YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E,F,G) -> evalfentryin(A,B,C,D,E,F,G) True (1,1) 1. evalfentryin(A,B,C,D,E,F,G) -> evalfbb5in(0,0,0,D,E,F,G) True (?,1) 2. evalfbb5in(A,B,C,D,E,F,G) -> evalfreturnin(A,B,C,D,E,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= D] (?,1) 3. evalfbb5in(A,B,C,D,E,F,G) -> evalfbbin(A,B,C,D,1 + C,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + C] (?,1) 4. evalfbbin(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= 1 + H] 5. evalfbbin(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && H >= 1] 6. evalfbbin(A,B,C,D,E,F,G) -> evalfbb3in(A,B,C,D,E,A,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 7. evalfbb1in(A,B,C,D,E,F,G) -> evalfbb5in(A,1 + F,E,D,E,F,G) [F >= 0 (?,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] 8. evalfbb1in(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,1 + F,G) [F >= 0 (?,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] 9. evalfbb3in(A,B,C,D,E,F,G) -> evalfbb5in(1 + F,B,E,D,E,F,G) [F >= 0 (?,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] 10. evalfbb3in(A,B,C,D,E,F,G) -> evalfbb3in(A,B,C,D,E,1 + F,G) [F >= 0 (?,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] 11. evalfreturnin(A,B,C,D,E,F,G) -> evalfstop(A,B,C,D,E,F,G) [C + -1*D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (?,1) Signature: {(evalfbb1in,7) ;(evalfbb3in,7) ;(evalfbb5in,7) ;(evalfbbin,7) ;(evalfentryin,7) ;(evalfreturnin,7) ;(evalfstart,7) ;(evalfstop,7)} Flow Graph: [0->{1},1->{2,3},2->{11},3->{4,5,6},4->{7,8},5->{7,8},6->{9,10},7->{2,3},8->{7,8},9->{2,3},10->{9,10} ,11->{}] + 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,G) -> evalfentryin(A,B,C,D,E,F,G) True (1,1) 1. evalfentryin(A,B,C,D,E,F,G) -> evalfbb5in(0,0,0,D,E,F,G) True (1,1) 2. evalfbb5in(A,B,C,D,E,F,G) -> evalfreturnin(A,B,C,D,E,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= D] (1,1) 3. evalfbb5in(A,B,C,D,E,F,G) -> evalfbbin(A,B,C,D,1 + C,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + C] (?,1) 4. evalfbbin(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= 1 + H] 5. evalfbbin(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && H >= 1] 6. evalfbbin(A,B,C,D,E,F,G) -> evalfbb3in(A,B,C,D,E,A,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 7. evalfbb1in(A,B,C,D,E,F,G) -> evalfbb5in(A,1 + F,E,D,E,F,G) [F >= 0 (?,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] 8. evalfbb1in(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,1 + F,G) [F >= 0 (?,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] 9. evalfbb3in(A,B,C,D,E,F,G) -> evalfbb5in(1 + F,B,E,D,E,F,G) [F >= 0 (?,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] 10. evalfbb3in(A,B,C,D,E,F,G) -> evalfbb3in(A,B,C,D,E,1 + F,G) [F >= 0 (?,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] 11. evalfreturnin(A,B,C,D,E,F,G) -> evalfstop(A,B,C,D,E,F,G) [C + -1*D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (1,1) Signature: {(evalfbb1in,7) ;(evalfbb3in,7) ;(evalfbb5in,7) ;(evalfbbin,7) ;(evalfentryin,7) ;(evalfreturnin,7) ;(evalfstart,7) ;(evalfstop,7)} Flow Graph: [0->{1},1->{2,3},2->{11},3->{4,5,6},4->{7,8},5->{7,8},6->{9,10},7->{2,3},8->{7,8},9->{2,3},10->{9,10} ,11->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb1in) = -1*x1 + x7 p(evalfbb3in) = -1*x6 + x7 p(evalfbb5in) = -1*x1 + x7 p(evalfbbin) = -1*x1 + x7 p(evalfentryin) = x7 p(evalfreturnin) = -1*x1 + x7 p(evalfstart) = x7 p(evalfstop) = -1*x1 + x7 Following rules are strictly oriented: [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] evalfbb3in(A,B,C,D,E,F,G) = -1*F + G > -1 + -1*F + G = evalfbb3in(A,B,C,D,E,1 + F,G) Following rules are weakly oriented: True ==> evalfstart(A,B,C,D,E,F,G) = G >= G = evalfentryin(A,B,C,D,E,F,G) True ==> evalfentryin(A,B,C,D,E,F,G) = G >= G = evalfbb5in(0,0,0,D,E,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= D] ==> evalfbb5in(A,B,C,D,E,F,G) = -1*A + G >= -1*A + G = evalfreturnin(A,B,C,D,E,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + C] ==> evalfbb5in(A,B,C,D,E,F,G) = -1*A + G >= -1*A + G = evalfbbin(A,B,C,D,1 + C,F,G) [D + -1*E >= 0 ==> && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= 1 + H] evalfbbin(A,B,C,D,E,F,G) = -1*A + G >= -1*A + G = evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 ==> && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && H >= 1] evalfbbin(A,B,C,D,E,F,G) = -1*A + G >= -1*A + G = evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 ==> && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalfbbin(A,B,C,D,E,F,G) = -1*A + G >= -1*A + G = evalfbb3in(A,B,C,D,E,A,G) [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] evalfbb1in(A,B,C,D,E,F,G) = -1*A + G >= -1*A + G = evalfbb5in(A,1 + F,E,D,E,F,G) [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] evalfbb1in(A,B,C,D,E,F,G) = -1*A + G >= -1*A + G = evalfbb1in(A,B,C,D,E,1 + F,G) [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] evalfbb3in(A,B,C,D,E,F,G) = -1*F + G >= -1 + -1*F + G = evalfbb5in(1 + F,B,E,D,E,F,G) [C + -1*D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] ==> evalfreturnin(A,B,C,D,E,F,G) = -1*A + G >= -1*A + G = evalfstop(A,B,C,D,E,F,G) * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E,F,G) -> evalfentryin(A,B,C,D,E,F,G) True (1,1) 1. evalfentryin(A,B,C,D,E,F,G) -> evalfbb5in(0,0,0,D,E,F,G) True (1,1) 2. evalfbb5in(A,B,C,D,E,F,G) -> evalfreturnin(A,B,C,D,E,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= D] (1,1) 3. evalfbb5in(A,B,C,D,E,F,G) -> evalfbbin(A,B,C,D,1 + C,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + C] (?,1) 4. evalfbbin(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= 1 + H] 5. evalfbbin(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && H >= 1] 6. evalfbbin(A,B,C,D,E,F,G) -> evalfbb3in(A,B,C,D,E,A,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 7. evalfbb1in(A,B,C,D,E,F,G) -> evalfbb5in(A,1 + F,E,D,E,F,G) [F >= 0 (?,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] 8. evalfbb1in(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,1 + F,G) [F >= 0 (?,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] 9. evalfbb3in(A,B,C,D,E,F,G) -> evalfbb5in(1 + F,B,E,D,E,F,G) [F >= 0 (?,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] 10. evalfbb3in(A,B,C,D,E,F,G) -> evalfbb3in(A,B,C,D,E,1 + F,G) [F >= 0 (G,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] 11. evalfreturnin(A,B,C,D,E,F,G) -> evalfstop(A,B,C,D,E,F,G) [C + -1*D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (1,1) Signature: {(evalfbb1in,7) ;(evalfbb3in,7) ;(evalfbb5in,7) ;(evalfbbin,7) ;(evalfentryin,7) ;(evalfreturnin,7) ;(evalfstart,7) ;(evalfstop,7)} Flow Graph: [0->{1},1->{2,3},2->{11},3->{4,5,6},4->{7,8},5->{7,8},6->{9,10},7->{2,3},8->{7,8},9->{2,3},10->{9,10} ,11->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb1in) = -1*x3 + x4 p(evalfbb3in) = -1*x3 + x4 p(evalfbb5in) = -1*x3 + x4 p(evalfbbin) = -1*x3 + x4 p(evalfentryin) = x4 p(evalfreturnin) = -1*x3 + x4 p(evalfstart) = x4 p(evalfstop) = -1*x3 + x4 Following rules are strictly oriented: [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] evalfbb3in(A,B,C,D,E,F,G) = -1*C + D > D + -1*E = evalfbb5in(1 + F,B,E,D,E,F,G) Following rules are weakly oriented: True ==> evalfstart(A,B,C,D,E,F,G) = D >= D = evalfentryin(A,B,C,D,E,F,G) True ==> evalfentryin(A,B,C,D,E,F,G) = D >= D = evalfbb5in(0,0,0,D,E,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= D] ==> evalfbb5in(A,B,C,D,E,F,G) = -1*C + D >= -1*C + D = evalfreturnin(A,B,C,D,E,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + C] ==> evalfbb5in(A,B,C,D,E,F,G) = -1*C + D >= -1*C + D = evalfbbin(A,B,C,D,1 + C,F,G) [D + -1*E >= 0 ==> && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= 1 + H] evalfbbin(A,B,C,D,E,F,G) = -1*C + D >= -1*C + D = evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 ==> && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && H >= 1] evalfbbin(A,B,C,D,E,F,G) = -1*C + D >= -1*C + D = evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 ==> && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalfbbin(A,B,C,D,E,F,G) = -1*C + D >= -1*C + D = evalfbb3in(A,B,C,D,E,A,G) [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] evalfbb1in(A,B,C,D,E,F,G) = -1*C + D >= D + -1*E = evalfbb5in(A,1 + F,E,D,E,F,G) [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] evalfbb1in(A,B,C,D,E,F,G) = -1*C + D >= -1*C + D = evalfbb1in(A,B,C,D,E,1 + F,G) [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] evalfbb3in(A,B,C,D,E,F,G) = -1*C + D >= -1*C + D = evalfbb3in(A,B,C,D,E,1 + F,G) [C + -1*D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] ==> evalfreturnin(A,B,C,D,E,F,G) = -1*C + D >= -1*C + D = evalfstop(A,B,C,D,E,F,G) * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E,F,G) -> evalfentryin(A,B,C,D,E,F,G) True (1,1) 1. evalfentryin(A,B,C,D,E,F,G) -> evalfbb5in(0,0,0,D,E,F,G) True (1,1) 2. evalfbb5in(A,B,C,D,E,F,G) -> evalfreturnin(A,B,C,D,E,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= D] (1,1) 3. evalfbb5in(A,B,C,D,E,F,G) -> evalfbbin(A,B,C,D,1 + C,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + C] (?,1) 4. evalfbbin(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= 1 + H] 5. evalfbbin(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && H >= 1] 6. evalfbbin(A,B,C,D,E,F,G) -> evalfbb3in(A,B,C,D,E,A,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 7. evalfbb1in(A,B,C,D,E,F,G) -> evalfbb5in(A,1 + F,E,D,E,F,G) [F >= 0 (?,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] 8. evalfbb1in(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,1 + F,G) [F >= 0 (?,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] 9. evalfbb3in(A,B,C,D,E,F,G) -> evalfbb5in(1 + F,B,E,D,E,F,G) [F >= 0 (D,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] 10. evalfbb3in(A,B,C,D,E,F,G) -> evalfbb3in(A,B,C,D,E,1 + F,G) [F >= 0 (G,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] 11. evalfreturnin(A,B,C,D,E,F,G) -> evalfstop(A,B,C,D,E,F,G) [C + -1*D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (1,1) Signature: {(evalfbb1in,7) ;(evalfbb3in,7) ;(evalfbb5in,7) ;(evalfbbin,7) ;(evalfentryin,7) ;(evalfreturnin,7) ;(evalfstart,7) ;(evalfstop,7)} Flow Graph: [0->{1},1->{2,3},2->{11},3->{4,5,6},4->{7,8},5->{7,8},6->{9,10},7->{2,3},8->{7,8},9->{2,3},10->{9,10} ,11->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb1in) = -1*x6 + x7 p(evalfbb3in) = -1*x2 + x7 p(evalfbb5in) = -1*x2 + x7 p(evalfbbin) = -1*x2 + x7 p(evalfentryin) = x7 p(evalfreturnin) = -1*x2 + x7 p(evalfstart) = x7 p(evalfstop) = -1*x2 + x7 Following rules are strictly oriented: [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] evalfbb1in(A,B,C,D,E,F,G) = -1*F + G > -1 + -1*F + G = evalfbb1in(A,B,C,D,E,1 + F,G) Following rules are weakly oriented: True ==> evalfstart(A,B,C,D,E,F,G) = G >= G = evalfentryin(A,B,C,D,E,F,G) True ==> evalfentryin(A,B,C,D,E,F,G) = G >= G = evalfbb5in(0,0,0,D,E,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= D] ==> evalfbb5in(A,B,C,D,E,F,G) = -1*B + G >= -1*B + G = evalfreturnin(A,B,C,D,E,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + C] ==> evalfbb5in(A,B,C,D,E,F,G) = -1*B + G >= -1*B + G = evalfbbin(A,B,C,D,1 + C,F,G) [D + -1*E >= 0 ==> && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= 1 + H] evalfbbin(A,B,C,D,E,F,G) = -1*B + G >= -1*B + G = evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 ==> && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && H >= 1] evalfbbin(A,B,C,D,E,F,G) = -1*B + G >= -1*B + G = evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 ==> && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalfbbin(A,B,C,D,E,F,G) = -1*B + G >= -1*B + G = evalfbb3in(A,B,C,D,E,A,G) [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] evalfbb1in(A,B,C,D,E,F,G) = -1*F + G >= -1 + -1*F + G = evalfbb5in(A,1 + F,E,D,E,F,G) [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] evalfbb3in(A,B,C,D,E,F,G) = -1*B + G >= -1*B + G = evalfbb5in(1 + F,B,E,D,E,F,G) [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] evalfbb3in(A,B,C,D,E,F,G) = -1*B + G >= -1*B + G = evalfbb3in(A,B,C,D,E,1 + F,G) [C + -1*D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] ==> evalfreturnin(A,B,C,D,E,F,G) = -1*B + G >= -1*B + G = evalfstop(A,B,C,D,E,F,G) * Step 5: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E,F,G) -> evalfentryin(A,B,C,D,E,F,G) True (1,1) 1. evalfentryin(A,B,C,D,E,F,G) -> evalfbb5in(0,0,0,D,E,F,G) True (1,1) 2. evalfbb5in(A,B,C,D,E,F,G) -> evalfreturnin(A,B,C,D,E,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= D] (1,1) 3. evalfbb5in(A,B,C,D,E,F,G) -> evalfbbin(A,B,C,D,1 + C,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + C] (?,1) 4. evalfbbin(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= 1 + H] 5. evalfbbin(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && H >= 1] 6. evalfbbin(A,B,C,D,E,F,G) -> evalfbb3in(A,B,C,D,E,A,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 7. evalfbb1in(A,B,C,D,E,F,G) -> evalfbb5in(A,1 + F,E,D,E,F,G) [F >= 0 (?,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] 8. evalfbb1in(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,1 + F,G) [F >= 0 (G,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] 9. evalfbb3in(A,B,C,D,E,F,G) -> evalfbb5in(1 + F,B,E,D,E,F,G) [F >= 0 (D,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] 10. evalfbb3in(A,B,C,D,E,F,G) -> evalfbb3in(A,B,C,D,E,1 + F,G) [F >= 0 (G,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] 11. evalfreturnin(A,B,C,D,E,F,G) -> evalfstop(A,B,C,D,E,F,G) [C + -1*D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (1,1) Signature: {(evalfbb1in,7) ;(evalfbb3in,7) ;(evalfbb5in,7) ;(evalfbbin,7) ;(evalfentryin,7) ;(evalfreturnin,7) ;(evalfstart,7) ;(evalfstop,7)} Flow Graph: [0->{1},1->{2,3},2->{11},3->{4,5,6},4->{7,8},5->{7,8},6->{9,10},7->{2,3},8->{7,8},9->{2,3},10->{9,10} ,11->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb1in) = -1*x3 + x4 p(evalfbb3in) = 1 + x4 + -1*x5 p(evalfbb5in) = -1*x3 + x4 p(evalfbbin) = -1*x3 + x4 p(evalfentryin) = x4 p(evalfreturnin) = -1*x3 + x4 p(evalfstart) = x4 p(evalfstop) = -1*x3 + x4 Following rules are strictly oriented: [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] evalfbb1in(A,B,C,D,E,F,G) = -1*C + D > D + -1*E = evalfbb5in(A,1 + F,E,D,E,F,G) [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] evalfbb3in(A,B,C,D,E,F,G) = 1 + D + -1*E > D + -1*E = evalfbb5in(1 + F,B,E,D,E,F,G) Following rules are weakly oriented: True ==> evalfstart(A,B,C,D,E,F,G) = D >= D = evalfentryin(A,B,C,D,E,F,G) True ==> evalfentryin(A,B,C,D,E,F,G) = D >= D = evalfbb5in(0,0,0,D,E,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= D] ==> evalfbb5in(A,B,C,D,E,F,G) = -1*C + D >= -1*C + D = evalfreturnin(A,B,C,D,E,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + C] ==> evalfbb5in(A,B,C,D,E,F,G) = -1*C + D >= -1*C + D = evalfbbin(A,B,C,D,1 + C,F,G) [D + -1*E >= 0 ==> && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= 1 + H] evalfbbin(A,B,C,D,E,F,G) = -1*C + D >= -1*C + D = evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 ==> && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && H >= 1] evalfbbin(A,B,C,D,E,F,G) = -1*C + D >= -1*C + D = evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 ==> && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] evalfbbin(A,B,C,D,E,F,G) = -1*C + D >= 1 + D + -1*E = evalfbb3in(A,B,C,D,E,A,G) [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] evalfbb1in(A,B,C,D,E,F,G) = -1*C + D >= -1*C + D = evalfbb1in(A,B,C,D,E,1 + F,G) [F >= 0 ==> && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] evalfbb3in(A,B,C,D,E,F,G) = 1 + D + -1*E >= 1 + D + -1*E = evalfbb3in(A,B,C,D,E,1 + F,G) [C + -1*D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] ==> evalfreturnin(A,B,C,D,E,F,G) = -1*C + D >= -1*C + D = evalfstop(A,B,C,D,E,F,G) * Step 6: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D,E,F,G) -> evalfentryin(A,B,C,D,E,F,G) True (1,1) 1. evalfentryin(A,B,C,D,E,F,G) -> evalfbb5in(0,0,0,D,E,F,G) True (1,1) 2. evalfbb5in(A,B,C,D,E,F,G) -> evalfreturnin(A,B,C,D,E,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= D] (1,1) 3. evalfbb5in(A,B,C,D,E,F,G) -> evalfbbin(A,B,C,D,1 + C,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + C] (?,1) 4. evalfbbin(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= 1 + H] 5. evalfbbin(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && H >= 1] 6. evalfbbin(A,B,C,D,E,F,G) -> evalfbb3in(A,B,C,D,E,A,G) [D + -1*E >= 0 (?,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 7. evalfbb1in(A,B,C,D,E,F,G) -> evalfbb5in(A,1 + F,E,D,E,F,G) [F >= 0 (D,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] 8. evalfbb1in(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,1 + F,G) [F >= 0 (G,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] 9. evalfbb3in(A,B,C,D,E,F,G) -> evalfbb5in(1 + F,B,E,D,E,F,G) [F >= 0 (D,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] 10. evalfbb3in(A,B,C,D,E,F,G) -> evalfbb3in(A,B,C,D,E,1 + F,G) [F >= 0 (G,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] 11. evalfreturnin(A,B,C,D,E,F,G) -> evalfstop(A,B,C,D,E,F,G) [C + -1*D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (1,1) Signature: {(evalfbb1in,7) ;(evalfbb3in,7) ;(evalfbb5in,7) ;(evalfbbin,7) ;(evalfentryin,7) ;(evalfreturnin,7) ;(evalfstart,7) ;(evalfstop,7)} Flow Graph: [0->{1},1->{2,3},2->{11},3->{4,5,6},4->{7,8},5->{7,8},6->{9,10},7->{2,3},8->{7,8},9->{2,3},10->{9,10} ,11->{}] + 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,G) -> evalfentryin(A,B,C,D,E,F,G) True (1,1) 1. evalfentryin(A,B,C,D,E,F,G) -> evalfbb5in(0,0,0,D,E,F,G) True (1,1) 2. evalfbb5in(A,B,C,D,E,F,G) -> evalfreturnin(A,B,C,D,E,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && C >= D] (1,1) 3. evalfbb5in(A,B,C,D,E,F,G) -> evalfbbin(A,B,C,D,1 + C,F,G) [C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && D >= 1 + C] (1 + 2*D,1) 4. evalfbbin(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 (1 + 2*D,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && 0 >= 1 + H] 5. evalfbbin(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,B,G) [D + -1*E >= 0 (1 + 2*D,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && H >= 1] 6. evalfbbin(A,B,C,D,E,F,G) -> evalfbb3in(A,B,C,D,E,A,G) [D + -1*E >= 0 (1 + 2*D,1) && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] 7. evalfbb1in(A,B,C,D,E,F,G) -> evalfbb5in(A,1 + F,E,D,E,F,G) [F >= 0 (D,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] 8. evalfbb1in(A,B,C,D,E,F,G) -> evalfbb1in(A,B,C,D,E,1 + F,G) [F >= 0 (G,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && -1*B + F >= 0 && A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] 9. evalfbb3in(A,B,C,D,E,F,G) -> evalfbb5in(1 + F,B,E,D,E,F,G) [F >= 0 (D,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && F >= G] 10. evalfbb3in(A,B,C,D,E,F,G) -> evalfbb3in(A,B,C,D,E,1 + F,G) [F >= 0 (G,1) && -1 + E + F >= 0 && -1 + D + F >= 0 && C + F >= 0 && B + F >= 0 && A + F >= 0 && -1*A + F >= 0 && D + -1*E >= 0 && 1 + C + -1*E >= 0 && -1 + E >= 0 && -2 + D + E >= 0 && -1 + C + E >= 0 && -1 + -1*C + E >= 0 && -1 + B + E >= 0 && -1 + A + E >= 0 && -1 + D >= 0 && -1 + C + D >= 0 && -1 + -1*C + D >= 0 && -1 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0 && G >= 1 + F] 11. evalfreturnin(A,B,C,D,E,F,G) -> evalfstop(A,B,C,D,E,F,G) [C + -1*D >= 0 && C >= 0 && B + C >= 0 && A + C >= 0 && B >= 0 && A + B >= 0 && A >= 0] (1,1) Signature: {(evalfbb1in,7) ;(evalfbb3in,7) ;(evalfbb5in,7) ;(evalfbbin,7) ;(evalfentryin,7) ;(evalfreturnin,7) ;(evalfstart,7) ;(evalfstop,7)} Flow Graph: [0->{1},1->{2,3},2->{11},3->{4,5,6},4->{7,8},5->{7,8},6->{9,10},7->{2,3},8->{7,8},9->{2,3},10->{9,10} ,11->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))