YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb5in(B,B,C,D) True (?,1) 2. evalfbb5in(A,B,C,D) -> evalfbbin(A,B,C,D) [B >= 2] (?,1) 3. evalfbb5in(A,B,C,D) -> evalfreturnin(A,B,C,D) [1 >= B] (?,1) 4. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,-1 + B,-1 + A + B) [-2 + B >= 0] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= 1 + D] (?,1) 6. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= C] (?,1) 7. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -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 + E] 8. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && E >= 1] 9. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 10. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,C,-1 + D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 11. evalfbb4in(A,B,C,D) -> evalfbb5in(1 + -1*C + D,-1 + C,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] (?,1) 12. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [1 + -1*B >= 0] (?,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb5in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{12},4->{5,6},5->{11},6->{7,8,9},7->{10},8->{10},9->{11},10->{5,6},11->{2,3} ,12->{}] + 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) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb5in(B,B,C,D) True (1,1) 2. evalfbb5in(A,B,C,D) -> evalfbbin(A,B,C,D) [B >= 2] (?,1) 3. evalfbb5in(A,B,C,D) -> evalfreturnin(A,B,C,D) [1 >= B] (1,1) 4. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,-1 + B,-1 + A + B) [-2 + B >= 0] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= 1 + D] (?,1) 6. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= C] (?,1) 7. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -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 + E] 8. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && E >= 1] 9. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 10. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,C,-1 + D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 11. evalfbb4in(A,B,C,D) -> evalfbb5in(1 + -1*C + D,-1 + C,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] (?,1) 12. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [1 + -1*B >= 0] (1,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb5in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{12},4->{5,6},5->{11},6->{7,8,9},7->{10},8->{10},9->{11},10->{5,6},11->{2,3} ,12->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb1in) = x3 p(evalfbb2in) = x3 p(evalfbb3in) = x3 p(evalfbb4in) = x3 p(evalfbb5in) = x2 p(evalfbbin) = -1 + x2 p(evalfentryin) = x2 p(evalfreturnin) = x2 p(evalfstart) = x2 p(evalfstop) = 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] ==> evalfbb4in(A,B,C,D) = C > -1 + C = evalfbb5in(1 + -1*C + D,-1 + C,C,D) Following rules are weakly oriented: True ==> evalfstart(A,B,C,D) = B >= B = evalfentryin(A,B,C,D) True ==> evalfentryin(A,B,C,D) = B >= B = evalfbb5in(B,B,C,D) [B >= 2] ==> evalfbb5in(A,B,C,D) = B >= -1 + B = evalfbbin(A,B,C,D) [1 >= B] ==> evalfbb5in(A,B,C,D) = B >= B = evalfreturnin(A,B,C,D) [-2 + B >= 0] ==> evalfbbin(A,B,C,D) = -1 + B >= -1 + B = evalfbb2in(A,B,-1 + B,-1 + A + B) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= 1 + D] ==> evalfbb2in(A,B,C,D) = C >= C = evalfbb4in(A,B,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= C] ==> evalfbb2in(A,B,C,D) = C >= C = evalfbb3in(A,B,C,D) [-1 + D >= 0 ==> && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -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 + E] evalfbb3in(A,B,C,D) = C >= C = evalfbb1in(A,B,C,D) [-1 + D >= 0 ==> && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && E >= 1] evalfbb3in(A,B,C,D) = C >= C = evalfbb1in(A,B,C,D) [-1 + D >= 0 ==> && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -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) = C >= C = evalfbb4in(A,B,C,D) [-1 + D >= 0 ==> && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -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) = C >= C = evalfbb2in(A,B,C,-1 + D) [1 + -1*B >= 0] ==> evalfreturnin(A,B,C,D) = B >= B = evalfstop(A,B,C,D) * Step 3: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb5in(B,B,C,D) True (1,1) 2. evalfbb5in(A,B,C,D) -> evalfbbin(A,B,C,D) [B >= 2] (?,1) 3. evalfbb5in(A,B,C,D) -> evalfreturnin(A,B,C,D) [1 >= B] (1,1) 4. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,-1 + B,-1 + A + B) [-2 + B >= 0] (?,1) 5. evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= 1 + D] (?,1) 6. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= C] (?,1) 7. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -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 + E] 8. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && E >= 1] 9. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 10. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,C,-1 + D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 11. evalfbb4in(A,B,C,D) -> evalfbb5in(1 + -1*C + D,-1 + C,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] (B,1) 12. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [1 + -1*B >= 0] (1,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb5in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{12},4->{5,6},5->{11},6->{7,8,9},7->{10},8->{10},9->{11},10->{5,6},11->{2,3} ,12->{}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb5in(B,B,C,D) True (1,1) 2. evalfbb5in(A,B,C,D) -> evalfbbin(A,B,C,D) [B >= 2] (1 + B,1) 3. evalfbb5in(A,B,C,D) -> evalfreturnin(A,B,C,D) [1 >= B] (1,1) 4. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,-1 + B,-1 + A + B) [-2 + B >= 0] (1 + B,1) 5. evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= 1 + D] (?,1) 6. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= C] (?,1) 7. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -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 + E] 8. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && E >= 1] 9. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 10. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,C,-1 + D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 11. evalfbb4in(A,B,C,D) -> evalfbb5in(1 + -1*C + D,-1 + C,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] (B,1) 12. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [1 + -1*B >= 0] (1,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb5in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{12},4->{5,6},5->{11},6->{7,8,9},7->{10},8->{10},9->{11},10->{5,6},11->{2,3} ,12->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(evalfbb1in) = x4 p(evalfbb2in) = x4 p(evalfbb3in) = x4 p(evalfbb4in) = x4 p(evalfbb5in) = 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: [-1 + D >= 0 ==> && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -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) = D > -1 + D = evalfbb2in(A,B,C,-1 + D) Following rules are weakly oriented: True ==> evalfstart(A,B,C,D) = 2*B >= 2*B = evalfentryin(A,B,C,D) True ==> evalfentryin(A,B,C,D) = 2*B >= 2*B = evalfbb5in(B,B,C,D) [B >= 2] ==> evalfbb5in(A,B,C,D) = A + B >= A + B = evalfbbin(A,B,C,D) [1 >= B] ==> evalfbb5in(A,B,C,D) = A + B >= A + B = evalfreturnin(A,B,C,D) [-2 + B >= 0] ==> evalfbbin(A,B,C,D) = A + B >= -1 + A + B = evalfbb2in(A,B,-1 + B,-1 + A + B) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= 1 + D] ==> evalfbb2in(A,B,C,D) = D >= D = evalfbb4in(A,B,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= C] ==> evalfbb2in(A,B,C,D) = D >= D = evalfbb3in(A,B,C,D) [-1 + D >= 0 ==> && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -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 + E] evalfbb3in(A,B,C,D) = D >= D = evalfbb1in(A,B,C,D) [-1 + D >= 0 ==> && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && E >= 1] evalfbb3in(A,B,C,D) = D >= D = evalfbb1in(A,B,C,D) [-1 + D >= 0 ==> && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -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) = D >= D = evalfbb4in(A,B,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] ==> evalfbb4in(A,B,C,D) = D >= D = evalfbb5in(1 + -1*C + D,-1 + C,C,D) [1 + -1*B >= 0] ==> evalfreturnin(A,B,C,D) = A + B >= A + B = evalfstop(A,B,C,D) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb5in(B,B,C,D) True (1,1) 2. evalfbb5in(A,B,C,D) -> evalfbbin(A,B,C,D) [B >= 2] (1 + B,1) 3. evalfbb5in(A,B,C,D) -> evalfreturnin(A,B,C,D) [1 >= B] (1,1) 4. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,-1 + B,-1 + A + B) [-2 + B >= 0] (1 + B,1) 5. evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= 1 + D] (?,1) 6. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= C] (?,1) 7. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -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 + E] 8. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && E >= 1] 9. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + D >= 0 (?,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 10. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,C,-1 + D) [-1 + D >= 0 (2*B,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 11. evalfbb4in(A,B,C,D) -> evalfbb5in(1 + -1*C + D,-1 + C,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] (B,1) 12. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [1 + -1*B >= 0] (1,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb5in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{12},4->{5,6},5->{11},6->{7,8,9},7->{10},8->{10},9->{11},10->{5,6},11->{2,3} ,12->{}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb5in(B,B,C,D) True (1,1) 2. evalfbb5in(A,B,C,D) -> evalfbbin(A,B,C,D) [B >= 2] (1 + B,1) 3. evalfbb5in(A,B,C,D) -> evalfreturnin(A,B,C,D) [1 >= B] (1,1) 4. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,-1 + B,-1 + A + B) [-2 + B >= 0] (1 + B,1) 5. evalfbb2in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && C >= 1 + D] (1 + 3*B,1) 6. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && D >= C] (1 + 3*B,1) 7. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + D >= 0 (1 + 3*B,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -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 + E] 8. evalfbb3in(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + D >= 0 (1 + 3*B,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0 && E >= 1] 9. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [-1 + D >= 0 (1 + 3*B,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 10. evalfbb1in(A,B,C,D) -> evalfbb2in(A,B,C,-1 + D) [-1 + D >= 0 (2*B,1) && -2 + C + D >= 0 && -1*C + D >= 0 && -3 + B + D >= 0 && 1 + -1*B + D >= 0 && -1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] 11. evalfbb4in(A,B,C,D) -> evalfbb5in(1 + -1*C + D,-1 + C,C,D) [-1 + B + -1*C >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && 1 + -1*B + C >= 0 && -2 + B >= 0] (B,1) 12. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [1 + -1*B >= 0] (1,1) Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbb5in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{12},4->{5,6},5->{11},6->{7,8,9},7->{10},8->{10},9->{11},10->{5,6},11->{2,3} ,12->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))