YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E,F) -> evalfentryin(A,B,C,D,E,F) True (1,1) 1. evalfentryin(A,B,C,D,E,F) -> evalfbb9in(B,B,C,D,E,F) True (?,1) 2. evalfbb9in(A,B,C,D,E,F) -> evalfreturnin(A,B,C,D,E,F) [1 >= B] (?,1) 3. evalfbb9in(A,B,C,D,E,F) -> evalfbbin(A,B,C,D,E,F) [B >= 2] (?,1) 4. evalfreturnin(A,B,C,D,E,F) -> evalfstop(A,B,C,D,E,F) [1 + -1*B >= 0] (?,1) 5. evalfbbin(A,B,C,D,E,F) -> evalfbb6in(A,B,-1 + B,-1 + A + B,E,F) [-2 + B >= 0] (?,1) 6. evalfbb6in(A,B,C,D,E,F) -> evalfbb7in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= 1 + C] (?,1) 7. evalfbb6in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= D] (?,1) 8. evalfbb7in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 9. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && G >= 1] 10. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && 0 >= 1 + G] 11. evalfbb8in(A,B,C,D,E,F) -> evalfbb9in(1 + -1*C + D,-1 + C,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] (?,1) 12. evalfbb1in(A,B,C,D,E,F) -> evalfbb3in(A,B,C,D,C,-1 + D) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 13. evalfbb3in(A,B,C,D,E,F) -> evalfbb5in(A,B,C,D,E,F) [-1 + D + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 14. evalfbb5in(A,B,C,D,E,F) -> evalfbb6in(A,B,E,-1 + F,E,F) [-1 + D + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] Signature: {(evalfbb1in,6) ;(evalfbb3in,6) ;(evalfbb5in,6) ;(evalfbb6in,6) ;(evalfbb7in,6) ;(evalfbb8in,6) ;(evalfbb9in,6) ;(evalfbbin,6) ;(evalfentryin,6) ;(evalfreturnin,6) ;(evalfstart,6) ;(evalfstop,6)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{},5->{6,7},6->{8,9,10},7->{11},8->{11},9->{12},10->{12},11->{2,3} ,12->{13},13->{14},14->{6,7}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E,F) -> evalfentryin(A,B,C,D,E,F) True (1,1) 1. evalfentryin(A,B,C,D,E,F) -> evalfbb9in(B,B,C,D,E,F) True (1,1) 2. evalfbb9in(A,B,C,D,E,F) -> evalfreturnin(A,B,C,D,E,F) [1 >= B] (1,1) 3. evalfbb9in(A,B,C,D,E,F) -> evalfbbin(A,B,C,D,E,F) [B >= 2] (?,1) 4. evalfreturnin(A,B,C,D,E,F) -> evalfstop(A,B,C,D,E,F) [1 + -1*B >= 0] (1,1) 5. evalfbbin(A,B,C,D,E,F) -> evalfbb6in(A,B,-1 + B,-1 + A + B,E,F) [-2 + B >= 0] (?,1) 6. evalfbb6in(A,B,C,D,E,F) -> evalfbb7in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= 1 + C] (?,1) 7. evalfbb6in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= D] (?,1) 8. evalfbb7in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 9. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && G >= 1] 10. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && 0 >= 1 + G] 11. evalfbb8in(A,B,C,D,E,F) -> evalfbb9in(1 + -1*C + D,-1 + C,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] (?,1) 12. evalfbb1in(A,B,C,D,E,F) -> evalfbb3in(A,B,C,D,C,-1 + D) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 13. evalfbb3in(A,B,C,D,E,F) -> evalfbb5in(A,B,C,D,E,F) [-1 + D + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 14. evalfbb5in(A,B,C,D,E,F) -> evalfbb6in(A,B,E,-1 + F,E,F) [-1 + D + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] Signature: {(evalfbb1in,6) ;(evalfbb3in,6) ;(evalfbb5in,6) ;(evalfbb6in,6) ;(evalfbb7in,6) ;(evalfbb8in,6) ;(evalfbb9in,6) ;(evalfbbin,6) ;(evalfentryin,6) ;(evalfreturnin,6) ;(evalfstart,6) ;(evalfstop,6)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{},5->{6,7},6->{8,9,10},7->{11},8->{11},9->{12},10->{12},11->{2,3} ,12->{13},13->{14},14->{6,7}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb1in) = -1 + x4 p(evalfbb3in) = -1*x3 + x5 + x6 p(evalfbb5in) = x6 p(evalfbb6in) = -1 + x4 p(evalfbb7in) = -1 + x4 p(evalfbb8in) = -1 + x4 p(evalfbb9in) = -1 + x1 + x2 p(evalfbbin) = -2 + x1 + x2 p(evalfentryin) = 2*x2 p(evalfreturnin) = -1 + x1 + x2 p(evalfstart) = 2*x2 p(evalfstop) = -1 + x1 + x2 Following rules are strictly oriented: [-1 + D + -1*F >= 0 ==> && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] evalfbb5in(A,B,C,D,E,F) = F > -2 + F = evalfbb6in(A,B,E,-1 + F,E,F) Following rules are weakly oriented: True ==> evalfstart(A,B,C,D,E,F) = 2*B >= 2*B = evalfentryin(A,B,C,D,E,F) True ==> evalfentryin(A,B,C,D,E,F) = 2*B >= -1 + 2*B = evalfbb9in(B,B,C,D,E,F) [1 >= B] ==> evalfbb9in(A,B,C,D,E,F) = -1 + A + B >= -1 + A + B = evalfreturnin(A,B,C,D,E,F) [B >= 2] ==> evalfbb9in(A,B,C,D,E,F) = -1 + A + B >= -2 + A + B = evalfbbin(A,B,C,D,E,F) [1 + -1*B >= 0] ==> evalfreturnin(A,B,C,D,E,F) = -1 + A + B >= -1 + A + B = evalfstop(A,B,C,D,E,F) [-2 + B >= 0] ==> evalfbbin(A,B,C,D,E,F) = -2 + A + B >= -2 + A + B = evalfbb6in(A,B,-1 + B,-1 + A + B,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= 1 + C] ==> evalfbb6in(A,B,C,D,E,F) = -1 + D >= -1 + D = evalfbb7in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= D] ==> evalfbb6in(A,B,C,D,E,F) = -1 + D >= -1 + D = evalfbb8in(A,B,C,D,E,F) [-2 + D >= 0 ==> && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] evalfbb7in(A,B,C,D,E,F) = -1 + D >= -1 + D = evalfbb8in(A,B,C,D,E,F) [-2 + D >= 0 ==> && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && G >= 1] evalfbb7in(A,B,C,D,E,F) = -1 + D >= -1 + D = evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 ==> && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && 0 >= 1 + G] evalfbb7in(A,B,C,D,E,F) = -1 + D >= -1 + D = evalfbb1in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] ==> evalfbb8in(A,B,C,D,E,F) = -1 + D >= -1 + D = evalfbb9in(1 + -1*C + D,-1 + C,C,D,E,F) [-2 + D >= 0 ==> && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] evalfbb1in(A,B,C,D,E,F) = -1 + D >= -1 + D = evalfbb3in(A,B,C,D,C,-1 + D) [-1 + D + -1*F >= 0 ==> && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] evalfbb3in(A,B,C,D,E,F) = -1*C + E + F >= F = evalfbb5in(A,B,C,D,E,F) * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E,F) -> evalfentryin(A,B,C,D,E,F) True (1,1) 1. evalfentryin(A,B,C,D,E,F) -> evalfbb9in(B,B,C,D,E,F) True (1,1) 2. evalfbb9in(A,B,C,D,E,F) -> evalfreturnin(A,B,C,D,E,F) [1 >= B] (1,1) 3. evalfbb9in(A,B,C,D,E,F) -> evalfbbin(A,B,C,D,E,F) [B >= 2] (?,1) 4. evalfreturnin(A,B,C,D,E,F) -> evalfstop(A,B,C,D,E,F) [1 + -1*B >= 0] (1,1) 5. evalfbbin(A,B,C,D,E,F) -> evalfbb6in(A,B,-1 + B,-1 + A + B,E,F) [-2 + B >= 0] (?,1) 6. evalfbb6in(A,B,C,D,E,F) -> evalfbb7in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= 1 + C] (?,1) 7. evalfbb6in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= D] (?,1) 8. evalfbb7in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 9. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && G >= 1] 10. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && 0 >= 1 + G] 11. evalfbb8in(A,B,C,D,E,F) -> evalfbb9in(1 + -1*C + D,-1 + C,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] (?,1) 12. evalfbb1in(A,B,C,D,E,F) -> evalfbb3in(A,B,C,D,C,-1 + D) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 13. evalfbb3in(A,B,C,D,E,F) -> evalfbb5in(A,B,C,D,E,F) [-1 + D + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 14. evalfbb5in(A,B,C,D,E,F) -> evalfbb6in(A,B,E,-1 + F,E,F) [-1 + D + -1*F >= 0 (2*B,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] Signature: {(evalfbb1in,6) ;(evalfbb3in,6) ;(evalfbb5in,6) ;(evalfbb6in,6) ;(evalfbb7in,6) ;(evalfbb8in,6) ;(evalfbb9in,6) ;(evalfbbin,6) ;(evalfentryin,6) ;(evalfreturnin,6) ;(evalfstart,6) ;(evalfstop,6)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{},5->{6,7},6->{8,9,10},7->{11},8->{11},9->{12},10->{12},11->{2,3} ,12->{13},13->{14},14->{6,7}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb1in) = 1 + x2 p(evalfbb3in) = 1 + x2 p(evalfbb5in) = 1 + x2 p(evalfbb6in) = 1 + x2 p(evalfbb7in) = 1 + x2 p(evalfbb8in) = 1 + x3 p(evalfbb9in) = 1 + x2 p(evalfbbin) = 1 + x2 p(evalfentryin) = 1 + x2 p(evalfreturnin) = 1 + x2 p(evalfstart) = 1 + x2 p(evalfstop) = 1 + x2 Following rules are strictly oriented: [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= D] ==> evalfbb6in(A,B,C,D,E,F) = 1 + B > 1 + C = evalfbb8in(A,B,C,D,E,F) [-2 + D >= 0 ==> && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] evalfbb7in(A,B,C,D,E,F) = 1 + B > 1 + C = evalfbb8in(A,B,C,D,E,F) Following rules are weakly oriented: True ==> evalfstart(A,B,C,D,E,F) = 1 + B >= 1 + B = evalfentryin(A,B,C,D,E,F) True ==> evalfentryin(A,B,C,D,E,F) = 1 + B >= 1 + B = evalfbb9in(B,B,C,D,E,F) [1 >= B] ==> evalfbb9in(A,B,C,D,E,F) = 1 + B >= 1 + B = evalfreturnin(A,B,C,D,E,F) [B >= 2] ==> evalfbb9in(A,B,C,D,E,F) = 1 + B >= 1 + B = evalfbbin(A,B,C,D,E,F) [1 + -1*B >= 0] ==> evalfreturnin(A,B,C,D,E,F) = 1 + B >= 1 + B = evalfstop(A,B,C,D,E,F) [-2 + B >= 0] ==> evalfbbin(A,B,C,D,E,F) = 1 + B >= 1 + B = evalfbb6in(A,B,-1 + B,-1 + A + B,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= 1 + C] ==> evalfbb6in(A,B,C,D,E,F) = 1 + B >= 1 + B = evalfbb7in(A,B,C,D,E,F) [-2 + D >= 0 ==> && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && G >= 1] evalfbb7in(A,B,C,D,E,F) = 1 + B >= 1 + B = evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 ==> && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && 0 >= 1 + G] evalfbb7in(A,B,C,D,E,F) = 1 + B >= 1 + B = evalfbb1in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] ==> evalfbb8in(A,B,C,D,E,F) = 1 + C >= C = evalfbb9in(1 + -1*C + D,-1 + C,C,D,E,F) [-2 + D >= 0 ==> && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] evalfbb1in(A,B,C,D,E,F) = 1 + B >= 1 + B = evalfbb3in(A,B,C,D,C,-1 + D) [-1 + D + -1*F >= 0 ==> && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] evalfbb3in(A,B,C,D,E,F) = 1 + B >= 1 + B = evalfbb5in(A,B,C,D,E,F) [-1 + D + -1*F >= 0 ==> && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] evalfbb5in(A,B,C,D,E,F) = 1 + B >= 1 + B = evalfbb6in(A,B,E,-1 + F,E,F) * Step 4: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E,F) -> evalfentryin(A,B,C,D,E,F) True (1,1) 1. evalfentryin(A,B,C,D,E,F) -> evalfbb9in(B,B,C,D,E,F) True (1,1) 2. evalfbb9in(A,B,C,D,E,F) -> evalfreturnin(A,B,C,D,E,F) [1 >= B] (1,1) 3. evalfbb9in(A,B,C,D,E,F) -> evalfbbin(A,B,C,D,E,F) [B >= 2] (?,1) 4. evalfreturnin(A,B,C,D,E,F) -> evalfstop(A,B,C,D,E,F) [1 + -1*B >= 0] (1,1) 5. evalfbbin(A,B,C,D,E,F) -> evalfbb6in(A,B,-1 + B,-1 + A + B,E,F) [-2 + B >= 0] (?,1) 6. evalfbb6in(A,B,C,D,E,F) -> evalfbb7in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= 1 + C] (?,1) 7. evalfbb6in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= D] (1 + B,1) 8. evalfbb7in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-2 + D >= 0 (1 + B,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 9. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && G >= 1] 10. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && 0 >= 1 + G] 11. evalfbb8in(A,B,C,D,E,F) -> evalfbb9in(1 + -1*C + D,-1 + C,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] (?,1) 12. evalfbb1in(A,B,C,D,E,F) -> evalfbb3in(A,B,C,D,C,-1 + D) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 13. evalfbb3in(A,B,C,D,E,F) -> evalfbb5in(A,B,C,D,E,F) [-1 + D + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 14. evalfbb5in(A,B,C,D,E,F) -> evalfbb6in(A,B,E,-1 + F,E,F) [-1 + D + -1*F >= 0 (2*B,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] Signature: {(evalfbb1in,6) ;(evalfbb3in,6) ;(evalfbb5in,6) ;(evalfbb6in,6) ;(evalfbb7in,6) ;(evalfbb8in,6) ;(evalfbb9in,6) ;(evalfbbin,6) ;(evalfentryin,6) ;(evalfreturnin,6) ;(evalfstart,6) ;(evalfstop,6)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{},5->{6,7},6->{8,9,10},7->{11},8->{11},9->{12},10->{12},11->{2,3} ,12->{13},13->{14},14->{6,7}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 5: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E,F) -> evalfentryin(A,B,C,D,E,F) True (1,1) 1. evalfentryin(A,B,C,D,E,F) -> evalfbb9in(B,B,C,D,E,F) True (1,1) 2. evalfbb9in(A,B,C,D,E,F) -> evalfreturnin(A,B,C,D,E,F) [1 >= B] (1,1) 3. evalfbb9in(A,B,C,D,E,F) -> evalfbbin(A,B,C,D,E,F) [B >= 2] (?,1) 4. evalfreturnin(A,B,C,D,E,F) -> evalfstop(A,B,C,D,E,F) [1 + -1*B >= 0] (1,1) 5. evalfbbin(A,B,C,D,E,F) -> evalfbb6in(A,B,-1 + B,-1 + A + B,E,F) [-2 + B >= 0] (?,1) 6. evalfbb6in(A,B,C,D,E,F) -> evalfbb7in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= 1 + C] (?,1) 7. evalfbb6in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= D] (1 + B,1) 8. evalfbb7in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-2 + D >= 0 (1 + B,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 9. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && G >= 1] 10. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && 0 >= 1 + G] 11. evalfbb8in(A,B,C,D,E,F) -> evalfbb9in(1 + -1*C + D,-1 + C,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] (2 + 2*B,1) 12. evalfbb1in(A,B,C,D,E,F) -> evalfbb3in(A,B,C,D,C,-1 + D) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 13. evalfbb3in(A,B,C,D,E,F) -> evalfbb5in(A,B,C,D,E,F) [-1 + D + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 14. evalfbb5in(A,B,C,D,E,F) -> evalfbb6in(A,B,E,-1 + F,E,F) [-1 + D + -1*F >= 0 (2*B,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] Signature: {(evalfbb1in,6) ;(evalfbb3in,6) ;(evalfbb5in,6) ;(evalfbb6in,6) ;(evalfbb7in,6) ;(evalfbb8in,6) ;(evalfbb9in,6) ;(evalfbbin,6) ;(evalfentryin,6) ;(evalfreturnin,6) ;(evalfstart,6) ;(evalfstop,6)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{},5->{6,7},6->{8,9,10},7->{11},8->{11},9->{12},10->{12},11->{2,3} ,12->{13},13->{14},14->{6,7}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb1in) = -2 + x4 p(evalfbb3in) = -1 + x6 p(evalfbb5in) = -1 + x6 p(evalfbb6in) = x4 p(evalfbb7in) = x4 p(evalfbb8in) = x4 p(evalfbb9in) = x1 + x2 p(evalfbbin) = x1 + x2 p(evalfentryin) = 2*x2 p(evalfreturnin) = x1 + x2 p(evalfstart) = 2*x2 p(evalfstop) = x1 + x2 Following rules are strictly oriented: [-2 + D >= 0 ==> && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && 0 >= 1 + G] evalfbb7in(A,B,C,D,E,F) = D > -2 + D = evalfbb1in(A,B,C,D,E,F) Following rules are weakly oriented: True ==> evalfstart(A,B,C,D,E,F) = 2*B >= 2*B = evalfentryin(A,B,C,D,E,F) True ==> evalfentryin(A,B,C,D,E,F) = 2*B >= 2*B = evalfbb9in(B,B,C,D,E,F) [1 >= B] ==> evalfbb9in(A,B,C,D,E,F) = A + B >= A + B = evalfreturnin(A,B,C,D,E,F) [B >= 2] ==> evalfbb9in(A,B,C,D,E,F) = A + B >= A + B = evalfbbin(A,B,C,D,E,F) [1 + -1*B >= 0] ==> evalfreturnin(A,B,C,D,E,F) = A + B >= A + B = evalfstop(A,B,C,D,E,F) [-2 + B >= 0] ==> evalfbbin(A,B,C,D,E,F) = A + B >= -1 + A + B = evalfbb6in(A,B,-1 + B,-1 + A + B,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= 1 + C] ==> evalfbb6in(A,B,C,D,E,F) = D >= D = evalfbb7in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= D] ==> evalfbb6in(A,B,C,D,E,F) = D >= D = evalfbb8in(A,B,C,D,E,F) [-2 + D >= 0 ==> && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] evalfbb7in(A,B,C,D,E,F) = D >= D = evalfbb8in(A,B,C,D,E,F) [-2 + D >= 0 ==> && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && G >= 1] evalfbb7in(A,B,C,D,E,F) = D >= -2 + D = evalfbb1in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] ==> evalfbb8in(A,B,C,D,E,F) = D >= D = evalfbb9in(1 + -1*C + D,-1 + C,C,D,E,F) [-2 + D >= 0 ==> && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] evalfbb1in(A,B,C,D,E,F) = -2 + D >= -2 + D = evalfbb3in(A,B,C,D,C,-1 + D) [-1 + D + -1*F >= 0 ==> && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] evalfbb3in(A,B,C,D,E,F) = -1 + F >= -1 + F = evalfbb5in(A,B,C,D,E,F) [-1 + D + -1*F >= 0 ==> && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] evalfbb5in(A,B,C,D,E,F) = -1 + F >= -1 + F = evalfbb6in(A,B,E,-1 + F,E,F) * Step 6: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E,F) -> evalfentryin(A,B,C,D,E,F) True (1,1) 1. evalfentryin(A,B,C,D,E,F) -> evalfbb9in(B,B,C,D,E,F) True (1,1) 2. evalfbb9in(A,B,C,D,E,F) -> evalfreturnin(A,B,C,D,E,F) [1 >= B] (1,1) 3. evalfbb9in(A,B,C,D,E,F) -> evalfbbin(A,B,C,D,E,F) [B >= 2] (?,1) 4. evalfreturnin(A,B,C,D,E,F) -> evalfstop(A,B,C,D,E,F) [1 + -1*B >= 0] (1,1) 5. evalfbbin(A,B,C,D,E,F) -> evalfbb6in(A,B,-1 + B,-1 + A + B,E,F) [-2 + B >= 0] (?,1) 6. evalfbb6in(A,B,C,D,E,F) -> evalfbb7in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= 1 + C] (?,1) 7. evalfbb6in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= D] (1 + B,1) 8. evalfbb7in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-2 + D >= 0 (1 + B,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 9. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && G >= 1] 10. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (2*B,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && 0 >= 1 + G] 11. evalfbb8in(A,B,C,D,E,F) -> evalfbb9in(1 + -1*C + D,-1 + C,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] (2 + 2*B,1) 12. evalfbb1in(A,B,C,D,E,F) -> evalfbb3in(A,B,C,D,C,-1 + D) [-2 + D >= 0 (?,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 13. evalfbb3in(A,B,C,D,E,F) -> evalfbb5in(A,B,C,D,E,F) [-1 + D + -1*F >= 0 (?,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 14. evalfbb5in(A,B,C,D,E,F) -> evalfbb6in(A,B,E,-1 + F,E,F) [-1 + D + -1*F >= 0 (2*B,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] Signature: {(evalfbb1in,6) ;(evalfbb3in,6) ;(evalfbb5in,6) ;(evalfbb6in,6) ;(evalfbb7in,6) ;(evalfbb8in,6) ;(evalfbb9in,6) ;(evalfbbin,6) ;(evalfentryin,6) ;(evalfreturnin,6) ;(evalfstart,6) ;(evalfstop,6)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{},5->{6,7},6->{8,9,10},7->{11},8->{11},9->{12},10->{12},11->{2,3} ,12->{13},13->{14},14->{6,7}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 7: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E,F) -> evalfentryin(A,B,C,D,E,F) True (1,1) 1. evalfentryin(A,B,C,D,E,F) -> evalfbb9in(B,B,C,D,E,F) True (1,1) 2. evalfbb9in(A,B,C,D,E,F) -> evalfreturnin(A,B,C,D,E,F) [1 >= B] (1,1) 3. evalfbb9in(A,B,C,D,E,F) -> evalfbbin(A,B,C,D,E,F) [B >= 2] (3 + 2*B,1) 4. evalfreturnin(A,B,C,D,E,F) -> evalfstop(A,B,C,D,E,F) [1 + -1*B >= 0] (1,1) 5. evalfbbin(A,B,C,D,E,F) -> evalfbb6in(A,B,-1 + B,-1 + A + B,E,F) [-2 + B >= 0] (3 + 2*B,1) 6. evalfbb6in(A,B,C,D,E,F) -> evalfbb7in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= 1 + C] (3 + 4*B,1) 7. evalfbb6in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= D] (1 + B,1) 8. evalfbb7in(A,B,C,D,E,F) -> evalfbb8in(A,B,C,D,E,F) [-2 + D >= 0 (1 + B,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 9. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (3 + 4*B,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && G >= 1] 10. evalfbb7in(A,B,C,D,E,F) -> evalfbb1in(A,B,C,D,E,F) [-2 + D >= 0 (2*B,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && 0 >= 1 + G] 11. evalfbb8in(A,B,C,D,E,F) -> evalfbb9in(1 + -1*C + D,-1 + C,C,D,E,F) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] (2 + 2*B,1) 12. evalfbb1in(A,B,C,D,E,F) -> evalfbb3in(A,B,C,D,C,-1 + D) [-2 + D >= 0 (3 + 6*B,1) && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 13. evalfbb3in(A,B,C,D,E,F) -> evalfbb5in(A,B,C,D,E,F) [-1 + D + -1*F >= 0 (3 + 6*B,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 14. evalfbb5in(A,B,C,D,E,F) -> evalfbb6in(A,B,E,-1 + F,E,F) [-1 + D + -1*F >= 0 (2*B,1) && -1 + F >= 0 && -2 + E + F >= 0 && -1*E + F >= 0 && -3 + D + F >= 0 && 1 + -1*D + F >= 0 && -2 + C + F >= 0 && -1*C + F >= 0 && -3 + B + F >= 0 && 1 + -1*B + F >= 0 && -1 + D + -1*E >= 0 && C + -1*E >= 0 && -1 + B + -1*E >= 0 && -1 + E >= 0 && -3 + D + E >= 0 && -2 + C + E >= 0 && -1*C + E >= 0 && -3 + B + E >= 0 && 1 + -1*B + E >= 0 && -2 + D >= 0 && -3 + C + D >= 0 && -1 + -1*C + D >= 0 && -4 + B + D >= 0 && -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] Signature: {(evalfbb1in,6) ;(evalfbb3in,6) ;(evalfbb5in,6) ;(evalfbb6in,6) ;(evalfbb7in,6) ;(evalfbb8in,6) ;(evalfbb9in,6) ;(evalfbbin,6) ;(evalfentryin,6) ;(evalfreturnin,6) ;(evalfstart,6) ;(evalfstop,6)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{5},4->{},5->{6,7},6->{8,9,10},7->{11},8->{11},9->{12},10->{12},11->{2,3} ,12->{13},13->{14},14->{6,7}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))