YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1) 1. evalfentryin(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (?,1) 2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [-1 + A >= 0 && B >= A] (?,1) 3. evalfbb10in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [-1 + A >= 0 && A >= 1 + B] (?,1) 4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [1 + B + -1*C >= 0 (?,1) && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && A >= C] 5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [1 + B + -1*C >= 0 (?,1) && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + A] 6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [1 + B + -1*D >= 0 (?,1) && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && B >= D] 7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [1 + B + -1*D >= 0 (?,1) && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && D >= 1 + B] 8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [-1 + E >= 0 (?,1) && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= E] 9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [-1 + E >= 0 (?,1) && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1 + D] 10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D + -1*E >= 0 (?,1) && B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [-3 + E >= 0 (?,1) && -5 + D + E >= 0 && -1 + -1*D + E >= 0 && -4 + C + E >= 0 && -2 + -1*C + E >= 0 && -5 + B + E >= 0 && -4 + A + E >= 0 && -2 + -1*A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [1 + B + -1*D >= 0 (?,1) && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + -1*B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 13. evalfreturnin(A,B,C,D,E) -> evalfstop(A,B,C,D,E) [-1 + A + -1*B >= 0 && -1 + A >= 0] (?,1) Signature: {(evalfbb10in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbb8in,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [0->{1},1->{2,3},2->{4,5},3->{13},4->{6,7},5->{2,3},6->{8,9},7->{12},8->{10},9->{11},10->{8,9},11->{6,7} ,12->{4,5},13->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(2,5),(6,9)] * Step 2: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True (1,1) 1. evalfentryin(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True (?,1) 2. evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [-1 + A >= 0 && B >= A] (?,1) 3. evalfbb10in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [-1 + A >= 0 && A >= 1 + B] (?,1) 4. evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [1 + B + -1*C >= 0 (?,1) && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && A >= C] 5. evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [1 + B + -1*C >= 0 (?,1) && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + A] 6. evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [1 + B + -1*D >= 0 (?,1) && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && B >= D] 7. evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [1 + B + -1*D >= 0 (?,1) && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && D >= 1 + B] 8. evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [-1 + E >= 0 (?,1) && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= E] 9. evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [-1 + E >= 0 (?,1) && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1 + D] 10. evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D + -1*E >= 0 (?,1) && B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 11. evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [-3 + E >= 0 (?,1) && -5 + D + E >= 0 && -1 + -1*D + E >= 0 && -4 + C + E >= 0 && -2 + -1*C + E >= 0 && -5 + B + E >= 0 && -4 + A + E >= 0 && -2 + -1*A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 12. evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [1 + B + -1*D >= 0 (?,1) && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + -1*B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] 13. evalfreturnin(A,B,C,D,E) -> evalfstop(A,B,C,D,E) [-1 + A + -1*B >= 0 && -1 + A >= 0] (?,1) Signature: {(evalfbb10in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbb8in,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{13},4->{6,7},5->{2,3},6->{8},7->{12},8->{10},9->{11},10->{8,9},11->{6,7} ,12->{4,5},13->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True evalfentryin(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [-1 + A >= 0 && B >= A] evalfbb10in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [-1 + A >= 0 && A >= 1 + B] evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [1 + B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && A >= C] evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [1 + B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + A] evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [1 + B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && B >= D] evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [1 + B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && D >= 1 + B] evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [-1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= E] evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [-1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1 + D] evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D + -1*E >= 0 && B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [-3 + E >= 0 && -5 + D + E >= 0 && -1 + -1*D + E >= 0 && -4 + C + E >= 0 && -2 + -1*C + E >= 0 && -5 + B + E >= 0 && -4 + A + E >= 0 && -2 + -1*A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [1 + B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + -1*B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfreturnin(A,B,C,D,E) -> evalfstop(A,B,C,D,E) [-1 + A + -1*B >= 0 && -1 + A >= 0] Signature: {(evalfbb10in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbb8in,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{13},4->{6,7},5->{2,3},6->{8},7->{12},8->{10},9->{11},10->{8,9},11->{6,7} ,12->{4,5},13->{}] + Applied Processor: AddSinks + Details: () * Step 4: Unfold WORST_CASE(?,POLY) + Considered Problem: Rules: evalfstart(A,B,C,D,E) -> evalfentryin(A,B,C,D,E) True evalfentryin(A,B,C,D,E) -> evalfbb10in(1,B,C,D,E) True evalfbb10in(A,B,C,D,E) -> evalfbb8in(A,B,1,D,E) [-1 + A >= 0 && B >= A] evalfbb10in(A,B,C,D,E) -> evalfreturnin(A,B,C,D,E) [-1 + A >= 0 && A >= 1 + B] evalfbb8in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + A,E) [1 + B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && A >= C] evalfbb8in(A,B,C,D,E) -> evalfbb10in(1 + A,B,C,D,E) [1 + B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + A] evalfbb6in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1) [1 + B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && B >= D] evalfbb6in(A,B,C,D,E) -> evalfbb7in(A,B,C,D,E) [1 + B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && D >= 1 + B] evalfbb4in(A,B,C,D,E) -> evalfbb3in(A,B,C,D,E) [-1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= E] evalfbb4in(A,B,C,D,E) -> evalfbb5in(A,B,C,D,E) [-1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1 + D] evalfbb3in(A,B,C,D,E) -> evalfbb4in(A,B,C,D,1 + E) [D + -1*E >= 0 && B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb5in(A,B,C,D,E) -> evalfbb6in(A,B,C,1 + D,E) [-3 + E >= 0 && -5 + D + E >= 0 && -1 + -1*D + E >= 0 && -4 + C + E >= 0 && -2 + -1*C + E >= 0 && -5 + B + E >= 0 && -4 + A + E >= 0 && -2 + -1*A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb7in(A,B,C,D,E) -> evalfbb8in(A,B,1 + C,D,E) [1 + B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + -1*B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfreturnin(A,B,C,D,E) -> evalfstop(A,B,C,D,E) [-1 + A + -1*B >= 0 && -1 + A >= 0] evalfstop(A,B,C,D,E) -> exitus616(A,B,C,D,E) True Signature: {(evalfbb10in,5) ;(evalfbb3in,5) ;(evalfbb4in,5) ;(evalfbb5in,5) ;(evalfbb6in,5) ;(evalfbb7in,5) ;(evalfbb8in,5) ;(evalfentryin,5) ;(evalfreturnin,5) ;(evalfstart,5) ;(evalfstop,5) ;(exitus616,5)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{13},4->{6,7},5->{2,3},6->{8},7->{12},8->{10},9->{11},10->{8,9},11->{6,7} ,12->{4,5},13->{14}] + Applied Processor: Unfold + Details: () * Step 5: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: evalfstart.0(A,B,C,D,E) -> evalfentryin.1(A,B,C,D,E) True evalfentryin.1(A,B,C,D,E) -> evalfbb10in.2(1,B,C,D,E) True evalfentryin.1(A,B,C,D,E) -> evalfbb10in.3(1,B,C,D,E) True evalfbb10in.2(A,B,C,D,E) -> evalfbb8in.4(A,B,1,D,E) [-1 + A >= 0 && B >= A] evalfbb10in.3(A,B,C,D,E) -> evalfreturnin.13(A,B,C,D,E) [-1 + A >= 0 && A >= 1 + B] evalfbb8in.4(A,B,C,D,E) -> evalfbb6in.6(A,B,C,1 + A,E) [1 + B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && A >= C] evalfbb8in.4(A,B,C,D,E) -> evalfbb6in.7(A,B,C,1 + A,E) [1 + B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && A >= C] evalfbb8in.5(A,B,C,D,E) -> evalfbb10in.2(1 + A,B,C,D,E) [1 + B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + A] evalfbb8in.5(A,B,C,D,E) -> evalfbb10in.3(1 + A,B,C,D,E) [1 + B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + A] evalfbb6in.6(A,B,C,D,E) -> evalfbb4in.8(A,B,C,D,1) [1 + B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && B >= D] evalfbb6in.7(A,B,C,D,E) -> evalfbb7in.12(A,B,C,D,E) [1 + B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && D >= 1 + B] evalfbb4in.8(A,B,C,D,E) -> evalfbb3in.10(A,B,C,D,E) [-1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= E] evalfbb4in.9(A,B,C,D,E) -> evalfbb5in.11(A,B,C,D,E) [-1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1 + D] evalfbb3in.10(A,B,C,D,E) -> evalfbb4in.8(A,B,C,D,1 + E) [D + -1*E >= 0 && B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb3in.10(A,B,C,D,E) -> evalfbb4in.9(A,B,C,D,1 + E) [D + -1*E >= 0 && B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb5in.11(A,B,C,D,E) -> evalfbb6in.6(A,B,C,1 + D,E) [-3 + E >= 0 && -5 + D + E >= 0 && -1 + -1*D + E >= 0 && -4 + C + E >= 0 && -2 + -1*C + E >= 0 && -5 + B + E >= 0 && -4 + A + E >= 0 && -2 + -1*A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb5in.11(A,B,C,D,E) -> evalfbb6in.7(A,B,C,1 + D,E) [-3 + E >= 0 && -5 + D + E >= 0 && -1 + -1*D + E >= 0 && -4 + C + E >= 0 && -2 + -1*C + E >= 0 && -5 + B + E >= 0 && -4 + A + E >= 0 && -2 + -1*A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb7in.12(A,B,C,D,E) -> evalfbb8in.4(A,B,1 + C,D,E) [1 + B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + -1*B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfbb7in.12(A,B,C,D,E) -> evalfbb8in.5(A,B,1 + C,D,E) [1 + B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + -1*B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfreturnin.13(A,B,C,D,E) -> evalfstop.14(A,B,C,D,E) [-1 + A + -1*B >= 0 && -1 + A >= 0] evalfstop.14(A,B,C,D,E) -> exitus616.15(A,B,C,D,E) True Signature: {(evalfbb10in.2,5) ;(evalfbb10in.3,5) ;(evalfbb3in.10,5) ;(evalfbb4in.8,5) ;(evalfbb4in.9,5) ;(evalfbb5in.11,5) ;(evalfbb6in.6,5) ;(evalfbb6in.7,5) ;(evalfbb7in.12,5) ;(evalfbb8in.4,5) ;(evalfbb8in.5,5) ;(evalfentryin.1,5) ;(evalfreturnin.13,5) ;(evalfstart.0,5) ;(evalfstop.14,5) ;(exitus616.15,5)} Rule Graph: [0->{1,2},1->{3},2->{4},3->{5,6},4->{19},5->{9},6->{10},7->{3},8->{4},9->{11},10->{17,18},11->{13,14} ,12->{15,16},13->{11},14->{12},15->{9},16->{10},17->{5,6},18->{7,8},19->{20},20->{}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20] | `- p:[3,7,18,10,6,17,16,12,14,11,9,5,15,13] c: [3,7,18] | `- p:[5,17,10,6,16,12,14,11,9,15,13] c: [5,6,10,16,17] | `- p:[9,15,12,14,11,13] c: [9,12,14,15] | `- p:[11,13] c: [11,13] * Step 6: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: evalfstart.0(A,B,C,D,E) -> evalfentryin.1(A,B,C,D,E) True evalfentryin.1(A,B,C,D,E) -> evalfbb10in.2(1,B,C,D,E) True evalfentryin.1(A,B,C,D,E) -> evalfbb10in.3(1,B,C,D,E) True evalfbb10in.2(A,B,C,D,E) -> evalfbb8in.4(A,B,1,D,E) [-1 + A >= 0 && B >= A] evalfbb10in.3(A,B,C,D,E) -> evalfreturnin.13(A,B,C,D,E) [-1 + A >= 0 && A >= 1 + B] evalfbb8in.4(A,B,C,D,E) -> evalfbb6in.6(A,B,C,1 + A,E) [1 + B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && A >= C] evalfbb8in.4(A,B,C,D,E) -> evalfbb6in.7(A,B,C,1 + A,E) [1 + B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && A >= C] evalfbb8in.5(A,B,C,D,E) -> evalfbb10in.2(1 + A,B,C,D,E) [1 + B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + A] evalfbb8in.5(A,B,C,D,E) -> evalfbb10in.3(1 + A,B,C,D,E) [1 + B + -1*C >= 0 && 1 + A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && C >= 1 + A] evalfbb6in.6(A,B,C,D,E) -> evalfbb4in.8(A,B,C,D,1) [1 + B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && B >= D] evalfbb6in.7(A,B,C,D,E) -> evalfbb7in.12(A,B,C,D,E) [1 + B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0 && D >= 1 + B] evalfbb4in.8(A,B,C,D,E) -> evalfbb3in.10(A,B,C,D,E) [-1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= E] evalfbb4in.9(A,B,C,D,E) -> evalfbb5in.11(A,B,C,D,E) [-1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1 + D] evalfbb3in.10(A,B,C,D,E) -> evalfbb4in.8(A,B,C,D,1 + E) [D + -1*E >= 0 && B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb3in.10(A,B,C,D,E) -> evalfbb4in.9(A,B,C,D,1 + E) [D + -1*E >= 0 && B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -3 + B + E >= 0 && -2 + A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb5in.11(A,B,C,D,E) -> evalfbb6in.6(A,B,C,1 + D,E) [-3 + E >= 0 && -5 + D + E >= 0 && -1 + -1*D + E >= 0 && -4 + C + E >= 0 && -2 + -1*C + E >= 0 && -5 + B + E >= 0 && -4 + A + E >= 0 && -2 + -1*A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb5in.11(A,B,C,D,E) -> evalfbb6in.7(A,B,C,1 + D,E) [-3 + E >= 0 && -5 + D + E >= 0 && -1 + -1*D + E >= 0 && -4 + C + E >= 0 && -2 + -1*C + E >= 0 && -5 + B + E >= 0 && -4 + A + E >= 0 && -2 + -1*A + E >= 0 && B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && -1 + B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb7in.12(A,B,C,D,E) -> evalfbb8in.4(A,B,1 + C,D,E) [1 + B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + -1*B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfbb7in.12(A,B,C,D,E) -> evalfbb8in.5(A,B,1 + C,D,E) [1 + B + -1*D >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -3 + B + D >= 0 && -1 + -1*B + D >= 0 && -3 + A + D >= 0 && -1 + -1*A + D >= 0 && B + -1*C >= 0 && A + -1*C >= 0 && -1 + C >= 0 && -2 + B + C >= 0 && -2 + A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && -1 + A >= 0] evalfreturnin.13(A,B,C,D,E) -> evalfstop.14(A,B,C,D,E) [-1 + A + -1*B >= 0 && -1 + A >= 0] evalfstop.14(A,B,C,D,E) -> exitus616.15(A,B,C,D,E) True Signature: {(evalfbb10in.2,5) ;(evalfbb10in.3,5) ;(evalfbb3in.10,5) ;(evalfbb4in.8,5) ;(evalfbb4in.9,5) ;(evalfbb5in.11,5) ;(evalfbb6in.6,5) ;(evalfbb6in.7,5) ;(evalfbb7in.12,5) ;(evalfbb8in.4,5) ;(evalfbb8in.5,5) ;(evalfentryin.1,5) ;(evalfreturnin.13,5) ;(evalfstart.0,5) ;(evalfstop.14,5) ;(exitus616.15,5)} Rule Graph: [0->{1,2},1->{3},2->{4},3->{5,6},4->{19},5->{9},6->{10},7->{3},8->{4},9->{11},10->{17,18},11->{13,14} ,12->{15,16},13->{11},14->{12},15->{9},16->{10},17->{5,6},18->{7,8},19->{20},20->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20] | `- p:[3,7,18,10,6,17,16,12,14,11,9,5,15,13] c: [3,7,18] | `- p:[5,17,10,6,16,12,14,11,9,15,13] c: [5,6,10,16,17] | `- p:[9,15,12,14,11,13] c: [9,12,14,15] | `- p:[11,13] c: [11,13]) + Applied Processor: AbstractSize NoMinimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,E,0.0,0.0.0,0.0.0.0,0.0.0.0.0] evalfstart.0 ~> evalfentryin.1 [A <= A, B <= B, C <= C, D <= D, E <= E] evalfentryin.1 ~> evalfbb10in.2 [A <= K, B <= B, C <= C, D <= D, E <= E] evalfentryin.1 ~> evalfbb10in.3 [A <= K, B <= B, C <= C, D <= D, E <= E] evalfbb10in.2 ~> evalfbb8in.4 [A <= A, B <= B, C <= K, D <= D, E <= E] evalfbb10in.3 ~> evalfreturnin.13 [A <= A, B <= B, C <= C, D <= D, E <= E] evalfbb8in.4 ~> evalfbb6in.6 [A <= A, B <= B, C <= C, D <= 2*K + A, E <= E] evalfbb8in.4 ~> evalfbb6in.7 [A <= A, B <= B, C <= C, D <= 2*K + A, E <= E] evalfbb8in.5 ~> evalfbb10in.2 [A <= 2*K + A, B <= B, C <= C, D <= D, E <= E] evalfbb8in.5 ~> evalfbb10in.3 [A <= 2*K + A, B <= B, C <= C, D <= D, E <= E] evalfbb6in.6 ~> evalfbb4in.8 [A <= A, B <= B, C <= C, D <= D, E <= K] evalfbb6in.7 ~> evalfbb7in.12 [A <= A, B <= B, C <= C, D <= D, E <= E] evalfbb4in.8 ~> evalfbb3in.10 [A <= A, B <= B, C <= C, D <= D, E <= E] evalfbb4in.9 ~> evalfbb5in.11 [A <= A, B <= B, C <= C, D <= D, E <= E] evalfbb3in.10 ~> evalfbb4in.8 [A <= A, B <= B, C <= C, D <= D, E <= K + E] evalfbb3in.10 ~> evalfbb4in.9 [A <= A, B <= B, C <= C, D <= D, E <= K + E] evalfbb5in.11 ~> evalfbb6in.6 [A <= A, B <= B, C <= C, D <= K + D, E <= E] evalfbb5in.11 ~> evalfbb6in.7 [A <= A, B <= B, C <= C, D <= K + D, E <= E] evalfbb7in.12 ~> evalfbb8in.4 [A <= A, B <= B, C <= 2*K + C, D <= D, E <= E] evalfbb7in.12 ~> evalfbb8in.5 [A <= A, B <= B, C <= 2*K + C, D <= D, E <= E] evalfreturnin.13 ~> evalfstop.14 [A <= A, B <= B, C <= C, D <= D, E <= E] evalfstop.14 ~> exitus616.15 [A <= A, B <= B, C <= C, D <= D, E <= E] + Loop: [0.0 <= A + B] evalfbb10in.2 ~> evalfbb8in.4 [A <= A, B <= B, C <= K, D <= D, E <= E] evalfbb8in.5 ~> evalfbb10in.2 [A <= 2*K + A, B <= B, C <= C, D <= D, E <= E] evalfbb7in.12 ~> evalfbb8in.5 [A <= A, B <= B, C <= 2*K + C, D <= D, E <= E] evalfbb6in.7 ~> evalfbb7in.12 [A <= A, B <= B, C <= C, D <= D, E <= E] evalfbb8in.4 ~> evalfbb6in.7 [A <= A, B <= B, C <= C, D <= 2*K + A, E <= E] evalfbb7in.12 ~> evalfbb8in.4 [A <= A, B <= B, C <= 2*K + C, D <= D, E <= E] evalfbb5in.11 ~> evalfbb6in.7 [A <= A, B <= B, C <= C, D <= K + D, E <= E] evalfbb4in.9 ~> evalfbb5in.11 [A <= A, B <= B, C <= C, D <= D, E <= E] evalfbb3in.10 ~> evalfbb4in.9 [A <= A, B <= B, C <= C, D <= D, E <= K + E] evalfbb4in.8 ~> evalfbb3in.10 [A <= A, B <= B, C <= C, D <= D, E <= E] evalfbb6in.6 ~> evalfbb4in.8 [A <= A, B <= B, C <= C, D <= D, E <= K] evalfbb8in.4 ~> evalfbb6in.6 [A <= A, B <= B, C <= C, D <= 2*K + A, E <= E] evalfbb5in.11 ~> evalfbb6in.6 [A <= A, B <= B, C <= C, D <= K + D, E <= E] evalfbb3in.10 ~> evalfbb4in.8 [A <= A, B <= B, C <= C, D <= D, E <= K + E] + Loop: [0.0.0 <= A + C] evalfbb8in.4 ~> evalfbb6in.6 [A <= A, B <= B, C <= C, D <= 2*K + A, E <= E] evalfbb7in.12 ~> evalfbb8in.4 [A <= A, B <= B, C <= 2*K + C, D <= D, E <= E] evalfbb6in.7 ~> evalfbb7in.12 [A <= A, B <= B, C <= C, D <= D, E <= E] evalfbb8in.4 ~> evalfbb6in.7 [A <= A, B <= B, C <= C, D <= 2*K + A, E <= E] evalfbb5in.11 ~> evalfbb6in.7 [A <= A, B <= B, C <= C, D <= K + D, E <= E] evalfbb4in.9 ~> evalfbb5in.11 [A <= A, B <= B, C <= C, D <= D, E <= E] evalfbb3in.10 ~> evalfbb4in.9 [A <= A, B <= B, C <= C, D <= D, E <= K + E] evalfbb4in.8 ~> evalfbb3in.10 [A <= A, B <= B, C <= C, D <= D, E <= E] evalfbb6in.6 ~> evalfbb4in.8 [A <= A, B <= B, C <= C, D <= D, E <= K] evalfbb5in.11 ~> evalfbb6in.6 [A <= A, B <= B, C <= C, D <= K + D, E <= E] evalfbb3in.10 ~> evalfbb4in.8 [A <= A, B <= B, C <= C, D <= D, E <= K + E] + Loop: [0.0.0.0 <= B + D] evalfbb6in.6 ~> evalfbb4in.8 [A <= A, B <= B, C <= C, D <= D, E <= K] evalfbb5in.11 ~> evalfbb6in.6 [A <= A, B <= B, C <= C, D <= K + D, E <= E] evalfbb4in.9 ~> evalfbb5in.11 [A <= A, B <= B, C <= C, D <= D, E <= E] evalfbb3in.10 ~> evalfbb4in.9 [A <= A, B <= B, C <= C, D <= D, E <= K + E] evalfbb4in.8 ~> evalfbb3in.10 [A <= A, B <= B, C <= C, D <= D, E <= E] evalfbb3in.10 ~> evalfbb4in.8 [A <= A, B <= B, C <= C, D <= D, E <= K + E] + Loop: [0.0.0.0.0 <= D + E] evalfbb4in.8 ~> evalfbb3in.10 [A <= A, B <= B, C <= C, D <= D, E <= E] evalfbb3in.10 ~> evalfbb4in.8 [A <= A, B <= B, C <= C, D <= D, E <= K + E] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,POLY) + 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] evalfstart.0 ~> evalfentryin.1 [] evalfentryin.1 ~> evalfbb10in.2 [K ~=> A] evalfentryin.1 ~> evalfbb10in.3 [K ~=> A] evalfbb10in.2 ~> evalfbb8in.4 [K ~=> C] evalfbb10in.3 ~> evalfreturnin.13 [] evalfbb8in.4 ~> evalfbb6in.6 [A ~+> D,K ~*> D] evalfbb8in.4 ~> evalfbb6in.7 [A ~+> D,K ~*> D] evalfbb8in.5 ~> evalfbb10in.2 [A ~+> A,K ~*> A] evalfbb8in.5 ~> evalfbb10in.3 [A ~+> A,K ~*> A] evalfbb6in.6 ~> evalfbb4in.8 [K ~=> E] evalfbb6in.7 ~> evalfbb7in.12 [] evalfbb4in.8 ~> evalfbb3in.10 [] evalfbb4in.9 ~> evalfbb5in.11 [] evalfbb3in.10 ~> evalfbb4in.8 [E ~+> E,K ~+> E] evalfbb3in.10 ~> evalfbb4in.9 [E ~+> E,K ~+> E] evalfbb5in.11 ~> evalfbb6in.6 [D ~+> D,K ~+> D] evalfbb5in.11 ~> evalfbb6in.7 [D ~+> D,K ~+> D] evalfbb7in.12 ~> evalfbb8in.4 [C ~+> C,K ~*> C] evalfbb7in.12 ~> evalfbb8in.5 [C ~+> C,K ~*> C] evalfreturnin.13 ~> evalfstop.14 [] evalfstop.14 ~> exitus616.15 [] + Loop: [A ~+> 0.0,B ~+> 0.0] evalfbb10in.2 ~> evalfbb8in.4 [K ~=> C] evalfbb8in.5 ~> evalfbb10in.2 [A ~+> A,K ~*> A] evalfbb7in.12 ~> evalfbb8in.5 [C ~+> C,K ~*> C] evalfbb6in.7 ~> evalfbb7in.12 [] evalfbb8in.4 ~> evalfbb6in.7 [A ~+> D,K ~*> D] evalfbb7in.12 ~> evalfbb8in.4 [C ~+> C,K ~*> C] evalfbb5in.11 ~> evalfbb6in.7 [D ~+> D,K ~+> D] evalfbb4in.9 ~> evalfbb5in.11 [] evalfbb3in.10 ~> evalfbb4in.9 [E ~+> E,K ~+> E] evalfbb4in.8 ~> evalfbb3in.10 [] evalfbb6in.6 ~> evalfbb4in.8 [K ~=> E] evalfbb8in.4 ~> evalfbb6in.6 [A ~+> D,K ~*> D] evalfbb5in.11 ~> evalfbb6in.6 [D ~+> D,K ~+> D] evalfbb3in.10 ~> evalfbb4in.8 [E ~+> E,K ~+> E] + Loop: [A ~+> 0.0.0,C ~+> 0.0.0] evalfbb8in.4 ~> evalfbb6in.6 [A ~+> D,K ~*> D] evalfbb7in.12 ~> evalfbb8in.4 [C ~+> C,K ~*> C] evalfbb6in.7 ~> evalfbb7in.12 [] evalfbb8in.4 ~> evalfbb6in.7 [A ~+> D,K ~*> D] evalfbb5in.11 ~> evalfbb6in.7 [D ~+> D,K ~+> D] evalfbb4in.9 ~> evalfbb5in.11 [] evalfbb3in.10 ~> evalfbb4in.9 [E ~+> E,K ~+> E] evalfbb4in.8 ~> evalfbb3in.10 [] evalfbb6in.6 ~> evalfbb4in.8 [K ~=> E] evalfbb5in.11 ~> evalfbb6in.6 [D ~+> D,K ~+> D] evalfbb3in.10 ~> evalfbb4in.8 [E ~+> E,K ~+> E] + Loop: [B ~+> 0.0.0.0,D ~+> 0.0.0.0] evalfbb6in.6 ~> evalfbb4in.8 [K ~=> E] evalfbb5in.11 ~> evalfbb6in.6 [D ~+> D,K ~+> D] evalfbb4in.9 ~> evalfbb5in.11 [] evalfbb3in.10 ~> evalfbb4in.9 [E ~+> E,K ~+> E] evalfbb4in.8 ~> evalfbb3in.10 [] evalfbb3in.10 ~> evalfbb4in.8 [E ~+> E,K ~+> E] + Loop: [D ~+> 0.0.0.0.0,E ~+> 0.0.0.0.0] evalfbb4in.8 ~> evalfbb3in.10 [] evalfbb3in.10 ~> evalfbb4in.8 [E ~+> E,K ~+> E] + Applied Processor: Lare + Details: evalfstart.0 ~> exitus616.15 [K ~=> A ,B ~+> 0.0 ,B ~+> 0.0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> A ,K ~+> C ,K ~+> D ,K ~+> E ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> 0.0.0.0 ,K ~+> 0.0.0.0.0 ,K ~+> tick ,B ~*> A ,B ~*> C ,B ~*> D ,B ~*> E ,B ~*> 0.0.0 ,B ~*> 0.0.0.0 ,B ~*> 0.0.0.0.0 ,B ~*> tick ,K ~*> A ,K ~*> C ,K ~*> D ,K ~*> E ,K ~*> 0.0.0 ,K ~*> 0.0.0.0 ,K ~*> 0.0.0.0.0 ,K ~*> tick] + evalfbb8in.5> [A ~+> A ,A ~+> D ,A ~+> 0.0 ,A ~+> 0.0.0 ,A ~+> 0.0.0.0 ,A ~+> 0.0.0.0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> 0.0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> C ,K ~+> D ,K ~+> E ,K ~+> 0.0.0 ,K ~+> 0.0.0.0.0 ,K ~+> tick ,A ~*> A ,A ~*> C ,A ~*> D ,A ~*> E ,A ~*> 0.0.0 ,A ~*> 0.0.0.0 ,A ~*> 0.0.0.0.0 ,A ~*> tick ,B ~*> A ,B ~*> C ,B ~*> D ,B ~*> E ,B ~*> 0.0.0 ,B ~*> 0.0.0.0 ,B ~*> 0.0.0.0.0 ,B ~*> tick ,K ~*> A ,K ~*> C ,K ~*> D ,K ~*> E ,K ~*> 0.0.0 ,K ~*> 0.0.0.0 ,K ~*> 0.0.0.0.0 ,K ~*> tick] + evalfbb7in.12> [A ~+> D ,A ~+> 0.0.0 ,A ~+> 0.0.0.0 ,A ~+> 0.0.0.0.0 ,A ~+> tick ,B ~+> 0.0.0.0 ,B ~+> tick ,C ~+> C ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> E ,K ~+> 0.0.0.0.0 ,K ~+> tick ,A ~*> C ,A ~*> D ,A ~*> E ,A ~*> 0.0.0.0.0 ,A ~*> tick ,B ~*> D ,B ~*> E ,B ~*> 0.0.0.0.0 ,B ~*> tick ,C ~*> C ,C ~*> tick ,K ~*> C ,K ~*> D ,K ~*> E ,K ~*> 0.0.0.0 ,K ~*> 0.0.0.0.0 ,K ~*> tick] + evalfbb5in.11> [B ~+> 0.0.0.0 ,B ~+> tick ,D ~+> D ,D ~+> 0.0.0.0 ,D ~+> 0.0.0.0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> D ,K ~+> E ,K ~+> 0.0.0.0.0 ,K ~+> tick ,B ~*> D ,B ~*> E ,B ~*> 0.0.0.0.0 ,B ~*> tick ,D ~*> D ,D ~*> E ,D ~*> 0.0.0.0.0 ,D ~*> tick ,K ~*> D ,K ~*> E ,K ~*> 0.0.0.0.0 ,K ~*> tick] + evalfbb3in.10> [D ~+> 0.0.0.0.0 ,D ~+> tick ,E ~+> E ,E ~+> 0.0.0.0.0 ,E ~+> tick ,tick ~+> tick ,K ~+> E ,D ~*> E ,E ~*> E ,K ~*> E] YES(?,POLY)