YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb3in(A,B,0,0) [A >= 1 && B >= 1 + A] (?,1) 2. evalfbb3in(A,B,C,D) -> evalfreturnin(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= B] 3. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] 4. evalfbb4in(A,B,C,D) -> evalfbbin(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + E] 5. evalfbb4in(A,B,C,D) -> evalfbbin(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1] 6. evalfbb4in(A,B,C,D) -> evalfreturnin(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 7. evalfbbin(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + C] 8. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= A] 9. evalfbb1in(A,B,C,D) -> evalfbb3in(A,B,1 + C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 10. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,0,1 + D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 11. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{2,3},2->{11},3->{4,5,6},4->{7,8},5->{7,8},6->{11},7->{9},8->{10},9->{2,3},10->{2,3},11->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,2),(9,2)] * Step 2: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True (1,1) 1. evalfentryin(A,B,C,D) -> evalfbb3in(A,B,0,0) [A >= 1 && B >= 1 + A] (?,1) 2. evalfbb3in(A,B,C,D) -> evalfreturnin(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= B] 3. evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] 4. evalfbb4in(A,B,C,D) -> evalfbbin(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + E] 5. evalfbb4in(A,B,C,D) -> evalfbbin(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1] 6. evalfbb4in(A,B,C,D) -> evalfreturnin(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 7. evalfbbin(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + C] 8. evalfbbin(A,B,C,D) -> evalfbb2in(A,B,C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= A] 9. evalfbb1in(A,B,C,D) -> evalfbb3in(A,B,1 + C,D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 10. evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,0,1 + D) [-1 + B + -1*D >= 0 (?,1) && D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 11. evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [D >= 0 (?,1) && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Flow Graph: [0->{1},1->{3},2->{11},3->{4,5,6},4->{7,8},5->{7,8},6->{11},7->{9},8->{10},9->{3},10->{2,3},11->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True evalfentryin(A,B,C,D) -> evalfbb3in(A,B,0,0) [A >= 1 && B >= 1 + A] evalfbb3in(A,B,C,D) -> evalfreturnin(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= B] evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] evalfbb4in(A,B,C,D) -> evalfbbin(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + E] evalfbb4in(A,B,C,D) -> evalfbbin(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1] evalfbb4in(A,B,C,D) -> evalfreturnin(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbbin(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + C] evalfbbin(A,B,C,D) -> evalfbb2in(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= A] evalfbb1in(A,B,C,D) -> evalfbb3in(A,B,1 + C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,0,1 + D) [-1 + B + -1*D >= 0 && D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4)} Rule Graph: [0->{1},1->{3},2->{11},3->{4,5,6},4->{7,8},5->{7,8},6->{11},7->{9},8->{10},9->{3},10->{2,3},11->{}] + Applied Processor: AddSinks + Details: () * Step 4: Unfold WORST_CASE(?,POLY) + Considered Problem: Rules: evalfstart(A,B,C,D) -> evalfentryin(A,B,C,D) True evalfentryin(A,B,C,D) -> evalfbb3in(A,B,0,0) [A >= 1 && B >= 1 + A] evalfbb3in(A,B,C,D) -> evalfreturnin(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= B] evalfbb3in(A,B,C,D) -> evalfbb4in(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] evalfbb4in(A,B,C,D) -> evalfbbin(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + E] evalfbb4in(A,B,C,D) -> evalfbbin(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1] evalfbb4in(A,B,C,D) -> evalfreturnin(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbbin(A,B,C,D) -> evalfbb1in(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + C] evalfbbin(A,B,C,D) -> evalfbb2in(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= A] evalfbb1in(A,B,C,D) -> evalfbb3in(A,B,1 + C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb2in(A,B,C,D) -> evalfbb3in(A,B,0,1 + D) [-1 + B + -1*D >= 0 && D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfreturnin(A,B,C,D) -> evalfstop(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfstop(A,B,C,D) -> exitus616(A,B,C,D) True evalfstop(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(evalfbb1in,4) ;(evalfbb2in,4) ;(evalfbb3in,4) ;(evalfbb4in,4) ;(evalfbbin,4) ;(evalfentryin,4) ;(evalfreturnin,4) ;(evalfstart,4) ;(evalfstop,4) ;(exitus616,4)} Rule Graph: [0->{1},1->{3},2->{11},3->{4,5,6},4->{7,8},5->{7,8},6->{11},7->{9},8->{10},9->{3},10->{2,3},11->{12,13}] + Applied Processor: Unfold + Details: () * Step 5: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: evalfstart.0(A,B,C,D) -> evalfentryin.1(A,B,C,D) True evalfentryin.1(A,B,C,D) -> evalfbb3in.3(A,B,0,0) [A >= 1 && B >= 1 + A] evalfbb3in.2(A,B,C,D) -> evalfreturnin.11(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= B] evalfbb3in.3(A,B,C,D) -> evalfbb4in.4(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] evalfbb3in.3(A,B,C,D) -> evalfbb4in.5(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] evalfbb3in.3(A,B,C,D) -> evalfbb4in.6(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] evalfbb4in.4(A,B,C,D) -> evalfbbin.7(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + E] evalfbb4in.4(A,B,C,D) -> evalfbbin.8(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + E] evalfbb4in.5(A,B,C,D) -> evalfbbin.7(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1] evalfbb4in.5(A,B,C,D) -> evalfbbin.8(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1] evalfbb4in.6(A,B,C,D) -> evalfreturnin.11(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbbin.7(A,B,C,D) -> evalfbb1in.9(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + C] evalfbbin.8(A,B,C,D) -> evalfbb2in.10(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= A] evalfbb1in.9(A,B,C,D) -> evalfbb3in.3(A,B,1 + C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb2in.10(A,B,C,D) -> evalfbb3in.2(A,B,0,1 + D) [-1 + B + -1*D >= 0 && D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb2in.10(A,B,C,D) -> evalfbb3in.3(A,B,0,1 + D) [-1 + B + -1*D >= 0 && D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfreturnin.11(A,B,C,D) -> evalfstop.12(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfreturnin.11(A,B,C,D) -> evalfstop.13(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfstop.12(A,B,C,D) -> exitus616.14(A,B,C,D) True evalfstop.13(A,B,C,D) -> exitus616.14(A,B,C,D) True Signature: {(evalfbb1in.9,4) ;(evalfbb2in.10,4) ;(evalfbb3in.2,4) ;(evalfbb3in.3,4) ;(evalfbb4in.4,4) ;(evalfbb4in.5,4) ;(evalfbb4in.6,4) ;(evalfbbin.7,4) ;(evalfbbin.8,4) ;(evalfentryin.1,4) ;(evalfreturnin.11,4) ;(evalfstart.0,4) ;(evalfstop.12,4) ;(evalfstop.13,4) ;(exitus616.14,4)} Rule Graph: [0->{1},1->{3,4,5},2->{16,17},3->{6,7},4->{8,9},5->{10},6->{11},7->{12},8->{11},9->{12},10->{16,17} ,11->{13},12->{14,15},13->{3,4,5},14->{2},15->{3,4,5},16->{18},17->{19},18->{},19->{}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] | `- p:[3,13,11,6,8,4,15,12,7,9] c: [7,9,12,15] | `- p:[3,13,11,6,8,4] c: [3,4,6,8,11,13] * Step 6: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: evalfstart.0(A,B,C,D) -> evalfentryin.1(A,B,C,D) True evalfentryin.1(A,B,C,D) -> evalfbb3in.3(A,B,0,0) [A >= 1 && B >= 1 + A] evalfbb3in.2(A,B,C,D) -> evalfreturnin.11(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= B] evalfbb3in.3(A,B,C,D) -> evalfbb4in.4(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] evalfbb3in.3(A,B,C,D) -> evalfbb4in.5(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] evalfbb3in.3(A,B,C,D) -> evalfbb4in.6(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && B >= 1 + D] evalfbb4in.4(A,B,C,D) -> evalfbbin.7(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + E] evalfbb4in.4(A,B,C,D) -> evalfbbin.8(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + E] evalfbb4in.5(A,B,C,D) -> evalfbbin.7(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1] evalfbb4in.5(A,B,C,D) -> evalfbbin.8(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1] evalfbb4in.6(A,B,C,D) -> evalfreturnin.11(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbbin.7(A,B,C,D) -> evalfbb1in.9(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && A >= 1 + C] evalfbbin.8(A,B,C,D) -> evalfbb2in.10(A,B,C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= A] evalfbb1in.9(A,B,C,D) -> evalfbb3in.3(A,B,1 + C,D) [-1 + B + -1*D >= 0 && D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B + -1*C >= 0 && -1 + A + -1*C >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb2in.10(A,B,C,D) -> evalfbb3in.2(A,B,0,1 + D) [-1 + B + -1*D >= 0 && D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfbb2in.10(A,B,C,D) -> evalfbb3in.3(A,B,0,1 + D) [-1 + B + -1*D >= 0 && D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -1 + C >= 0 && -3 + B + C >= 0 && -2 + A + C >= 0 && -1*A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfreturnin.11(A,B,C,D) -> evalfstop.12(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfreturnin.11(A,B,C,D) -> evalfstop.13(A,B,C,D) [D >= 0 && C + D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && C >= 0 && -2 + B + C >= 0 && -1 + A + C >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalfstop.12(A,B,C,D) -> exitus616.14(A,B,C,D) True evalfstop.13(A,B,C,D) -> exitus616.14(A,B,C,D) True Signature: {(evalfbb1in.9,4) ;(evalfbb2in.10,4) ;(evalfbb3in.2,4) ;(evalfbb3in.3,4) ;(evalfbb4in.4,4) ;(evalfbb4in.5,4) ;(evalfbb4in.6,4) ;(evalfbbin.7,4) ;(evalfbbin.8,4) ;(evalfentryin.1,4) ;(evalfreturnin.11,4) ;(evalfstart.0,4) ;(evalfstop.12,4) ;(evalfstop.13,4) ;(exitus616.14,4)} Rule Graph: [0->{1},1->{3,4,5},2->{16,17},3->{6,7},4->{8,9},5->{10},6->{11},7->{12},8->{11},9->{12},10->{16,17} ,11->{13},12->{14,15},13->{3,4,5},14->{2},15->{3,4,5},16->{18},17->{19},18->{},19->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19] | `- p:[3,13,11,6,8,4,15,12,7,9] c: [7,9,12,15] | `- p:[3,13,11,6,8,4] c: [3,4,6,8,11,13]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,0.0,0.0.0] evalfstart.0 ~> evalfentryin.1 [A <= A, B <= B, C <= C, D <= D] evalfentryin.1 ~> evalfbb3in.3 [A <= A, B <= B, C <= 0*K, D <= 0*K] evalfbb3in.2 ~> evalfreturnin.11 [A <= A, B <= B, C <= C, D <= D] evalfbb3in.3 ~> evalfbb4in.4 [A <= A, B <= B, C <= C, D <= D] evalfbb3in.3 ~> evalfbb4in.5 [A <= A, B <= B, C <= C, D <= D] evalfbb3in.3 ~> evalfbb4in.6 [A <= A, B <= B, C <= C, D <= D] evalfbb4in.4 ~> evalfbbin.7 [A <= A, B <= B, C <= C, D <= D] evalfbb4in.4 ~> evalfbbin.8 [A <= A, B <= B, C <= C, D <= D] evalfbb4in.5 ~> evalfbbin.7 [A <= A, B <= B, C <= C, D <= D] evalfbb4in.5 ~> evalfbbin.8 [A <= A, B <= B, C <= C, D <= D] evalfbb4in.6 ~> evalfreturnin.11 [A <= A, B <= B, C <= C, D <= D] evalfbbin.7 ~> evalfbb1in.9 [A <= A, B <= B, C <= C, D <= D] evalfbbin.8 ~> evalfbb2in.10 [A <= A, B <= B, C <= C, D <= D] evalfbb1in.9 ~> evalfbb3in.3 [A <= A, B <= B, C <= B, D <= D] evalfbb2in.10 ~> evalfbb3in.2 [A <= A, B <= B, C <= 0*K, D <= B] evalfbb2in.10 ~> evalfbb3in.3 [A <= A, B <= B, C <= 0*K, D <= B] evalfreturnin.11 ~> evalfstop.12 [A <= A, B <= B, C <= C, D <= D] evalfreturnin.11 ~> evalfstop.13 [A <= A, B <= B, C <= C, D <= D] evalfstop.12 ~> exitus616.14 [A <= A, B <= B, C <= C, D <= D] evalfstop.13 ~> exitus616.14 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= B + D] evalfbb3in.3 ~> evalfbb4in.4 [A <= A, B <= B, C <= C, D <= D] evalfbb1in.9 ~> evalfbb3in.3 [A <= A, B <= B, C <= B, D <= D] evalfbbin.7 ~> evalfbb1in.9 [A <= A, B <= B, C <= C, D <= D] evalfbb4in.4 ~> evalfbbin.7 [A <= A, B <= B, C <= C, D <= D] evalfbb4in.5 ~> evalfbbin.7 [A <= A, B <= B, C <= C, D <= D] evalfbb3in.3 ~> evalfbb4in.5 [A <= A, B <= B, C <= C, D <= D] evalfbb2in.10 ~> evalfbb3in.3 [A <= A, B <= B, C <= 0*K, D <= B] evalfbbin.8 ~> evalfbb2in.10 [A <= A, B <= B, C <= C, D <= D] evalfbb4in.4 ~> evalfbbin.8 [A <= A, B <= B, C <= C, D <= D] evalfbb4in.5 ~> evalfbbin.8 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0.0 <= 2*K + B + C] evalfbb3in.3 ~> evalfbb4in.4 [A <= A, B <= B, C <= C, D <= D] evalfbb1in.9 ~> evalfbb3in.3 [A <= A, B <= B, C <= B, D <= D] evalfbbin.7 ~> evalfbb1in.9 [A <= A, B <= B, C <= C, D <= D] evalfbb4in.4 ~> evalfbbin.7 [A <= A, B <= B, C <= C, D <= D] evalfbb4in.5 ~> evalfbbin.7 [A <= A, B <= B, C <= C, D <= D] evalfbb3in.3 ~> evalfbb4in.5 [A <= A, B <= B, C <= C, D <= D] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0,0.0.0] evalfstart.0 ~> evalfentryin.1 [] evalfentryin.1 ~> evalfbb3in.3 [K ~=> C,K ~=> D] evalfbb3in.2 ~> evalfreturnin.11 [] evalfbb3in.3 ~> evalfbb4in.4 [] evalfbb3in.3 ~> evalfbb4in.5 [] evalfbb3in.3 ~> evalfbb4in.6 [] evalfbb4in.4 ~> evalfbbin.7 [] evalfbb4in.4 ~> evalfbbin.8 [] evalfbb4in.5 ~> evalfbbin.7 [] evalfbb4in.5 ~> evalfbbin.8 [] evalfbb4in.6 ~> evalfreturnin.11 [] evalfbbin.7 ~> evalfbb1in.9 [] evalfbbin.8 ~> evalfbb2in.10 [] evalfbb1in.9 ~> evalfbb3in.3 [B ~=> C] evalfbb2in.10 ~> evalfbb3in.2 [B ~=> D,K ~=> C] evalfbb2in.10 ~> evalfbb3in.3 [B ~=> D,K ~=> C] evalfreturnin.11 ~> evalfstop.12 [] evalfreturnin.11 ~> evalfstop.13 [] evalfstop.12 ~> exitus616.14 [] evalfstop.13 ~> exitus616.14 [] + Loop: [B ~+> 0.0,D ~+> 0.0] evalfbb3in.3 ~> evalfbb4in.4 [] evalfbb1in.9 ~> evalfbb3in.3 [B ~=> C] evalfbbin.7 ~> evalfbb1in.9 [] evalfbb4in.4 ~> evalfbbin.7 [] evalfbb4in.5 ~> evalfbbin.7 [] evalfbb3in.3 ~> evalfbb4in.5 [] evalfbb2in.10 ~> evalfbb3in.3 [B ~=> D,K ~=> C] evalfbbin.8 ~> evalfbb2in.10 [] evalfbb4in.4 ~> evalfbbin.8 [] evalfbb4in.5 ~> evalfbbin.8 [] + Loop: [B ~+> 0.0.0,C ~+> 0.0.0,K ~*> 0.0.0] evalfbb3in.3 ~> evalfbb4in.4 [] evalfbb1in.9 ~> evalfbb3in.3 [B ~=> C] evalfbbin.7 ~> evalfbb1in.9 [] evalfbb4in.4 ~> evalfbbin.7 [] evalfbb4in.5 ~> evalfbbin.7 [] evalfbb3in.3 ~> evalfbb4in.5 [] + Applied Processor: Lare + Details: evalfstart.0 ~> exitus616.14 [B ~=> C ,B ~=> D ,K ~=> C ,K ~=> D ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> 0.0 ,B ~*> 0.0.0 ,B ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + evalfbb3in.3> [B ~=> C ,B ~=> D ,K ~=> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> 0.0.0 ,B ~*> tick ,C ~*> tick ,D ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] evalfbb2in.10> [B ~=> C ,B ~=> D ,K ~=> C ,B ~+> 0.0 ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> tick ,B ~*> 0.0.0 ,B ~*> tick ,C ~*> tick ,D ~*> tick ,K ~*> 0.0.0 ,K ~*> tick] + evalfbb4in.4> [B ~=> C ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~*> 0.0.0 ,K ~*> tick] evalfbb4in.5> [B ~=> C ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~*> 0.0.0 ,K ~*> tick] evalfbb3in.3> [B ~=> C ,B ~+> 0.0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~*> 0.0.0 ,K ~*> tick] YES(?,POLY)