YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb3in(A,B,0,0) [A >= 1 && B >= 1 + A] (?,1) 2. evalfbb3in(A,B,C,D) -> evalfreturnin(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] 3. evalfbb3in(A,B,C,D) -> evalfbb4in(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] 4. evalfbb4in(A,B,C,D) -> evalfbbin(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 && 0 >= 1 + E] 5. evalfbb4in(A,B,C,D) -> evalfbbin(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 && E >= 1] 6. evalfbb4in(A,B,C,D) -> evalfreturnin(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] 7. evalfbbin(A,B,C,D) -> evalfbb1in(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] 8. evalfbbin(A,B,C,D) -> evalfbb2in(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] 9. evalfbb1in(A,B,C,D) -> evalfbb3in(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] 10. evalfbb2in(A,B,C,D) -> evalfbb3in(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] 11. evalfreturnin(A,B,C,D) -> evalfstop(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] Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{11},3->{4,5,6},4->{7,8},5->{7,8},6->{11},7->{9},8->{10},9->{2,3},10->{2,3},11->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb3in(A,B,0,0) [A >= 1 && B >= 1 + A] (1,1) 2. evalfbb3in(A,B,C,D) -> evalfreturnin(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] 3. evalfbb3in(A,B,C,D) -> evalfbb4in(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] 4. evalfbb4in(A,B,C,D) -> evalfbbin(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 && 0 >= 1 + E] 5. evalfbb4in(A,B,C,D) -> evalfbbin(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 && E >= 1] 6. evalfbb4in(A,B,C,D) -> evalfreturnin(A,B,C,D) [-1 + B + -1*D >= 0 (1,1) && 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] 7. evalfbbin(A,B,C,D) -> evalfbb1in(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] 8. evalfbbin(A,B,C,D) -> evalfbb2in(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] 9. evalfbb1in(A,B,C,D) -> evalfbb3in(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] 10. evalfbb2in(A,B,C,D) -> evalfbb3in(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] 11. evalfreturnin(A,B,C,D) -> evalfstop(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] Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{11},3->{4,5,6},4->{7,8},5->{7,8},6->{11},7->{9},8->{10},9->{2,3},10->{2,3},11->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,2),(9,2)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb3in(A,B,0,0) [A >= 1 && B >= 1 + A] (1,1) 2. evalfbb3in(A,B,C,D) -> evalfreturnin(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] 3. evalfbb3in(A,B,C,D) -> evalfbb4in(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] 4. evalfbb4in(A,B,C,D) -> evalfbbin(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 && 0 >= 1 + E] 5. evalfbb4in(A,B,C,D) -> evalfbbin(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 && E >= 1] 6. evalfbb4in(A,B,C,D) -> evalfreturnin(A,B,C,D) [-1 + B + -1*D >= 0 (1,1) && 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] 7. evalfbbin(A,B,C,D) -> evalfbb1in(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] 8. evalfbbin(A,B,C,D) -> evalfbb2in(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] 9. evalfbb1in(A,B,C,D) -> evalfbb3in(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] 10. evalfbb2in(A,B,C,D) -> evalfbb3in(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] 11. evalfreturnin(A,B,C,D) -> evalfstop(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] Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{3},2->{11},3->{4,5,6},4->{7,8},5->{7,8},6->{11},7->{9},8->{10},9->{3},10->{2,3},11->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb3in(A,B,0,0) [A >= 1 && B >= 1 + A] (?,1) 2. evalfbb3in(A,B,C,D) -> evalfreturnin(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] 3. evalfbb3in(A,B,C,D) -> evalfbb4in(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] 4. evalfbb4in(A,B,C,D) -> evalfbbin(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 && 0 >= 1 + E] 5. evalfbb4in(A,B,C,D) -> evalfbbin(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 && E >= 1] 6. evalfbb4in(A,B,C,D) -> evalfreturnin(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] 7. evalfbbin(A,B,C,D) -> evalfbb1in(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] 8. evalfbbin(A,B,C,D) -> evalfbb2in(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] 9. evalfbb1in(A,B,C,D) -> evalfbb3in(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] 10. evalfbb2in(A,B,C,D) -> evalfbb3in(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] 11. evalfreturnin(A,B,C,D) -> evalfstop(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] 12. evalfreturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2,3},2->{11,12},3->{4,5,6},4->{7,8},5->{7,8},6->{11,12},7->{9},8->{10},9->{2,3},10->{2,3} ,11->{},12->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,2),(9,2)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb3in(A,B,0,0) [A >= 1 && B >= 1 + A] (?,1) 2. evalfbb3in(A,B,C,D) -> evalfreturnin(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] 3. evalfbb3in(A,B,C,D) -> evalfbb4in(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] 4. evalfbb4in(A,B,C,D) -> evalfbbin(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 && 0 >= 1 + E] 5. evalfbb4in(A,B,C,D) -> evalfbbin(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 && E >= 1] 6. evalfbb4in(A,B,C,D) -> evalfreturnin(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] 7. evalfbbin(A,B,C,D) -> evalfbb1in(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] 8. evalfbbin(A,B,C,D) -> evalfbb2in(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] 9. evalfbb1in(A,B,C,D) -> evalfbb3in(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] 10. evalfbb2in(A,B,C,D) -> evalfbb3in(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] 11. evalfreturnin(A,B,C,D) -> evalfstop(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] 12. evalfreturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{3},2->{11,12},3->{4,5,6},4->{7,8},5->{7,8},6->{11,12},7->{9},8->{10},9->{3},10->{2,3},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:[3,9,7,4,5,10,8] c: [10] | `- p:[3,9,7,4,5] c: [9] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb3in(A,B,0,0) [A >= 1 && B >= 1 + A] (?,1) 2. evalfbb3in(A,B,C,D) -> evalfreturnin(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] 3. evalfbb3in(A,B,C,D) -> evalfbb4in(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] 4. evalfbb4in(A,B,C,D) -> evalfbbin(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 && 0 >= 1 + E] 5. evalfbb4in(A,B,C,D) -> evalfbbin(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 && E >= 1] 6. evalfbb4in(A,B,C,D) -> evalfreturnin(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] 7. evalfbbin(A,B,C,D) -> evalfbb1in(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] 8. evalfbbin(A,B,C,D) -> evalfbb2in(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] 9. evalfbb1in(A,B,C,D) -> evalfbb3in(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] 10. evalfbb2in(A,B,C,D) -> evalfbb3in(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] 11. evalfreturnin(A,B,C,D) -> evalfstop(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] 12. evalfreturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{3},2->{11,12},3->{4,5,6},4->{7,8},5->{7,8},6->{11,12},7->{9},8->{10},9->{3},10->{2,3},11->{} ,12->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[3,9,7,4,5,10,8] c: [10] | `- p:[3,9,7,4,5] c: [9]) + 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] evalfstart ~> evalfentryin [A <= A, B <= B, C <= C, D <= D] evalfentryin ~> evalfbb3in [A <= A, B <= B, C <= 0*K, D <= 0*K] evalfbb3in ~> evalfreturnin [A <= A, B <= B, C <= C, D <= D] evalfbb3in ~> evalfbb4in [A <= A, B <= B, C <= C, D <= D] evalfbb4in ~> evalfbbin [A <= A, B <= B, C <= C, D <= D] evalfbb4in ~> evalfbbin [A <= A, B <= B, C <= C, D <= D] evalfbb4in ~> evalfreturnin [A <= A, B <= B, C <= C, D <= D] evalfbbin ~> evalfbb1in [A <= A, B <= B, C <= C, D <= D] evalfbbin ~> evalfbb2in [A <= A, B <= B, C <= C, D <= D] evalfbb1in ~> evalfbb3in [A <= A, B <= B, C <= B, D <= D] evalfbb2in ~> evalfbb3in [A <= A, B <= B, C <= 0*K, D <= B] evalfreturnin ~> evalfstop [A <= A, B <= B, C <= C, D <= D] evalfreturnin ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= B + D] evalfbb3in ~> evalfbb4in [A <= A, B <= B, C <= C, D <= D] evalfbb1in ~> evalfbb3in [A <= A, B <= B, C <= B, D <= D] evalfbbin ~> evalfbb1in [A <= A, B <= B, C <= C, D <= D] evalfbb4in ~> evalfbbin [A <= A, B <= B, C <= C, D <= D] evalfbb4in ~> evalfbbin [A <= A, B <= B, C <= C, D <= D] evalfbb2in ~> evalfbb3in [A <= A, B <= B, C <= 0*K, D <= B] evalfbbin ~> evalfbb2in [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0.0 <= K + B + C] evalfbb3in ~> evalfbb4in [A <= A, B <= B, C <= C, D <= D] evalfbb1in ~> evalfbb3in [A <= A, B <= B, C <= B, D <= D] evalfbbin ~> evalfbb1in [A <= A, B <= B, C <= C, D <= D] evalfbb4in ~> evalfbbin [A <= A, B <= B, C <= C, D <= D] evalfbb4in ~> evalfbbin [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] evalfstart ~> evalfentryin [] evalfentryin ~> evalfbb3in [K ~=> C,K ~=> D] evalfbb3in ~> evalfreturnin [] evalfbb3in ~> evalfbb4in [] evalfbb4in ~> evalfbbin [] evalfbb4in ~> evalfbbin [] evalfbb4in ~> evalfreturnin [] evalfbbin ~> evalfbb1in [] evalfbbin ~> evalfbb2in [] evalfbb1in ~> evalfbb3in [B ~=> C] evalfbb2in ~> evalfbb3in [B ~=> D,K ~=> C] evalfreturnin ~> evalfstop [] evalfreturnin ~> exitus616 [] + Loop: [B ~+> 0.0,D ~+> 0.0] evalfbb3in ~> evalfbb4in [] evalfbb1in ~> evalfbb3in [B ~=> C] evalfbbin ~> evalfbb1in [] evalfbb4in ~> evalfbbin [] evalfbb4in ~> evalfbbin [] evalfbb2in ~> evalfbb3in [B ~=> D,K ~=> C] evalfbbin ~> evalfbb2in [] + Loop: [B ~+> 0.0.0,C ~+> 0.0.0,K ~+> 0.0.0] evalfbb3in ~> evalfbb4in [] evalfbb1in ~> evalfbb3in [B ~=> C] evalfbbin ~> evalfbb1in [] evalfbb4in ~> evalfbbin [] evalfbb4in ~> evalfbbin [] + Applied Processor: LareProcessor + Details: evalfstart ~> 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 ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] evalfstart ~> evalfstop [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 ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + evalfbb4in> [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] evalfbb3in> [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] + evalfbbin> [B ~=> C ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] evalfbb4in> [B ~=> C ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] evalfbb3in> [B ~=> C ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick] YES(?,POLY)