YES(?,POLY) * Step 1: TrivialSCCs WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalEx4start(A,B,C,D) -> evalEx4entryin(A,B,C,D) True (1,1) 1. evalEx4entryin(A,B,C,D) -> evalEx4bb4in(1,A,C,D) True (?,1) 2. evalEx4bb4in(A,B,C,D) -> evalEx4bb2in(A,B,0,B) [A = 1] (?,1) 3. evalEx4bb4in(A,B,C,D) -> evalEx4returnin(A,B,C,D) [0 >= A] (?,1) 4. evalEx4bb4in(A,B,C,D) -> evalEx4returnin(A,B,C,D) [A >= 2] (?,1) 5. evalEx4bb2in(A,B,C,D) -> evalEx4bb4in(C,D,C,D) [B + -1*D >= 0 && C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && 0 >= D] (?,1) 6. evalEx4bb2in(A,B,C,D) -> evalEx4bb3in(A,B,C,D) [B + -1*D >= 0 && C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && D >= 1] (?,1) 7. evalEx4bb3in(A,B,C,D) -> evalEx4bb1in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && 0 >= 1 + E] 8. evalEx4bb3in(A,B,C,D) -> evalEx4bb1in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && E >= 1] 9. evalEx4bb3in(A,B,C,D) -> evalEx4bb4in(C,D,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0] 10. evalEx4bb1in(A,B,C,D) -> evalEx4bb2in(A,B,1,-1 + D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0] 11. evalEx4returnin(A,B,C,D) -> evalEx4stop(A,B,C,D) True (?,1) Signature: {(evalEx4bb1in,4) ;(evalEx4bb2in,4) ;(evalEx4bb3in,4) ;(evalEx4bb4in,4) ;(evalEx4entryin,4) ;(evalEx4returnin,4) ;(evalEx4start,4) ;(evalEx4stop,4)} Flow Graph: [0->{1},1->{2,3,4},2->{5,6},3->{11},4->{11},5->{2,3,4},6->{7,8,9},7->{10},8->{10},9->{2,3,4},10->{5,6} ,11->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalEx4start(A,B,C,D) -> evalEx4entryin(A,B,C,D) True (1,1) 1. evalEx4entryin(A,B,C,D) -> evalEx4bb4in(1,A,C,D) True (1,1) 2. evalEx4bb4in(A,B,C,D) -> evalEx4bb2in(A,B,0,B) [A = 1] (?,1) 3. evalEx4bb4in(A,B,C,D) -> evalEx4returnin(A,B,C,D) [0 >= A] (1,1) 4. evalEx4bb4in(A,B,C,D) -> evalEx4returnin(A,B,C,D) [A >= 2] (1,1) 5. evalEx4bb2in(A,B,C,D) -> evalEx4bb4in(C,D,C,D) [B + -1*D >= 0 && C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && 0 >= D] (?,1) 6. evalEx4bb2in(A,B,C,D) -> evalEx4bb3in(A,B,C,D) [B + -1*D >= 0 && C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && D >= 1] (?,1) 7. evalEx4bb3in(A,B,C,D) -> evalEx4bb1in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && 0 >= 1 + E] 8. evalEx4bb3in(A,B,C,D) -> evalEx4bb1in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && E >= 1] 9. evalEx4bb3in(A,B,C,D) -> evalEx4bb4in(C,D,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0] 10. evalEx4bb1in(A,B,C,D) -> evalEx4bb2in(A,B,1,-1 + D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0] 11. evalEx4returnin(A,B,C,D) -> evalEx4stop(A,B,C,D) True (1,1) Signature: {(evalEx4bb1in,4) ;(evalEx4bb2in,4) ;(evalEx4bb3in,4) ;(evalEx4bb4in,4) ;(evalEx4entryin,4) ;(evalEx4returnin,4) ;(evalEx4start,4) ;(evalEx4stop,4)} Flow Graph: [0->{1},1->{2,3,4},2->{5,6},3->{11},4->{11},5->{2,3,4},6->{7,8,9},7->{10},8->{10},9->{2,3,4},10->{5,6} ,11->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,3),(1,4)] * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalEx4start(A,B,C,D) -> evalEx4entryin(A,B,C,D) True (1,1) 1. evalEx4entryin(A,B,C,D) -> evalEx4bb4in(1,A,C,D) True (1,1) 2. evalEx4bb4in(A,B,C,D) -> evalEx4bb2in(A,B,0,B) [A = 1] (?,1) 3. evalEx4bb4in(A,B,C,D) -> evalEx4returnin(A,B,C,D) [0 >= A] (1,1) 4. evalEx4bb4in(A,B,C,D) -> evalEx4returnin(A,B,C,D) [A >= 2] (1,1) 5. evalEx4bb2in(A,B,C,D) -> evalEx4bb4in(C,D,C,D) [B + -1*D >= 0 && C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && 0 >= D] (?,1) 6. evalEx4bb2in(A,B,C,D) -> evalEx4bb3in(A,B,C,D) [B + -1*D >= 0 && C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && D >= 1] (?,1) 7. evalEx4bb3in(A,B,C,D) -> evalEx4bb1in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && 0 >= 1 + E] 8. evalEx4bb3in(A,B,C,D) -> evalEx4bb1in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && E >= 1] 9. evalEx4bb3in(A,B,C,D) -> evalEx4bb4in(C,D,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0] 10. evalEx4bb1in(A,B,C,D) -> evalEx4bb2in(A,B,1,-1 + D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0] 11. evalEx4returnin(A,B,C,D) -> evalEx4stop(A,B,C,D) True (1,1) Signature: {(evalEx4bb1in,4) ;(evalEx4bb2in,4) ;(evalEx4bb3in,4) ;(evalEx4bb4in,4) ;(evalEx4entryin,4) ;(evalEx4returnin,4) ;(evalEx4start,4) ;(evalEx4stop,4)} Flow Graph: [0->{1},1->{2},2->{5,6},3->{11},4->{11},5->{2,3,4},6->{7,8,9},7->{10},8->{10},9->{2,3,4},10->{5,6},11->{}] + Applied Processor: AddSinks + Details: () * Step 4: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalEx4start(A,B,C,D) -> evalEx4entryin(A,B,C,D) True (1,1) 1. evalEx4entryin(A,B,C,D) -> evalEx4bb4in(1,A,C,D) True (?,1) 2. evalEx4bb4in(A,B,C,D) -> evalEx4bb2in(A,B,0,B) [A = 1] (?,1) 3. evalEx4bb4in(A,B,C,D) -> evalEx4returnin(A,B,C,D) [0 >= A] (?,1) 4. evalEx4bb4in(A,B,C,D) -> evalEx4returnin(A,B,C,D) [A >= 2] (?,1) 5. evalEx4bb2in(A,B,C,D) -> evalEx4bb4in(C,D,C,D) [B + -1*D >= 0 && C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && 0 >= D] (?,1) 6. evalEx4bb2in(A,B,C,D) -> evalEx4bb3in(A,B,C,D) [B + -1*D >= 0 && C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && D >= 1] (?,1) 7. evalEx4bb3in(A,B,C,D) -> evalEx4bb1in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && 0 >= 1 + E] 8. evalEx4bb3in(A,B,C,D) -> evalEx4bb1in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && E >= 1] 9. evalEx4bb3in(A,B,C,D) -> evalEx4bb4in(C,D,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0] 10. evalEx4bb1in(A,B,C,D) -> evalEx4bb2in(A,B,1,-1 + D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0] 11. evalEx4returnin(A,B,C,D) -> evalEx4stop(A,B,C,D) True (?,1) 12. evalEx4returnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalEx4bb1in,4) ;(evalEx4bb2in,4) ;(evalEx4bb3in,4) ;(evalEx4bb4in,4) ;(evalEx4entryin,4) ;(evalEx4returnin,4) ;(evalEx4start,4) ;(evalEx4stop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2,3,4},2->{5,6},3->{11,12},4->{11,12},5->{2,3,4},6->{7,8,9},7->{10},8->{10},9->{2,3,4},10->{5 ,6},11->{},12->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(1,3),(1,4)] * Step 5: LooptreeTransformer WORST_CASE(?,POLY) + Considered Problem: Rules: 0. evalEx4start(A,B,C,D) -> evalEx4entryin(A,B,C,D) True (1,1) 1. evalEx4entryin(A,B,C,D) -> evalEx4bb4in(1,A,C,D) True (?,1) 2. evalEx4bb4in(A,B,C,D) -> evalEx4bb2in(A,B,0,B) [A = 1] (?,1) 3. evalEx4bb4in(A,B,C,D) -> evalEx4returnin(A,B,C,D) [0 >= A] (?,1) 4. evalEx4bb4in(A,B,C,D) -> evalEx4returnin(A,B,C,D) [A >= 2] (?,1) 5. evalEx4bb2in(A,B,C,D) -> evalEx4bb4in(C,D,C,D) [B + -1*D >= 0 && C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && 0 >= D] (?,1) 6. evalEx4bb2in(A,B,C,D) -> evalEx4bb3in(A,B,C,D) [B + -1*D >= 0 && C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && D >= 1] (?,1) 7. evalEx4bb3in(A,B,C,D) -> evalEx4bb1in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && 0 >= 1 + E] 8. evalEx4bb3in(A,B,C,D) -> evalEx4bb1in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && E >= 1] 9. evalEx4bb3in(A,B,C,D) -> evalEx4bb4in(C,D,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0] 10. evalEx4bb1in(A,B,C,D) -> evalEx4bb2in(A,B,1,-1 + D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0] 11. evalEx4returnin(A,B,C,D) -> evalEx4stop(A,B,C,D) True (?,1) 12. evalEx4returnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalEx4bb1in,4) ;(evalEx4bb2in,4) ;(evalEx4bb3in,4) ;(evalEx4bb4in,4) ;(evalEx4entryin,4) ;(evalEx4returnin,4) ;(evalEx4start,4) ;(evalEx4stop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2},2->{5,6},3->{11,12},4->{11,12},5->{2,3,4},6->{7,8,9},7->{10},8->{10},9->{2,3,4},10->{5,6} ,11->{},12->{}] + Applied Processor: LooptreeTransformer + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[2,5,10,7,6,8,9] c: [10] | `- p:[2,5,9,6] c: [9] | `- p:[2,5] c: [5] * Step 6: SizeAbstraction WORST_CASE(?,POLY) + Considered Problem: (Rules: 0. evalEx4start(A,B,C,D) -> evalEx4entryin(A,B,C,D) True (1,1) 1. evalEx4entryin(A,B,C,D) -> evalEx4bb4in(1,A,C,D) True (?,1) 2. evalEx4bb4in(A,B,C,D) -> evalEx4bb2in(A,B,0,B) [A = 1] (?,1) 3. evalEx4bb4in(A,B,C,D) -> evalEx4returnin(A,B,C,D) [0 >= A] (?,1) 4. evalEx4bb4in(A,B,C,D) -> evalEx4returnin(A,B,C,D) [A >= 2] (?,1) 5. evalEx4bb2in(A,B,C,D) -> evalEx4bb4in(C,D,C,D) [B + -1*D >= 0 && C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && 0 >= D] (?,1) 6. evalEx4bb2in(A,B,C,D) -> evalEx4bb3in(A,B,C,D) [B + -1*D >= 0 && C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && D >= 1] (?,1) 7. evalEx4bb3in(A,B,C,D) -> evalEx4bb1in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && 0 >= 1 + E] 8. evalEx4bb3in(A,B,C,D) -> evalEx4bb1in(A,B,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0 && E >= 1] 9. evalEx4bb3in(A,B,C,D) -> evalEx4bb4in(C,D,C,D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0] 10. evalEx4bb1in(A,B,C,D) -> evalEx4bb2in(A,B,1,-1 + D) [B + -1*D >= 0 (?,1) && -1 + D >= 0 && -1 + C + D >= 0 && -2 + B + D >= 0 && -2 + A + D >= 0 && -1*A + D >= 0 && C >= 0 && -1 + B + C >= 0 && -1 + A + C >= 0 && 1 + -1*A + C >= 0 && -1 + B >= 0 && -2 + A + B >= 0 && -1*A + B >= 0 && 1 + -1*A >= 0 && -1 + A >= 0] 11. evalEx4returnin(A,B,C,D) -> evalEx4stop(A,B,C,D) True (?,1) 12. evalEx4returnin(A,B,C,D) -> exitus616(A,B,C,D) True (?,1) Signature: {(evalEx4bb1in,4) ;(evalEx4bb2in,4) ;(evalEx4bb3in,4) ;(evalEx4bb4in,4) ;(evalEx4entryin,4) ;(evalEx4returnin,4) ;(evalEx4start,4) ;(evalEx4stop,4) ;(exitus616,4)} Flow Graph: [0->{1},1->{2},2->{5,6},3->{11,12},4->{11,12},5->{2,3,4},6->{7,8,9},7->{10},8->{10},9->{2,3,4},10->{5,6} ,11->{},12->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12] | `- p:[2,5,10,7,6,8,9] c: [10] | `- p:[2,5,9,6] c: [9] | `- p:[2,5] c: [5]) + Applied Processor: SizeAbstraction UseCFG Minimize + Details: () * Step 7: FlowAbstraction WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [A,B,C,D,0.0,0.0.0,0.0.0.0] evalEx4start ~> evalEx4entryin [A <= A, B <= B, C <= C, D <= D] evalEx4entryin ~> evalEx4bb4in [A <= K, B <= A, C <= C, D <= D] evalEx4bb4in ~> evalEx4bb2in [A <= A, B <= B, C <= 0*K, D <= B] evalEx4bb4in ~> evalEx4returnin [A <= A, B <= B, C <= C, D <= D] evalEx4bb4in ~> evalEx4returnin [A <= A, B <= B, C <= C, D <= D] evalEx4bb2in ~> evalEx4bb4in [A <= C, B <= D, C <= C, D <= D] evalEx4bb2in ~> evalEx4bb3in [A <= A, B <= B, C <= C, D <= D] evalEx4bb3in ~> evalEx4bb1in [A <= A, B <= B, C <= C, D <= D] evalEx4bb3in ~> evalEx4bb1in [A <= A, B <= B, C <= C, D <= D] evalEx4bb3in ~> evalEx4bb4in [A <= C, B <= D, C <= C, D <= D] evalEx4bb1in ~> evalEx4bb2in [A <= A, B <= B, C <= K, D <= D] evalEx4returnin ~> evalEx4stop [A <= A, B <= B, C <= C, D <= D] evalEx4returnin ~> exitus616 [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0 <= B + D] evalEx4bb4in ~> evalEx4bb2in [A <= A, B <= B, C <= 0*K, D <= B] evalEx4bb2in ~> evalEx4bb4in [A <= C, B <= D, C <= C, D <= D] evalEx4bb1in ~> evalEx4bb2in [A <= A, B <= B, C <= K, D <= D] evalEx4bb3in ~> evalEx4bb1in [A <= A, B <= B, C <= C, D <= D] evalEx4bb2in ~> evalEx4bb3in [A <= A, B <= B, C <= C, D <= D] evalEx4bb3in ~> evalEx4bb1in [A <= A, B <= B, C <= C, D <= D] evalEx4bb3in ~> evalEx4bb4in [A <= C, B <= D, C <= C, D <= D] + Loop: [0.0.0 <= A + C] evalEx4bb4in ~> evalEx4bb2in [A <= A, B <= B, C <= 0*K, D <= B] evalEx4bb2in ~> evalEx4bb4in [A <= C, B <= D, C <= C, D <= D] evalEx4bb3in ~> evalEx4bb4in [A <= C, B <= D, C <= C, D <= D] evalEx4bb2in ~> evalEx4bb3in [A <= A, B <= B, C <= C, D <= D] + Loop: [0.0.0.0 <= A + C] evalEx4bb4in ~> evalEx4bb2in [A <= A, B <= B, C <= 0*K, D <= B] evalEx4bb2in ~> evalEx4bb4in [A <= C, B <= D, C <= C, D <= D] + Applied Processor: FlowAbstraction + Details: () * Step 8: LareProcessor WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,A,B,C,D,0.0,0.0.0,0.0.0.0] evalEx4start ~> evalEx4entryin [] evalEx4entryin ~> evalEx4bb4in [A ~=> B,K ~=> A] evalEx4bb4in ~> evalEx4bb2in [B ~=> D,K ~=> C] evalEx4bb4in ~> evalEx4returnin [] evalEx4bb4in ~> evalEx4returnin [] evalEx4bb2in ~> evalEx4bb4in [C ~=> A,D ~=> B] evalEx4bb2in ~> evalEx4bb3in [] evalEx4bb3in ~> evalEx4bb1in [] evalEx4bb3in ~> evalEx4bb1in [] evalEx4bb3in ~> evalEx4bb4in [C ~=> A,D ~=> B] evalEx4bb1in ~> evalEx4bb2in [K ~=> C] evalEx4returnin ~> evalEx4stop [] evalEx4returnin ~> exitus616 [] + Loop: [B ~+> 0.0,D ~+> 0.0] evalEx4bb4in ~> evalEx4bb2in [B ~=> D,K ~=> C] evalEx4bb2in ~> evalEx4bb4in [C ~=> A,D ~=> B] evalEx4bb1in ~> evalEx4bb2in [K ~=> C] evalEx4bb3in ~> evalEx4bb1in [] evalEx4bb2in ~> evalEx4bb3in [] evalEx4bb3in ~> evalEx4bb1in [] evalEx4bb3in ~> evalEx4bb4in [C ~=> A,D ~=> B] + Loop: [A ~+> 0.0.0,C ~+> 0.0.0] evalEx4bb4in ~> evalEx4bb2in [B ~=> D,K ~=> C] evalEx4bb2in ~> evalEx4bb4in [C ~=> A,D ~=> B] evalEx4bb3in ~> evalEx4bb4in [C ~=> A,D ~=> B] evalEx4bb2in ~> evalEx4bb3in [] + Loop: [A ~+> 0.0.0.0,C ~+> 0.0.0.0] evalEx4bb4in ~> evalEx4bb2in [B ~=> D,K ~=> C] evalEx4bb2in ~> evalEx4bb4in [C ~=> A,D ~=> B] + Applied Processor: LareProcessor + Details: evalEx4start ~> exitus616 [A ~=> B ,A ~=> D ,C ~=> A ,D ~=> B ,K ~=> A ,K ~=> C ,A ~+> 0.0 ,A ~+> tick ,C ~+> 0.0.0 ,C ~+> 0.0.0.0 ,C ~+> tick ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> 0.0.0.0 ,K ~+> tick ,A ~*> tick ,C ~*> 0.0.0.0 ,C ~*> tick ,D ~*> tick ,K ~*> 0.0.0 ,K ~*> 0.0.0.0 ,K ~*> tick] evalEx4start ~> evalEx4stop [A ~=> B ,A ~=> D ,C ~=> A ,D ~=> B ,K ~=> A ,K ~=> C ,A ~+> 0.0 ,A ~+> tick ,C ~+> 0.0.0 ,C ~+> 0.0.0.0 ,C ~+> tick ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> 0.0.0.0 ,K ~+> tick ,A ~*> tick ,C ~*> 0.0.0.0 ,C ~*> tick ,D ~*> tick ,K ~*> 0.0.0 ,K ~*> 0.0.0.0 ,K ~*> tick] + evalEx4bb4in> [B ~=> D ,C ~=> A ,D ~=> B ,K ~=> A ,K ~=> C ,A ~+> 0.0.0 ,A ~+> 0.0.0.0 ,A ~+> tick ,B ~+> 0.0 ,B ~+> tick ,C ~+> 0.0.0 ,C ~+> 0.0.0.0 ,C ~+> tick ,D ~+> 0.0 ,D ~+> tick ,tick ~+> tick ,K ~+> 0.0.0 ,K ~+> 0.0.0.0 ,K ~+> tick ,A ~*> tick ,B ~*> tick ,C ~*> 0.0.0.0 ,C ~*> tick ,D ~*> tick ,K ~*> 0.0.0 ,K ~*> 0.0.0.0 ,K ~*> tick] + evalEx4bb4in> [B ~=> D ,C ~=> A ,D ~=> B ,K ~=> A ,K ~=> C ,A ~+> 0.0.0 ,A ~+> 0.0.0.0 ,A ~+> tick ,C ~+> 0.0.0 ,C ~+> 0.0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0.0.0 ,K ~+> tick ,A ~*> tick ,C ~*> 0.0.0.0 ,C ~*> tick ,K ~*> 0.0.0.0 ,K ~*> tick] evalEx4bb3in> [B ~=> D ,C ~=> A ,D ~=> B ,K ~=> A ,K ~=> C ,A ~+> 0.0.0 ,A ~+> 0.0.0.0 ,A ~+> tick ,C ~+> 0.0.0 ,C ~+> 0.0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0.0.0 ,K ~+> tick ,A ~*> tick ,C ~*> 0.0.0.0 ,C ~*> tick ,K ~*> 0.0.0.0 ,K ~*> tick] evalEx4bb4in> [B ~=> D ,C ~=> A ,D ~=> B ,K ~=> A ,K ~=> C ,A ~+> 0.0.0 ,A ~+> 0.0.0.0 ,A ~+> tick ,C ~+> 0.0.0 ,C ~+> 0.0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0.0.0 ,K ~+> tick ,A ~*> tick ,C ~*> 0.0.0.0 ,C ~*> tick ,K ~*> 0.0.0.0 ,K ~*> tick] evalEx4bb3in> [B ~=> D ,C ~=> A ,D ~=> B ,K ~=> A ,K ~=> C ,A ~+> 0.0.0 ,A ~+> 0.0.0.0 ,A ~+> tick ,C ~+> 0.0.0 ,C ~+> 0.0.0.0 ,C ~+> tick ,tick ~+> tick ,K ~+> 0.0.0.0 ,K ~+> tick ,A ~*> tick ,C ~*> 0.0.0.0 ,C ~*> tick ,K ~*> 0.0.0.0 ,K ~*> tick] + evalEx4bb2in> [C ~=> A ,D ~=> B ,K ~=> A ,K ~=> C ,A ~+> 0.0.0.0 ,A ~+> tick ,C ~+> 0.0.0.0 ,C ~+> tick ,tick ~+> tick] evalEx4bb4in> [C ~=> A ,D ~=> B ,K ~=> A ,K ~=> C ,A ~+> 0.0.0.0 ,A ~+> tick ,C ~+> 0.0.0.0 ,C ~+> tick ,tick ~+> tick] evalEx4bb2in> [B ~=> D ,K ~=> A ,K ~=> C ,A ~+> 0.0.0.0 ,A ~+> tick ,C ~+> 0.0.0.0 ,C ~+> tick ,tick ~+> tick] evalEx4bb4in> [B ~=> D ,K ~=> A ,K ~=> C ,A ~+> 0.0.0.0 ,A ~+> tick ,C ~+> 0.0.0.0 ,C ~+> tick ,tick ~+> tick] YES(?,POLY)