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) -> evalfbb6in(0,B,C,D) True (?,1) 2. evalfbb6in(A,B,C,D) -> evalfbbin(A,B,C,D) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb6in(A,B,C,D) -> evalfreturnin(A,B,C,D) [A >= 0 && A >= B] (?,1) 4. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,0,1 + A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= B] 6. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + D] 7. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + E] 8. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && E >= 1] 9. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 10. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,1 + D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 11. evalfbb4in(A,B,C,D) -> evalfbb6in(-1 + D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1] 12. evalfbb4in(A,B,C,D) -> evalfbb6in(D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= C] 13. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [A + -1*B >= 0 && A >= 0] (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb6in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{13},4->{5,6},5->{11,12},6->{7,8,9},7->{10},8->{10},9->{11,12},10->{5,6},11->{2 ,3},12->{2,3},13->{}] + 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) -> evalfbb6in(0,B,C,D) True (1,1) 2. evalfbb6in(A,B,C,D) -> evalfbbin(A,B,C,D) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb6in(A,B,C,D) -> evalfreturnin(A,B,C,D) [A >= 0 && A >= B] (1,1) 4. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,0,1 + A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= B] 6. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + D] 7. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + E] 8. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && E >= 1] 9. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 10. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,1 + D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 11. evalfbb4in(A,B,C,D) -> evalfbb6in(-1 + D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1] 12. evalfbb4in(A,B,C,D) -> evalfbb6in(D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= C] 13. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [A + -1*B >= 0 && A >= 0] (1,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb6in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{13},4->{5,6},5->{11,12},6->{7,8,9},7->{10},8->{10},9->{11,12},10->{5,6},11->{2 ,3},12->{2,3},13->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(11,3)] * 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) -> evalfbb6in(0,B,C,D) True (1,1) 2. evalfbb6in(A,B,C,D) -> evalfbbin(A,B,C,D) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb6in(A,B,C,D) -> evalfreturnin(A,B,C,D) [A >= 0 && A >= B] (1,1) 4. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,0,1 + A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= B] 6. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + D] 7. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + E] 8. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && E >= 1] 9. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 10. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,1 + D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 11. evalfbb4in(A,B,C,D) -> evalfbb6in(-1 + D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1] 12. evalfbb4in(A,B,C,D) -> evalfbb6in(D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= C] 13. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [A + -1*B >= 0 && A >= 0] (1,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb6in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{13},4->{5,6},5->{11,12},6->{7,8,9},7->{10},8->{10},9->{11,12},10->{5,6} ,11->{2},12->{2,3},13->{}] + 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) -> evalfbb6in(0,B,C,D) True (?,1) 2. evalfbb6in(A,B,C,D) -> evalfbbin(A,B,C,D) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb6in(A,B,C,D) -> evalfreturnin(A,B,C,D) [A >= 0 && A >= B] (?,1) 4. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,0,1 + A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= B] 6. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + D] 7. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + E] 8. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && E >= 1] 9. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 10. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,1 + D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 11. evalfbb4in(A,B,C,D) -> evalfbb6in(-1 + D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1] 12. evalfbb4in(A,B,C,D) -> evalfbb6in(D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= C] 13. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [A + -1*B >= 0 && A >= 0] (?,1) 14. evalfreturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb6in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{13,14},4->{5,6},5->{11,12},6->{7,8,9},7->{10},8->{10},9->{11,12},10->{5,6} ,11->{2,3},12->{2,3},13->{},14->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(11,3)] * 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) -> evalfbb6in(0,B,C,D) True (?,1) 2. evalfbb6in(A,B,C,D) -> evalfbbin(A,B,C,D) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb6in(A,B,C,D) -> evalfreturnin(A,B,C,D) [A >= 0 && A >= B] (?,1) 4. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,0,1 + A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= B] 6. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + D] 7. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + E] 8. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && E >= 1] 9. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 10. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,1 + D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 11. evalfbb4in(A,B,C,D) -> evalfbb6in(-1 + D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1] 12. evalfbb4in(A,B,C,D) -> evalfbb6in(D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= C] 13. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [A + -1*B >= 0 && A >= 0] (?,1) 14. evalfreturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb6in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{13,14},4->{5,6},5->{11,12},6->{7,8,9},7->{10},8->{10},9->{11,12},10->{5,6} ,11->{2},12->{2,3},13->{},14->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14] | `- p:[2,11,5,4,10,7,6,8,9,12] c: [12] | `- p:[2,11,5,4,10,7,6,8,9] c: [11] | `- p:[6,10,7,8] c: [10] * 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) -> evalfbb6in(0,B,C,D) True (?,1) 2. evalfbb6in(A,B,C,D) -> evalfbbin(A,B,C,D) [A >= 0 && B >= 1 + A] (?,1) 3. evalfbb6in(A,B,C,D) -> evalfreturnin(A,B,C,D) [A >= 0 && A >= B] (?,1) 4. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,0,1 + A) [-1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && D >= B] 6. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && B >= 1 + D] 7. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && 0 >= 1 + E] 8. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0 && E >= 1] 9. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 10. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,1 + C,1 + D) [-1 + B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -2 + B + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && A + C >= 0 && -2 + B >= 0 && -2 + A + B >= 0 && -2 + -1*A + B >= 0 && A >= 0] 11. evalfbb4in(A,B,C,D) -> evalfbb6in(-1 + D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && C >= 1] 12. evalfbb4in(A,B,C,D) -> evalfbb6in(D,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && C >= 0 && -1 + B + C >= 0 && A + C >= 0 && -1 + B >= 0 && -1 + A + B >= 0 && -1 + -1*A + B >= 0 && A >= 0 && 0 >= C] 13. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [A + -1*B >= 0 && A >= 0] (?,1) 14. evalfreturnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb6in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{13,14},4->{5,6},5->{11,12},6->{7,8,9},7->{10},8->{10},9->{11,12},10->{5,6} ,11->{2},12->{2,3},13->{},14->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14] | `- p:[2,11,5,4,10,7,6,8,9,12] c: [12] | `- p:[2,11,5,4,10,7,6,8,9] c: [11] | `- p:[6,10,7,8] c: [10]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,0.0,0.0.0,0.0.0.0] evalfstart ~> evalfentryin [A <= A, B <= B, C <= C, D <= D] evalfentryin ~> evalfbb6in [A <= 0*K, B <= B, C <= C, D <= D] evalfbb6in ~> evalfbbin [A <= A, B <= B, C <= C, D <= D] evalfbb6in ~> evalfreturnin [A <= A, B <= B, C <= C, D <= D] evalfbbin ~> evalfbb2in [A <= A, B <= B, C <= 0*K, D <= B] evalfbb2in ~> evalfbb4in [A <= A, B <= B, C <= C, D <= D] evalfbb2in ~> evalfbb3in [A <= A, B <= B, C <= C, D <= D] evalfbb3in ~> evalfbb1in [A <= A, B <= B, C <= C, D <= D] evalfbb3in ~> evalfbb1in [A <= A, B <= B, C <= C, D <= D] evalfbb3in ~> evalfbb4in [A <= A, B <= B, C <= C, D <= D] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= D, D <= B] evalfbb4in ~> evalfbb6in [A <= D, B <= B, C <= C, D <= D] evalfbb4in ~> evalfbb6in [A <= D, B <= B, C <= C, D <= D] evalfreturnin ~> evalfstop [A <= A, B <= B, C <= C, D <= D] evalfreturnin ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= K + A + 2*B + D] evalfbb6in ~> evalfbbin [A <= A, B <= B, C <= C, D <= D] evalfbb4in ~> evalfbb6in [A <= D, B <= B, C <= C, D <= D] evalfbb2in ~> evalfbb4in [A <= A, B <= B, C <= C, D <= D] evalfbbin ~> evalfbb2in [A <= A, B <= B, C <= 0*K, D <= B] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= D, D <= B] evalfbb3in ~> evalfbb1in [A <= A, B <= B, C <= C, D <= D] evalfbb2in ~> evalfbb3in [A <= A, B <= B, C <= C, D <= D] evalfbb3in ~> evalfbb1in [A <= A, B <= B, C <= C, D <= D] evalfbb3in ~> evalfbb4in [A <= A, B <= B, C <= C, D <= D] evalfbb4in ~> evalfbb6in [A <= D, B <= B, C <= C, D <= D] + Loop: [0.0.0 <= K + A + B + C + D] evalfbb6in ~> evalfbbin [A <= A, B <= B, C <= C, D <= D] evalfbb4in ~> evalfbb6in [A <= D, B <= B, C <= C, D <= D] evalfbb2in ~> evalfbb4in [A <= A, B <= B, C <= C, D <= D] evalfbbin ~> evalfbb2in [A <= A, B <= B, C <= 0*K, D <= B] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= D, D <= B] evalfbb3in ~> evalfbb1in [A <= A, B <= B, C <= C, D <= D] evalfbb2in ~> evalfbb3in [A <= A, B <= B, C <= C, D <= D] evalfbb3in ~> evalfbb1in [A <= A, B <= B, C <= C, D <= D] evalfbb3in ~> evalfbb4in [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0.0.0 <= B + D] evalfbb2in ~> evalfbb3in [A <= A, B <= B, C <= C, D <= D] evalfbb1in ~> evalfbb2in [A <= A, B <= B, C <= D, D <= B] evalfbb3in ~> evalfbb1in [A <= A, B <= B, C <= C, D <= D] evalfbb3in ~> evalfbb1in [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,0.0,0.0.0,0.0.0.0] evalfstart ~> evalfentryin [] evalfentryin ~> evalfbb6in [K ~=> A] evalfbb6in ~> evalfbbin [] evalfbb6in ~> evalfreturnin [] evalfbbin ~> evalfbb2in [B ~=> D,K ~=> C] evalfbb2in ~> evalfbb4in [] evalfbb2in ~> evalfbb3in [] evalfbb3in ~> evalfbb1in [] evalfbb3in ~> evalfbb1in [] evalfbb3in ~> evalfbb4in [] evalfbb1in ~> evalfbb2in [B ~=> D,D ~=> C] evalfbb4in ~> evalfbb6in [D ~=> A] evalfbb4in ~> evalfbb6in [D ~=> A] evalfreturnin ~> evalfstop [] evalfreturnin ~> exitus616 [] + Loop: [A ~+> 0.0,D ~+> 0.0,K ~+> 0.0,B ~*> 0.0] evalfbb6in ~> evalfbbin [] evalfbb4in ~> evalfbb6in [D ~=> A] evalfbb2in ~> evalfbb4in [] evalfbbin ~> evalfbb2in [B ~=> D,K ~=> C] evalfbb1in ~> evalfbb2in [B ~=> D,D ~=> C] evalfbb3in ~> evalfbb1in [] evalfbb2in ~> evalfbb3in [] evalfbb3in ~> evalfbb1in [] evalfbb3in ~> evalfbb4in [] evalfbb4in ~> evalfbb6in [D ~=> A] + Loop: [A ~+> 0.0.0,B ~+> 0.0.0,C ~+> 0.0.0,D ~+> 0.0.0,K ~+> 0.0.0] evalfbb6in ~> evalfbbin [] evalfbb4in ~> evalfbb6in [D ~=> A] evalfbb2in ~> evalfbb4in [] evalfbbin ~> evalfbb2in [B ~=> D,K ~=> C] evalfbb1in ~> evalfbb2in [B ~=> D,D ~=> C] evalfbb3in ~> evalfbb1in [] evalfbb2in ~> evalfbb3in [] evalfbb3in ~> evalfbb1in [] evalfbb3in ~> evalfbb4in [] + Loop: [B ~+> 0.0.0.0,D ~+> 0.0.0.0] evalfbb2in ~> evalfbb3in [] evalfbb1in ~> evalfbb2in [B ~=> D,D ~=> C] evalfbb3in ~> evalfbb1in [] evalfbb3in ~> evalfbb1in [] + Applied Processor: LareProcessor + Details: evalfstart ~> exitus616 [B ~=> A ,B ~=> C ,B ~=> D ,K ~=> A ,K ~=> C ,B ~+> 0.0.0 ,B ~+> 0.0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,D ~+> 0.0 ,D ~+> 0.0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> 0.0 ,B ~*> 0.0.0 ,B ~*> 0.0.0.0 ,B ~*> tick ,C ~*> tick ,D ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] evalfstart ~> evalfstop [B ~=> A ,B ~=> C ,B ~=> D ,K ~=> A ,K ~=> C ,B ~+> 0.0.0 ,B ~+> 0.0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,D ~+> 0.0 ,D ~+> 0.0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> 0.0 ,B ~*> 0.0.0 ,B ~*> 0.0.0.0 ,B ~*> tick ,C ~*> tick ,D ~*> tick ,K ~*> 0.0 ,K ~*> 0.0.0 ,K ~*> tick] + evalfbb6in> [B ~=> A ,B ~=> C ,B ~=> D ,K ~=> C ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> 0.0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,D ~+> 0.0 ,D ~+> 0.0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,B ~*> 0.0 ,B ~*> 0.0.0 ,B ~*> 0.0.0.0 ,B ~*> tick ,C ~*> tick ,D ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + evalfbb6in> [B ~=> A ,B ~=> C ,B ~=> D ,K ~=> C ,A ~+> 0.0.0 ,A ~+> tick ,B ~+> 0.0.0 ,B ~+> 0.0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,D ~+> 0.0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,A ~*> tick ,B ~*> 0.0.0.0 ,B ~*> tick ,C ~*> tick ,D ~*> tick ,K ~*> tick] + evalfbb3in> [B ~=> C ,B ~=> D ,D ~=> C ,B ~+> 0.0.0.0 ,B ~+> tick ,D ~+> 0.0.0.0 ,D ~+> tick ,tick ~+> tick] evalfbb2in> [B ~=> C ,B ~=> D ,D ~=> C ,B ~+> 0.0.0.0 ,B ~+> tick ,D ~+> 0.0.0.0 ,D ~+> tick ,tick ~+> tick] YES(?,POLY)