= D] evalspeedpldi3bb3in ~> evalspeedpldi3bb5in [A <= A, B <= B, C <= B, D <= D] evalspeedpldi3bb2in ~> evalspeedpldi3bb3in [A <= A, B <= B, C <= C, D <= D] evalspeedpldi3bb4in ~> evalspeedpldi3bb5in [A <= A, B <= B, C <= 0*K, D <= B] evalspeedpldi3bb2in ~> evalspeedpldi3bb4in [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0.0 <= K + B + C] evalspeedpldi3bb5in ~> evalspeedpldi3bb2in [A <= A, B <= B, C <= C, D <= D] evalspeedpldi3bb3in ~> evalspeedpldi3bb5in [A <= A, B <= B, C <= B, D <= D] evalspeedpldi3bb2in ~> evalspeedpldi3bb3in [A <= A, B <= B, C <= C, D <= D] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0,0.0.0] evalspeedpldi3start ~> evalspeedpldi3entryin [] evalspeedpldi3entryin ~> evalspeedpldi3returnin [] evalspeedpldi3entryin ~> evalspeedpldi3returnin [] evalspeedpldi3entryin ~> evalspeedpldi3bb5in [K ~=> C,K ~=> D] evalspeedpldi3bb5in ~> evalspeedpldi3bb2in [] evalspeedpldi3bb5in ~> evalspeedpldi3returnin [] evalspeedpldi3bb2in ~> evalspeedpldi3bb3in [] evalspeedpldi3bb2in ~> evalspeedpldi3bb4in [] evalspeedpldi3bb3in ~> evalspeedpldi3bb5in [B ~=> C] evalspeedpldi3bb4in ~> evalspeedpldi3bb5in [B ~=> D,K ~=> C] evalspeedpldi3returnin ~> evalspeedpldi3stop [] evalspeedpldi3returnin ~> exitus616 [] + Loop: [B ~+> 0.0,D ~+> 0.0] evalspeedpldi3bb5in ~> evalspeedpldi3bb2in [] evalspeedpldi3bb3in ~> evalspeedpldi3bb5in [B ~=> C] evalspeedpldi3bb2in ~> evalspeedpldi3bb3in [] evalspeedpldi3bb4in ~> evalspeedpldi3bb5in [B ~=> D,K ~=> C] evalspeedpldi3bb2in ~> evalspeedpldi3bb4in [] + Loop: [B ~+> 0.0.0,C ~+> 0.0.0,K ~+> 0.0.0] evalspeedpldi3bb5in ~> evalspeedpldi3bb2in [] evalspeedpldi3bb3in ~> evalspeedpldi3bb5in [B ~=> C] evalspeedpldi3bb2in ~> evalspeedpldi3bb3in [] + Applied Processor: LareProcessor + Details: evalspeedpldi3start ~> exitus616 [B ~=> C ,B ~=> D ,K ~=> C ,K ~=> D ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] evalspeedpldi3start ~> evalspeedpldi3stop [B ~=> C ,B ~=> D ,K ~=> C ,K ~=> D ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + evalspeedpldi3bb5in> [B ~=> C ,B ~=> D ,K ~=> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> 0.0.0 ,B ~*> tick ,C ~*> tick ,D ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + evalspeedpldi3bb2in> [B ~=> C ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] evalspeedpldi3bb5in> [B ~=> C ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] YES(?,POLY)