YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= B] (?,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [C >= 0 (?,1) && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= C] 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [D >= 0 (?,1) && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= D] 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E && A >= 1 + F] 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E] 6. f16(A,B,C,D,E) -> f31(A,B,C,D,E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E] 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && E >= 5] 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 0 (?,1) && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && D >= 5] 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 0 (?,1) && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && C >= 5] 10. f7(A,B,C,D,E) -> f31(A,B,C,D,E) [B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && B >= 5] (?,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1,10},1->{2,9},2->{3,8},3->{4,5,6,7},4->{4,5,6,7},5->{4,5,6,7},6->{},7->{3,8},8->{2,9},9->{1,10} ,10->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= B] (?,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [C >= 0 (?,1) && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= C] 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [D >= 0 (?,1) && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= D] 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E && A >= 1 + F] 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E] 6. f16(A,B,C,D,E) -> f31(A,B,C,D,E) [E >= 0 (1,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E] 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && E >= 5] 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 0 (?,1) && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && D >= 5] 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 0 (?,1) && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && C >= 5] 10. f7(A,B,C,D,E) -> f31(A,B,C,D,E) [B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && B >= 5] (1,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1,10},1->{2,9},2->{3,8},3->{4,5,6,7},4->{4,5,6,7},5->{4,5,6,7},6->{},7->{3,8},8->{2,9},9->{1,10} ,10->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,10),(1,9),(2,8),(3,7)] * Step 3: AddSinks WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= B] (?,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [C >= 0 (?,1) && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= C] 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [D >= 0 (?,1) && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= D] 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E && A >= 1 + F] 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E] 6. f16(A,B,C,D,E) -> f31(A,B,C,D,E) [E >= 0 (1,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E] 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && E >= 5] 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 0 (?,1) && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && D >= 5] 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 0 (?,1) && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && C >= 5] 10. f7(A,B,C,D,E) -> f31(A,B,C,D,E) [B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && B >= 5] (1,1) Signature: {(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{4,5,6,7},5->{4,5,6,7},6->{},7->{3,8},8->{2,9},9->{1,10},10->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= B] (?,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [C >= 0 (?,1) && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= C] 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [D >= 0 (?,1) && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= D] 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E && A >= 1 + F] 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E] 6. f16(A,B,C,D,E) -> f31(A,B,C,D,E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E] 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && E >= 5] 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 0 (?,1) && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && D >= 5] 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 0 (?,1) && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && C >= 5] 10. f7(A,B,C,D,E) -> f31(A,B,C,D,E) [B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && B >= 5] (?,1) 11. f7(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) 12. f16(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1,10,11},1->{2,9},2->{3,8},3->{4,5,6,7,12},4->{4,5,6,7,12},5->{4,5,6,7,12},6->{},7->{3,8},8->{2,9} ,9->{1,10,11},10->{},11->{},12->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(0,10),(1,9),(2,8),(3,7)] * Step 5: LooptreeTransformer WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= B] (?,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [C >= 0 (?,1) && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= C] 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [D >= 0 (?,1) && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= D] 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E && A >= 1 + F] 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E] 6. f16(A,B,C,D,E) -> f31(A,B,C,D,E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E] 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && E >= 5] 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 0 (?,1) && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && D >= 5] 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 0 (?,1) && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && C >= 5] 10. f7(A,B,C,D,E) -> f31(A,B,C,D,E) [B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && B >= 5] (?,1) 11. f7(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) 12. f16(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1,11},1->{2},2->{3},3->{4,5,6,12},4->{4,5,6,7,12},5->{4,5,6,7,12},6->{},7->{3,8},8->{2,9},9->{1,10 ,11},10->{},11->{},12->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[1,9,8,7,4,3,2,5] c: [1] | `- p:[2,8,7,4,3,5] c: [2] | `- p:[3,7,4,5] c: [3] | `- p:[4,5] c: [5] | `- p:[4] c: [4] * Step 6: SizeAbstraction WORST_CASE(?,O(1)) + Considered Problem: (Rules: 0. f0(A,B,C,D,E) -> f7(400,0,C,D,E) True (1,1) 1. f7(A,B,C,D,E) -> f10(A,B,0,D,E) [B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= B] (?,1) 2. f10(A,B,C,D,E) -> f13(A,B,C,0,E) [C >= 0 (?,1) && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= C] 3. f13(A,B,C,D,E) -> f16(A,B,C,D,0) [D >= 0 (?,1) && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= D] 4. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E && A >= 1 + F] 5. f16(A,B,C,D,E) -> f16(A,B,C,D,1 + E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E] 6. f16(A,B,C,D,E) -> f31(A,B,C,D,E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && 4 >= E] 7. f16(A,B,C,D,E) -> f13(A,B,C,1 + D,E) [E >= 0 (?,1) && D + E >= 0 && C + E >= 0 && B + E >= 0 && -400 + A + E >= 0 && 400 + -1*A + E >= 0 && D >= 0 && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && E >= 5] 8. f13(A,B,C,D,E) -> f10(A,B,1 + C,D,E) [D >= 0 (?,1) && C + D >= 0 && B + D >= 0 && -400 + A + D >= 0 && 400 + -1*A + D >= 0 && C >= 0 && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && D >= 5] 9. f10(A,B,C,D,E) -> f7(A,1 + B,C,D,E) [C >= 0 (?,1) && B + C >= 0 && -400 + A + C >= 0 && 400 + -1*A + C >= 0 && B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && C >= 5] 10. f7(A,B,C,D,E) -> f31(A,B,C,D,E) [B >= 0 && -400 + A + B >= 0 && 400 + -1*A + B >= 0 && 400 + -1*A >= 0 && -400 + A >= 0 && B >= 5] (?,1) 11. f7(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) 12. f16(A,B,C,D,E) -> exitus616(A,B,C,D,E) True (?,1) Signature: {(exitus616,5);(f0,5);(f10,5);(f13,5);(f16,5);(f31,5);(f7,5)} Flow Graph: [0->{1,11},1->{2},2->{3},3->{4,5,6,12},4->{4,5,6,7,12},5->{4,5,6,7,12},6->{},7->{3,8},8->{2,9},9->{1,10 ,11},10->{},11->{},12->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[1,9,8,7,4,3,2,5] c: [1] | `- p:[2,8,7,4,3,5] c: [2] | `- p:[3,7,4,5] c: [3] | `- p:[4,5] c: [5] | `- p:[4] c: [4]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [A,B,C,D,E,0.0,0.0.0,0.0.0.0,0.0.0.0.0,0.0.0.0.0.0] f0 ~> f7 [A <= 400*K, B <= 0*K, C <= C, D <= D, E <= E] f7 ~> f10 [A <= A, B <= B, C <= 0*K, D <= D, E <= E] f10 ~> f13 [A <= A, B <= B, C <= C, D <= 0*K, E <= E] f13 ~> f16 [A <= A, B <= B, C <= C, D <= D, E <= 0*K] f16 ~> f16 [A <= A, B <= B, C <= C, D <= D, E <= 5*K] f16 ~> f16 [A <= A, B <= B, C <= C, D <= D, E <= 5*K] f16 ~> f31 [A <= A, B <= B, C <= C, D <= D, E <= E] f16 ~> f13 [A <= A, B <= B, C <= C, D <= D + E, E <= E] f13 ~> f10 [A <= A, B <= B, C <= C + D, D <= D, E <= E] f10 ~> f7 [A <= A, B <= B + C, C <= C, D <= D, E <= E] f7 ~> f31 [A <= A, B <= B, C <= C, D <= D, E <= E] f7 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E] f16 ~> exitus616 [A <= A, B <= B, C <= C, D <= D, E <= E] + Loop: [0.0 <= 5*K + B] f7 ~> f10 [A <= A, B <= B, C <= 0*K, D <= D, E <= E] f10 ~> f7 [A <= A, B <= B + C, C <= C, D <= D, E <= E] f13 ~> f10 [A <= A, B <= B, C <= C + D, D <= D, E <= E] f16 ~> f13 [A <= A, B <= B, C <= C, D <= D + E, E <= E] f16 ~> f16 [A <= A, B <= B, C <= C, D <= D, E <= 5*K] f13 ~> f16 [A <= A, B <= B, C <= C, D <= D, E <= 0*K] f10 ~> f13 [A <= A, B <= B, C <= C, D <= 0*K, E <= E] f16 ~> f16 [A <= A, B <= B, C <= C, D <= D, E <= 5*K] + Loop: [0.0.0 <= 5*K + C] f10 ~> f13 [A <= A, B <= B, C <= C, D <= 0*K, E <= E] f13 ~> f10 [A <= A, B <= B, C <= C + D, D <= D, E <= E] f16 ~> f13 [A <= A, B <= B, C <= C, D <= D + E, E <= E] f16 ~> f16 [A <= A, B <= B, C <= C, D <= D, E <= 5*K] f13 ~> f16 [A <= A, B <= B, C <= C, D <= D, E <= 0*K] f16 ~> f16 [A <= A, B <= B, C <= C, D <= D, E <= 5*K] + Loop: [0.0.0.0 <= 5*K + D] f13 ~> f16 [A <= A, B <= B, C <= C, D <= D, E <= 0*K] f16 ~> f13 [A <= A, B <= B, C <= C, D <= D + E, E <= E] f16 ~> f16 [A <= A, B <= B, C <= C, D <= D, E <= 5*K] f16 ~> f16 [A <= A, B <= B, C <= C, D <= D, E <= 5*K] + Loop: [0.0.0.0.0 <= 5*K + E] f16 ~> f16 [A <= A, B <= B, C <= C, D <= D, E <= 5*K] f16 ~> f16 [A <= A, B <= B, C <= C, D <= D, E <= 5*K] + Loop: [0.0.0.0.0.0 <= 5*K + E] f16 ~> f16 [A <= A, B <= B, C <= C, D <= D, E <= 5*K] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,O(1)) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,E,0.0,0.0.0,0.0.0.0,0.0.0.0.0,0.0.0.0.0.0] f0 ~> f7 [K ~=> A,K ~=> B] f7 ~> f10 [K ~=> C] f10 ~> f13 [K ~=> D] f13 ~> f16 [K ~=> E] f16 ~> f16 [K ~=> E] f16 ~> f16 [K ~=> E] f16 ~> f31 [] f16 ~> f13 [D ~+> D,E ~+> D] f13 ~> f10 [C ~+> C,D ~+> C] f10 ~> f7 [B ~+> B,C ~+> B] f7 ~> f31 [] f7 ~> exitus616 [] f16 ~> exitus616 [] + Loop: [B ~+> 0.0,K ~*> 0.0] f7 ~> f10 [K ~=> C] f10 ~> f7 [B ~+> B,C ~+> B] f13 ~> f10 [C ~+> C,D ~+> C] f16 ~> f13 [D ~+> D,E ~+> D] f16 ~> f16 [K ~=> E] f13 ~> f16 [K ~=> E] f10 ~> f13 [K ~=> D] f16 ~> f16 [K ~=> E] + Loop: [C ~+> 0.0.0,K ~*> 0.0.0] f10 ~> f13 [K ~=> D] f13 ~> f10 [C ~+> C,D ~+> C] f16 ~> f13 [D ~+> D,E ~+> D] f16 ~> f16 [K ~=> E] f13 ~> f16 [K ~=> E] f16 ~> f16 [K ~=> E] + Loop: [D ~+> 0.0.0.0,K ~*> 0.0.0.0] f13 ~> f16 [K ~=> E] f16 ~> f13 [D ~+> D,E ~+> D] f16 ~> f16 [K ~=> E] f16 ~> f16 [K ~=> E] + Loop: [E ~+> 0.0.0.0.0,K ~*> 0.0.0.0.0] f16 ~> f16 [K ~=> E] f16 ~> f16 [K ~=> E] + Loop: [E ~+> 0.0.0.0.0.0,K ~*> 0.0.0.0.0.0] f16 ~> f16 [K ~=> E] + Applied Processor: LareProcessor + Details: f0 ~> exitus616 [K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,K ~=> E ,tick ~+> tick ,K ~+> B ,K ~+> C ,K ~+> D ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> 0.0.0.0 ,K ~+> 0.0.0.0.0 ,K ~+> 0.0.0.0.0.0 ,K ~+> tick ,K ~*> B ,K ~*> C ,K ~*> D ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> 0.0.0.0 ,K ~*> 0.0.0.0.0 ,K ~*> 0.0.0.0.0.0 ,K ~*> tick ,K ~^> B ,K ~^> C ,K ~^> D ,K ~^> 0.0 ,K ~^> 0.0.0 ,K ~^> 0.0.0.0 ,K ~^> tick] f0 ~> f31 [K ~=> A ,K ~=> B ,K ~=> C ,K ~=> D ,K ~=> E ,tick ~+> tick ,K ~+> B ,K ~+> C ,K ~+> D ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> 0.0.0.0 ,K ~+> 0.0.0.0.0 ,K ~+> 0.0.0.0.0.0 ,K ~+> tick ,K ~*> B ,K ~*> C ,K ~*> D ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> 0.0.0.0 ,K ~*> 0.0.0.0.0 ,K ~*> 0.0.0.0.0.0 ,K ~*> tick ,K ~^> B ,K ~^> C ,K ~^> D ,K ~^> 0.0 ,K ~^> 0.0.0 ,K ~^> 0.0.0.0 ,K ~^> tick] + f7> [K ~=> C ,K ~=> D ,K ~=> E ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,K ~+> D ,K ~+> 0.0.0 ,K ~+> 0.0.0.0 ,K ~+> 0.0.0.0.0 ,K ~+> 0.0.0.0.0.0 ,K ~+> tick ,B ~*> B ,B ~*> C ,B ~*> tick ,K ~*> B ,K ~*> C ,K ~*> D ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> 0.0.0.0 ,K ~*> 0.0.0.0.0 ,K ~*> 0.0.0.0.0.0 ,K ~*> tick ,B ~^> B ,B ~^> C ,K ~^> B ,K ~^> C ,K ~^> D ,K ~^> 0.0.0 ,K ~^> tick] f16> [K ~=> C ,K ~=> D ,K ~=> E ,B ~+> B ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> B ,K ~+> C ,K ~+> D ,K ~+> 0.0.0 ,K ~+> 0.0.0.0 ,K ~+> 0.0.0.0.0 ,K ~+> 0.0.0.0.0.0 ,K ~+> tick ,B ~*> B ,B ~*> C ,B ~*> D ,B ~*> 0.0.0 ,B ~*> 0.0.0.0 ,B ~*> tick ,K ~*> B ,K ~*> C ,K ~*> D ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> 0.0.0.0 ,K ~*> 0.0.0.0.0 ,K ~*> 0.0.0.0.0.0 ,K ~*> tick ,B ~^> B ,B ~^> C ,B ~^> D ,B ~^> 0.0.0 ,B ~^> 0.0.0.0 ,B ~^> tick ,K ~^> B ,K ~^> C ,K ~^> D ,K ~^> 0.0.0 ,K ~^> 0.0.0.0 ,K ~^> tick] + f10> [K ~=> D ,K ~=> E ,C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> C ,K ~+> D ,K ~+> 0.0.0.0 ,K ~+> 0.0.0.0.0 ,K ~+> 0.0.0.0.0.0 ,K ~+> tick ,C ~*> C ,C ~*> D ,C ~*> tick ,K ~*> C ,K ~*> D ,K ~*> 0.0.0 ,K ~*> 0.0.0.0 ,K ~*> 0.0.0.0.0 ,K ~*> 0.0.0.0.0.0 ,K ~*> tick ,C ~^> C ,C ~^> D ,K ~^> C ,K ~^> D] f16> [K ~=> D ,K ~=> E ,C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> C ,K ~+> D ,K ~+> 0.0.0.0 ,K ~+> 0.0.0.0.0 ,K ~+> 0.0.0.0.0.0 ,K ~+> tick ,C ~*> C ,C ~*> D ,C ~*> 0.0.0.0 ,C ~*> tick ,K ~*> C ,K ~*> D ,K ~*> 0.0.0 ,K ~*> 0.0.0.0 ,K ~*> 0.0.0.0.0 ,K ~*> 0.0.0.0.0.0 ,K ~*> tick ,C ~^> C ,C ~^> D ,C ~^> 0.0.0.0 ,C ~^> tick ,K ~^> C ,K ~^> D ,K ~^> 0.0.0.0 ,K ~^> tick] + f16> [K ~=> E ,D ~+> D ,D ~+> 0.0.0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> 0.0.0.0.0 ,K ~+> 0.0.0.0.0.0 ,K ~+> tick ,D ~*> D ,D ~*> tick ,K ~*> D ,K ~*> 0.0.0.0 ,K ~*> 0.0.0.0.0 ,K ~*> 0.0.0.0.0.0 ,K ~*> tick] f13> [K ~=> E ,D ~+> D ,D ~+> 0.0.0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> 0.0.0.0.0 ,K ~+> 0.0.0.0.0.0 ,K ~+> tick ,D ~*> D ,D ~*> tick ,K ~*> D ,K ~*> 0.0.0.0 ,K ~*> 0.0.0.0.0 ,K ~*> 0.0.0.0.0.0 ,K ~*> tick] + f16> [K ~=> E ,E ~+> 0.0.0.0.0 ,E ~+> 0.0.0.0.0.0 ,E ~+> tick ,tick ~+> tick ,K ~+> 0.0.0.0.0.0 ,K ~+> tick ,E ~*> tick ,K ~*> 0.0.0.0.0 ,K ~*> 0.0.0.0.0.0 ,K ~*> tick] + f16> [K ~=> E,E ~+> 0.0.0.0.0.0,E ~+> tick,tick ~+> tick,K ~*> 0.0.0.0.0.0,K ~*> tick] YES(?,O(1))