YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalinsertsortstart(A,B,C,D) -> evalinsertsortentryin(A,B,C,D) True (1,1) 1. evalinsertsortentryin(A,B,C,D) -> evalinsertsortbb5in(1,B,C,D) True (?,1) 2. evalinsertsortbb5in(A,B,C,D) -> evalinsertsortbbin(A,B,C,D) [-1 + A >= 0 && B >= 1 + A] (?,1) 3. evalinsertsortbb5in(A,B,C,D) -> evalinsertsortreturnin(A,B,C,D) [-1 + A >= 0 && A >= B] (?,1) 4. evalinsertsortbbin(A,B,C,D) -> evalinsertsortbb2in(A,B,E,-1 + A) [-2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] (?,1) 5. evalinsertsortbb2in(A,B,C,D) -> evalinsertsortbb4in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + D] 6. evalinsertsortbb2in(A,B,C,D) -> evalinsertsortbb3in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= 0] 7. evalinsertsortbb3in(A,B,C,D) -> evalinsertsortbb1in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1 + C] 8. evalinsertsortbb3in(A,B,C,D) -> evalinsertsortbb4in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= E] 9. evalinsertsortbb1in(A,B,C,D) -> evalinsertsortbb2in(A,B,C,-1 + D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 10. evalinsertsortbb4in(A,B,C,D) -> evalinsertsortbb5in(1 + A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 11. evalinsertsortreturnin(A,B,C,D) -> evalinsertsortstop(A,B,C,D) [A + -1*B >= 0 && -1 + A >= 0] (?,1) Signature: {(evalinsertsortbb1in,4) ;(evalinsertsortbb2in,4) ;(evalinsertsortbb3in,4) ;(evalinsertsortbb4in,4) ;(evalinsertsortbb5in,4) ;(evalinsertsortbbin,4) ;(evalinsertsortentryin,4) ;(evalinsertsortreturnin,4) ;(evalinsertsortstart,4) ;(evalinsertsortstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{11},4->{5,6},5->{10},6->{7,8},7->{9},8->{10},9->{5,6},10->{2,3},11->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,5)] * Step 2: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalinsertsortstart(A,B,C,D) -> evalinsertsortentryin(A,B,C,D) True (1,1) 1. evalinsertsortentryin(A,B,C,D) -> evalinsertsortbb5in(1,B,C,D) True (?,1) 2. evalinsertsortbb5in(A,B,C,D) -> evalinsertsortbbin(A,B,C,D) [-1 + A >= 0 && B >= 1 + A] (?,1) 3. evalinsertsortbb5in(A,B,C,D) -> evalinsertsortreturnin(A,B,C,D) [-1 + A >= 0 && A >= B] (?,1) 4. evalinsertsortbbin(A,B,C,D) -> evalinsertsortbb2in(A,B,E,-1 + A) [-2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] (?,1) 5. evalinsertsortbb2in(A,B,C,D) -> evalinsertsortbb4in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + D] 6. evalinsertsortbb2in(A,B,C,D) -> evalinsertsortbb3in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= 0] 7. evalinsertsortbb3in(A,B,C,D) -> evalinsertsortbb1in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1 + C] 8. evalinsertsortbb3in(A,B,C,D) -> evalinsertsortbb4in(A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= E] 9. evalinsertsortbb1in(A,B,C,D) -> evalinsertsortbb2in(A,B,C,-1 + D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 10. evalinsertsortbb4in(A,B,C,D) -> evalinsertsortbb5in(1 + A,B,C,D) [-2 + B + -1*D >= 0 (?,1) && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] 11. evalinsertsortreturnin(A,B,C,D) -> evalinsertsortstop(A,B,C,D) [A + -1*B >= 0 && -1 + A >= 0] (?,1) Signature: {(evalinsertsortbb1in,4) ;(evalinsertsortbb2in,4) ;(evalinsertsortbb3in,4) ;(evalinsertsortbb4in,4) ;(evalinsertsortbb5in,4) ;(evalinsertsortbbin,4) ;(evalinsertsortentryin,4) ;(evalinsertsortreturnin,4) ;(evalinsertsortstart,4) ;(evalinsertsortstop,4)} Flow Graph: [0->{1},1->{2,3},2->{4},3->{11},4->{6},5->{10},6->{7,8},7->{9},8->{10},9->{5,6},10->{2,3},11->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: evalinsertsortstart(A,B,C,D) -> evalinsertsortentryin(A,B,C,D) True evalinsertsortentryin(A,B,C,D) -> evalinsertsortbb5in(1,B,C,D) True evalinsertsortbb5in(A,B,C,D) -> evalinsertsortbbin(A,B,C,D) [-1 + A >= 0 && B >= 1 + A] evalinsertsortbb5in(A,B,C,D) -> evalinsertsortreturnin(A,B,C,D) [-1 + A >= 0 && A >= B] evalinsertsortbbin(A,B,C,D) -> evalinsertsortbb2in(A,B,E,-1 + A) [-2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortbb2in(A,B,C,D) -> evalinsertsortbb4in(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + D] evalinsertsortbb2in(A,B,C,D) -> evalinsertsortbb3in(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= 0] evalinsertsortbb3in(A,B,C,D) -> evalinsertsortbb1in(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1 + C] evalinsertsortbb3in(A,B,C,D) -> evalinsertsortbb4in(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= E] evalinsertsortbb1in(A,B,C,D) -> evalinsertsortbb2in(A,B,C,-1 + D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortbb4in(A,B,C,D) -> evalinsertsortbb5in(1 + A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortreturnin(A,B,C,D) -> evalinsertsortstop(A,B,C,D) [A + -1*B >= 0 && -1 + A >= 0] Signature: {(evalinsertsortbb1in,4) ;(evalinsertsortbb2in,4) ;(evalinsertsortbb3in,4) ;(evalinsertsortbb4in,4) ;(evalinsertsortbb5in,4) ;(evalinsertsortbbin,4) ;(evalinsertsortentryin,4) ;(evalinsertsortreturnin,4) ;(evalinsertsortstart,4) ;(evalinsertsortstop,4)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{11},4->{6},5->{10},6->{7,8},7->{9},8->{10},9->{5,6},10->{2,3},11->{}] + Applied Processor: AddSinks + Details: () * Step 4: Unfold WORST_CASE(?,POLY) + Considered Problem: Rules: evalinsertsortstart(A,B,C,D) -> evalinsertsortentryin(A,B,C,D) True evalinsertsortentryin(A,B,C,D) -> evalinsertsortbb5in(1,B,C,D) True evalinsertsortbb5in(A,B,C,D) -> evalinsertsortbbin(A,B,C,D) [-1 + A >= 0 && B >= 1 + A] evalinsertsortbb5in(A,B,C,D) -> evalinsertsortreturnin(A,B,C,D) [-1 + A >= 0 && A >= B] evalinsertsortbbin(A,B,C,D) -> evalinsertsortbb2in(A,B,E,-1 + A) [-2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortbb2in(A,B,C,D) -> evalinsertsortbb4in(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + D] evalinsertsortbb2in(A,B,C,D) -> evalinsertsortbb3in(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= 0] evalinsertsortbb3in(A,B,C,D) -> evalinsertsortbb1in(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1 + C] evalinsertsortbb3in(A,B,C,D) -> evalinsertsortbb4in(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= E] evalinsertsortbb1in(A,B,C,D) -> evalinsertsortbb2in(A,B,C,-1 + D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortbb4in(A,B,C,D) -> evalinsertsortbb5in(1 + A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortreturnin(A,B,C,D) -> evalinsertsortstop(A,B,C,D) [A + -1*B >= 0 && -1 + A >= 0] evalinsertsortstop(A,B,C,D) -> exitus616(A,B,C,D) True Signature: {(evalinsertsortbb1in,4) ;(evalinsertsortbb2in,4) ;(evalinsertsortbb3in,4) ;(evalinsertsortbb4in,4) ;(evalinsertsortbb5in,4) ;(evalinsertsortbbin,4) ;(evalinsertsortentryin,4) ;(evalinsertsortreturnin,4) ;(evalinsertsortstart,4) ;(evalinsertsortstop,4) ;(exitus616,4)} Rule Graph: [0->{1},1->{2,3},2->{4},3->{11},4->{6},5->{10},6->{7,8},7->{9},8->{10},9->{5,6},10->{2,3},11->{12}] + Applied Processor: Unfold + Details: () * Step 5: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: evalinsertsortstart.0(A,B,C,D) -> evalinsertsortentryin.1(A,B,C,D) True evalinsertsortentryin.1(A,B,C,D) -> evalinsertsortbb5in.2(1,B,C,D) True evalinsertsortentryin.1(A,B,C,D) -> evalinsertsortbb5in.3(1,B,C,D) True evalinsertsortbb5in.2(A,B,C,D) -> evalinsertsortbbin.4(A,B,C,D) [-1 + A >= 0 && B >= 1 + A] evalinsertsortbb5in.3(A,B,C,D) -> evalinsertsortreturnin.11(A,B,C,D) [-1 + A >= 0 && A >= B] evalinsertsortbbin.4(A,B,C,D) -> evalinsertsortbb2in.6(A,B,E,-1 + A) [-2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortbb2in.5(A,B,C,D) -> evalinsertsortbb4in.10(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + D] evalinsertsortbb2in.6(A,B,C,D) -> evalinsertsortbb3in.7(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= 0] evalinsertsortbb2in.6(A,B,C,D) -> evalinsertsortbb3in.8(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= 0] evalinsertsortbb3in.7(A,B,C,D) -> evalinsertsortbb1in.9(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1 + C] evalinsertsortbb3in.8(A,B,C,D) -> evalinsertsortbb4in.10(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= E] evalinsertsortbb1in.9(A,B,C,D) -> evalinsertsortbb2in.5(A,B,C,-1 + D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortbb1in.9(A,B,C,D) -> evalinsertsortbb2in.6(A,B,C,-1 + D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortbb4in.10(A,B,C,D) -> evalinsertsortbb5in.2(1 + A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortbb4in.10(A,B,C,D) -> evalinsertsortbb5in.3(1 + A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortreturnin.11(A,B,C,D) -> evalinsertsortstop.12(A,B,C,D) [A + -1*B >= 0 && -1 + A >= 0] evalinsertsortstop.12(A,B,C,D) -> exitus616.13(A,B,C,D) True Signature: {(evalinsertsortbb1in.9,4) ;(evalinsertsortbb2in.5,4) ;(evalinsertsortbb2in.6,4) ;(evalinsertsortbb3in.7,4) ;(evalinsertsortbb3in.8,4) ;(evalinsertsortbb4in.10,4) ;(evalinsertsortbb5in.2,4) ;(evalinsertsortbb5in.3,4) ;(evalinsertsortbbin.4,4) ;(evalinsertsortentryin.1,4) ;(evalinsertsortreturnin.11,4) ;(evalinsertsortstart.0,4) ;(evalinsertsortstop.12,4) ;(exitus616.13,4)} Rule Graph: [0->{1,2},1->{3},2->{4},3->{5},4->{15},5->{7,8},6->{13,14},7->{9},8->{10},9->{11,12},10->{13,14},11->{6} ,12->{7,8},13->{3},14->{4},15->{16},16->{}] + 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] | `- p:[3,13,6,11,9,7,5,12,10,8] c: [3,5,6,8,10,11,13] | `- p:[7,12,9] c: [7,9,12] * Step 6: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: evalinsertsortstart.0(A,B,C,D) -> evalinsertsortentryin.1(A,B,C,D) True evalinsertsortentryin.1(A,B,C,D) -> evalinsertsortbb5in.2(1,B,C,D) True evalinsertsortentryin.1(A,B,C,D) -> evalinsertsortbb5in.3(1,B,C,D) True evalinsertsortbb5in.2(A,B,C,D) -> evalinsertsortbbin.4(A,B,C,D) [-1 + A >= 0 && B >= 1 + A] evalinsertsortbb5in.3(A,B,C,D) -> evalinsertsortreturnin.11(A,B,C,D) [-1 + A >= 0 && A >= B] evalinsertsortbbin.4(A,B,C,D) -> evalinsertsortbb2in.6(A,B,E,-1 + A) [-2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortbb2in.5(A,B,C,D) -> evalinsertsortbb4in.10(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && 0 >= 1 + D] evalinsertsortbb2in.6(A,B,C,D) -> evalinsertsortbb3in.7(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= 0] evalinsertsortbb2in.6(A,B,C,D) -> evalinsertsortbb3in.8(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && D >= 0] evalinsertsortbb3in.7(A,B,C,D) -> evalinsertsortbb1in.9(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && E >= 1 + C] evalinsertsortbb3in.8(A,B,C,D) -> evalinsertsortbb4in.10(A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0 && C >= E] evalinsertsortbb1in.9(A,B,C,D) -> evalinsertsortbb2in.5(A,B,C,-1 + D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortbb1in.9(A,B,C,D) -> evalinsertsortbb2in.6(A,B,C,-1 + D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && D >= 0 && -2 + B + D >= 0 && -1 + A + D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortbb4in.10(A,B,C,D) -> evalinsertsortbb5in.2(1 + A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortbb4in.10(A,B,C,D) -> evalinsertsortbb5in.3(1 + A,B,C,D) [-2 + B + -1*D >= 0 && -1 + A + -1*D >= 0 && -2 + B >= 0 && -3 + A + B >= 0 && -1 + -1*A + B >= 0 && -1 + A >= 0] evalinsertsortreturnin.11(A,B,C,D) -> evalinsertsortstop.12(A,B,C,D) [A + -1*B >= 0 && -1 + A >= 0] evalinsertsortstop.12(A,B,C,D) -> exitus616.13(A,B,C,D) True Signature: {(evalinsertsortbb1in.9,4) ;(evalinsertsortbb2in.5,4) ;(evalinsertsortbb2in.6,4) ;(evalinsertsortbb3in.7,4) ;(evalinsertsortbb3in.8,4) ;(evalinsertsortbb4in.10,4) ;(evalinsertsortbb5in.2,4) ;(evalinsertsortbb5in.3,4) ;(evalinsertsortbbin.4,4) ;(evalinsertsortentryin.1,4) ;(evalinsertsortreturnin.11,4) ;(evalinsertsortstart.0,4) ;(evalinsertsortstop.12,4) ;(exitus616.13,4)} Rule Graph: [0->{1,2},1->{3},2->{4},3->{5},4->{15},5->{7,8},6->{13,14},7->{9},8->{10},9->{11,12},10->{13,14},11->{6} ,12->{7,8},13->{3},14->{4},15->{16},16->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] | `- p:[3,13,6,11,9,7,5,12,10,8] c: [3,5,6,8,10,11,13] | `- p:[7,12,9] c: [7,9,12]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,0.0,0.0.0] evalinsertsortstart.0 ~> evalinsertsortentryin.1 [A <= A, B <= B, C <= C, D <= D] evalinsertsortentryin.1 ~> evalinsertsortbb5in.2 [A <= K, B <= B, C <= C, D <= D] evalinsertsortentryin.1 ~> evalinsertsortbb5in.3 [A <= K, B <= B, C <= C, D <= D] evalinsertsortbb5in.2 ~> evalinsertsortbbin.4 [A <= A, B <= B, C <= C, D <= D] evalinsertsortbb5in.3 ~> evalinsertsortreturnin.11 [A <= A, B <= B, C <= C, D <= D] evalinsertsortbbin.4 ~> evalinsertsortbb2in.6 [A <= A, B <= B, C <= unknown, D <= B] evalinsertsortbb2in.5 ~> evalinsertsortbb4in.10 [A <= A, B <= B, C <= C, D <= D] evalinsertsortbb2in.6 ~> evalinsertsortbb3in.7 [A <= A, B <= B, C <= C, D <= D] evalinsertsortbb2in.6 ~> evalinsertsortbb3in.8 [A <= A, B <= B, C <= C, D <= D] evalinsertsortbb3in.7 ~> evalinsertsortbb1in.9 [A <= A, B <= B, C <= C, D <= D] evalinsertsortbb3in.8 ~> evalinsertsortbb4in.10 [A <= A, B <= B, C <= C, D <= D] evalinsertsortbb1in.9 ~> evalinsertsortbb2in.5 [A <= A, B <= B, C <= C, D <= B] evalinsertsortbb1in.9 ~> evalinsertsortbb2in.6 [A <= A, B <= B, C <= C, D <= B] evalinsertsortbb4in.10 ~> evalinsertsortbb5in.2 [A <= B, B <= B, C <= C, D <= D] evalinsertsortbb4in.10 ~> evalinsertsortbb5in.3 [A <= B, B <= B, C <= C, D <= D] evalinsertsortreturnin.11 ~> evalinsertsortstop.12 [A <= A, B <= B, C <= C, D <= D] evalinsertsortstop.12 ~> exitus616.13 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= A + B] evalinsertsortbb5in.2 ~> evalinsertsortbbin.4 [A <= A, B <= B, C <= C, D <= D] evalinsertsortbb4in.10 ~> evalinsertsortbb5in.2 [A <= B, B <= B, C <= C, D <= D] evalinsertsortbb2in.5 ~> evalinsertsortbb4in.10 [A <= A, B <= B, C <= C, D <= D] evalinsertsortbb1in.9 ~> evalinsertsortbb2in.5 [A <= A, B <= B, C <= C, D <= B] evalinsertsortbb3in.7 ~> evalinsertsortbb1in.9 [A <= A, B <= B, C <= C, D <= D] evalinsertsortbb2in.6 ~> evalinsertsortbb3in.7 [A <= A, B <= B, C <= C, D <= D] evalinsertsortbbin.4 ~> evalinsertsortbb2in.6 [A <= A, B <= B, C <= unknown, D <= B] evalinsertsortbb1in.9 ~> evalinsertsortbb2in.6 [A <= A, B <= B, C <= C, D <= B] evalinsertsortbb3in.8 ~> evalinsertsortbb4in.10 [A <= A, B <= B, C <= C, D <= D] evalinsertsortbb2in.6 ~> evalinsertsortbb3in.8 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0.0 <= D] evalinsertsortbb2in.6 ~> evalinsertsortbb3in.7 [A <= A, B <= B, C <= C, D <= D] evalinsertsortbb1in.9 ~> evalinsertsortbb2in.6 [A <= A, B <= B, C <= C, D <= B] evalinsertsortbb3in.7 ~> evalinsertsortbb1in.9 [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] evalinsertsortstart.0 ~> evalinsertsortentryin.1 [] evalinsertsortentryin.1 ~> evalinsertsortbb5in.2 [K ~=> A] evalinsertsortentryin.1 ~> evalinsertsortbb5in.3 [K ~=> A] evalinsertsortbb5in.2 ~> evalinsertsortbbin.4 [] evalinsertsortbb5in.3 ~> evalinsertsortreturnin.11 [] evalinsertsortbbin.4 ~> evalinsertsortbb2in.6 [B ~=> D,huge ~=> C] evalinsertsortbb2in.5 ~> evalinsertsortbb4in.10 [] evalinsertsortbb2in.6 ~> evalinsertsortbb3in.7 [] evalinsertsortbb2in.6 ~> evalinsertsortbb3in.8 [] evalinsertsortbb3in.7 ~> evalinsertsortbb1in.9 [] evalinsertsortbb3in.8 ~> evalinsertsortbb4in.10 [] evalinsertsortbb1in.9 ~> evalinsertsortbb2in.5 [B ~=> D] evalinsertsortbb1in.9 ~> evalinsertsortbb2in.6 [B ~=> D] evalinsertsortbb4in.10 ~> evalinsertsortbb5in.2 [B ~=> A] evalinsertsortbb4in.10 ~> evalinsertsortbb5in.3 [B ~=> A] evalinsertsortreturnin.11 ~> evalinsertsortstop.12 [] evalinsertsortstop.12 ~> exitus616.13 [] + Loop: [A ~+> 0.0,B ~+> 0.0] evalinsertsortbb5in.2 ~> evalinsertsortbbin.4 [] evalinsertsortbb4in.10 ~> evalinsertsortbb5in.2 [B ~=> A] evalinsertsortbb2in.5 ~> evalinsertsortbb4in.10 [] evalinsertsortbb1in.9 ~> evalinsertsortbb2in.5 [B ~=> D] evalinsertsortbb3in.7 ~> evalinsertsortbb1in.9 [] evalinsertsortbb2in.6 ~> evalinsertsortbb3in.7 [] evalinsertsortbbin.4 ~> evalinsertsortbb2in.6 [B ~=> D,huge ~=> C] evalinsertsortbb1in.9 ~> evalinsertsortbb2in.6 [B ~=> D] evalinsertsortbb3in.8 ~> evalinsertsortbb4in.10 [] evalinsertsortbb2in.6 ~> evalinsertsortbb3in.8 [] + Loop: [D ~=> 0.0.0] evalinsertsortbb2in.6 ~> evalinsertsortbb3in.7 [] evalinsertsortbb1in.9 ~> evalinsertsortbb2in.6 [B ~=> D] evalinsertsortbb3in.7 ~> evalinsertsortbb1in.9 [] + Applied Processor: Lare + Details: evalinsertsortstart.0 ~> exitus616.13 [B ~=> A ,B ~=> D ,B ~=> 0.0.0 ,K ~=> A ,huge ~=> C ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,B ~*> tick ,K ~*> tick] + evalinsertsortbb4in.10> [B ~=> A ,B ~=> D ,B ~=> 0.0.0 ,huge ~=> C ,A ~+> 0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> tick ,tick ~+> tick ,A ~*> tick ,B ~*> tick] + evalinsertsortbb2in.6> [B ~=> D,D ~=> 0.0.0,D ~+> tick,tick ~+> tick] evalinsertsortbb1in.9> [B ~=> D,D ~=> 0.0.0,D ~+> tick,tick ~+> tick] YES(?,POLY)