YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_random1d_start(v_2,v_max,v_x_0) -> eval_random1d_bb0_in(v_2,v_max,v_x_0) True (1,1) 1. eval_random1d_bb0_in(v_2,v_max,v_x_0) -> eval_random1d_0(v_2,v_max,v_x_0) True (?,1) 2. eval_random1d_0(v_2,v_max,v_x_0) -> eval_random1d_1(v_2,v_max,v_x_0) True (?,1) 3. eval_random1d_1(v_2,v_max,v_x_0) -> eval_random1d_bb1_in(v_2,v_max,1) [-1 + v_max >= 0] (?,1) 4. eval_random1d_1(v_2,v_max,v_x_0) -> eval_random1d_bb3_in(v_2,v_max,v_x_0) [0 >= v_max] (?,1) 5. eval_random1d_bb1_in(v_2,v_max,v_x_0) -> eval_random1d_bb2_in(v_2,v_max,v_x_0) [-1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && v_max >= v_x_0] (?,1) 6. eval_random1d_bb1_in(v_2,v_max,v_x_0) -> eval_random1d_bb3_in(v_2,v_max,v_x_0) [-1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && -1 + v_x_0 >= v_max] (?,1) 7. eval_random1d_bb2_in(v_2,v_max,v_x_0) -> eval_random1d_2(v_2,v_max,v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0] (?,1) 8. eval_random1d_2(v_2,v_max,v_x_0) -> eval_random1d_3(nondef_0,v_max,v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0] (?,1) 9. eval_random1d_3(v_2,v_max,v_x_0) -> eval_random1d_bb1_in(v_2,v_max,1 + v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && -1 + v_2 >= 0] (?,1) 10. eval_random1d_3(v_2,v_max,v_x_0) -> eval_random1d_bb1_in(v_2,v_max,1 + v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && 0 >= v_2] (?,1) 11. eval_random1d_bb3_in(v_2,v_max,v_x_0) -> eval_random1d_stop(v_2,v_max,v_x_0) True (?,1) Signature: {(eval_random1d_0,3) ;(eval_random1d_1,3) ;(eval_random1d_2,3) ;(eval_random1d_3,3) ;(eval_random1d_bb0_in,3) ;(eval_random1d_bb1_in,3) ;(eval_random1d_bb2_in,3) ;(eval_random1d_bb3_in,3) ;(eval_random1d_start,3) ;(eval_random1d_stop,3)} Flow Graph: [0->{1},1->{2},2->{3,4},3->{5,6},4->{11},5->{7},6->{11},7->{8},8->{9,10},9->{5,6},10->{5,6},11->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(3,6)] * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_random1d_start(v_2,v_max,v_x_0) -> eval_random1d_bb0_in(v_2,v_max,v_x_0) True (1,1) 1. eval_random1d_bb0_in(v_2,v_max,v_x_0) -> eval_random1d_0(v_2,v_max,v_x_0) True (?,1) 2. eval_random1d_0(v_2,v_max,v_x_0) -> eval_random1d_1(v_2,v_max,v_x_0) True (?,1) 3. eval_random1d_1(v_2,v_max,v_x_0) -> eval_random1d_bb1_in(v_2,v_max,1) [-1 + v_max >= 0] (?,1) 4. eval_random1d_1(v_2,v_max,v_x_0) -> eval_random1d_bb3_in(v_2,v_max,v_x_0) [0 >= v_max] (?,1) 5. eval_random1d_bb1_in(v_2,v_max,v_x_0) -> eval_random1d_bb2_in(v_2,v_max,v_x_0) [-1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && v_max >= v_x_0] (?,1) 6. eval_random1d_bb1_in(v_2,v_max,v_x_0) -> eval_random1d_bb3_in(v_2,v_max,v_x_0) [-1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && -1 + v_x_0 >= v_max] (?,1) 7. eval_random1d_bb2_in(v_2,v_max,v_x_0) -> eval_random1d_2(v_2,v_max,v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0] (?,1) 8. eval_random1d_2(v_2,v_max,v_x_0) -> eval_random1d_3(nondef_0,v_max,v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0] (?,1) 9. eval_random1d_3(v_2,v_max,v_x_0) -> eval_random1d_bb1_in(v_2,v_max,1 + v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && -1 + v_2 >= 0] (?,1) 10. eval_random1d_3(v_2,v_max,v_x_0) -> eval_random1d_bb1_in(v_2,v_max,1 + v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && 0 >= v_2] (?,1) 11. eval_random1d_bb3_in(v_2,v_max,v_x_0) -> eval_random1d_stop(v_2,v_max,v_x_0) True (?,1) Signature: {(eval_random1d_0,3) ;(eval_random1d_1,3) ;(eval_random1d_2,3) ;(eval_random1d_3,3) ;(eval_random1d_bb0_in,3) ;(eval_random1d_bb1_in,3) ;(eval_random1d_bb2_in,3) ;(eval_random1d_bb3_in,3) ;(eval_random1d_start,3) ;(eval_random1d_stop,3)} Flow Graph: [0->{1},1->{2},2->{3,4},3->{5},4->{11},5->{7},6->{11},7->{8},8->{9,10},9->{5,6},10->{5,6},11->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: eval_random1d_start(v_2,v_max,v_x_0) -> eval_random1d_bb0_in(v_2,v_max,v_x_0) True eval_random1d_bb0_in(v_2,v_max,v_x_0) -> eval_random1d_0(v_2,v_max,v_x_0) True eval_random1d_0(v_2,v_max,v_x_0) -> eval_random1d_1(v_2,v_max,v_x_0) True eval_random1d_1(v_2,v_max,v_x_0) -> eval_random1d_bb1_in(v_2,v_max,1) [-1 + v_max >= 0] eval_random1d_1(v_2,v_max,v_x_0) -> eval_random1d_bb3_in(v_2,v_max,v_x_0) [0 >= v_max] eval_random1d_bb1_in(v_2,v_max,v_x_0) -> eval_random1d_bb2_in(v_2,v_max,v_x_0) [-1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && v_max >= v_x_0] eval_random1d_bb1_in(v_2,v_max,v_x_0) -> eval_random1d_bb3_in(v_2,v_max,v_x_0) [-1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && -1 + v_x_0 >= v_max] eval_random1d_bb2_in(v_2,v_max,v_x_0) -> eval_random1d_2(v_2,v_max,v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0] eval_random1d_2(v_2,v_max,v_x_0) -> eval_random1d_3(nondef_0,v_max,v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0] eval_random1d_3(v_2,v_max,v_x_0) -> eval_random1d_bb1_in(v_2,v_max,1 + v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && -1 + v_2 >= 0] eval_random1d_3(v_2,v_max,v_x_0) -> eval_random1d_bb1_in(v_2,v_max,1 + v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && 0 >= v_2] eval_random1d_bb3_in(v_2,v_max,v_x_0) -> eval_random1d_stop(v_2,v_max,v_x_0) True Signature: {(eval_random1d_0,3) ;(eval_random1d_1,3) ;(eval_random1d_2,3) ;(eval_random1d_3,3) ;(eval_random1d_bb0_in,3) ;(eval_random1d_bb1_in,3) ;(eval_random1d_bb2_in,3) ;(eval_random1d_bb3_in,3) ;(eval_random1d_start,3) ;(eval_random1d_stop,3)} Rule Graph: [0->{1},1->{2},2->{3,4},3->{5},4->{11},5->{7},6->{11},7->{8},8->{9,10},9->{5,6},10->{5,6},11->{}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: eval_random1d_start(v_2,v_max,v_x_0) -> eval_random1d_bb0_in(v_2,v_max,v_x_0) True eval_random1d_bb0_in(v_2,v_max,v_x_0) -> eval_random1d_0(v_2,v_max,v_x_0) True eval_random1d_0(v_2,v_max,v_x_0) -> eval_random1d_1(v_2,v_max,v_x_0) True eval_random1d_1(v_2,v_max,v_x_0) -> eval_random1d_bb1_in(v_2,v_max,1) [-1 + v_max >= 0] eval_random1d_1(v_2,v_max,v_x_0) -> eval_random1d_bb3_in(v_2,v_max,v_x_0) [0 >= v_max] eval_random1d_bb1_in(v_2,v_max,v_x_0) -> eval_random1d_bb2_in(v_2,v_max,v_x_0) [-1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && v_max >= v_x_0] eval_random1d_bb1_in(v_2,v_max,v_x_0) -> eval_random1d_bb3_in(v_2,v_max,v_x_0) [-1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && -1 + v_x_0 >= v_max] eval_random1d_bb2_in(v_2,v_max,v_x_0) -> eval_random1d_2(v_2,v_max,v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0] eval_random1d_2(v_2,v_max,v_x_0) -> eval_random1d_3(nondef_0,v_max,v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0] eval_random1d_3(v_2,v_max,v_x_0) -> eval_random1d_bb1_in(v_2,v_max,1 + v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && -1 + v_2 >= 0] eval_random1d_3(v_2,v_max,v_x_0) -> eval_random1d_bb1_in(v_2,v_max,1 + v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && 0 >= v_2] eval_random1d_bb3_in(v_2,v_max,v_x_0) -> eval_random1d_stop(v_2,v_max,v_x_0) True eval_random1d_stop(v_2,v_max,v_x_0) -> exitus616(v_2,v_max,v_x_0) True eval_random1d_stop(v_2,v_max,v_x_0) -> exitus616(v_2,v_max,v_x_0) True Signature: {(eval_random1d_0,3) ;(eval_random1d_1,3) ;(eval_random1d_2,3) ;(eval_random1d_3,3) ;(eval_random1d_bb0_in,3) ;(eval_random1d_bb1_in,3) ;(eval_random1d_bb2_in,3) ;(eval_random1d_bb3_in,3) ;(eval_random1d_start,3) ;(eval_random1d_stop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2},2->{3,4},3->{5},4->{11},5->{7},6->{11},7->{8},8->{9,10},9->{5,6},10->{5,6},11->{12,13}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[5,9,8,7,10] c: [5,7,8,9,10] * Step 5: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: eval_random1d_start(v_2,v_max,v_x_0) -> eval_random1d_bb0_in(v_2,v_max,v_x_0) True eval_random1d_bb0_in(v_2,v_max,v_x_0) -> eval_random1d_0(v_2,v_max,v_x_0) True eval_random1d_0(v_2,v_max,v_x_0) -> eval_random1d_1(v_2,v_max,v_x_0) True eval_random1d_1(v_2,v_max,v_x_0) -> eval_random1d_bb1_in(v_2,v_max,1) [-1 + v_max >= 0] eval_random1d_1(v_2,v_max,v_x_0) -> eval_random1d_bb3_in(v_2,v_max,v_x_0) [0 >= v_max] eval_random1d_bb1_in(v_2,v_max,v_x_0) -> eval_random1d_bb2_in(v_2,v_max,v_x_0) [-1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && v_max >= v_x_0] eval_random1d_bb1_in(v_2,v_max,v_x_0) -> eval_random1d_bb3_in(v_2,v_max,v_x_0) [-1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && -1 + v_x_0 >= v_max] eval_random1d_bb2_in(v_2,v_max,v_x_0) -> eval_random1d_2(v_2,v_max,v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0] eval_random1d_2(v_2,v_max,v_x_0) -> eval_random1d_3(nondef_0,v_max,v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0] eval_random1d_3(v_2,v_max,v_x_0) -> eval_random1d_bb1_in(v_2,v_max,1 + v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && -1 + v_2 >= 0] eval_random1d_3(v_2,v_max,v_x_0) -> eval_random1d_bb1_in(v_2,v_max,1 + v_x_0) [v_max + -1*v_x_0 >= 0 && -1 + v_x_0 >= 0 && -2 + v_max + v_x_0 >= 0 && -1 + v_max >= 0 && 0 >= v_2] eval_random1d_bb3_in(v_2,v_max,v_x_0) -> eval_random1d_stop(v_2,v_max,v_x_0) True eval_random1d_stop(v_2,v_max,v_x_0) -> exitus616(v_2,v_max,v_x_0) True eval_random1d_stop(v_2,v_max,v_x_0) -> exitus616(v_2,v_max,v_x_0) True Signature: {(eval_random1d_0,3) ;(eval_random1d_1,3) ;(eval_random1d_2,3) ;(eval_random1d_3,3) ;(eval_random1d_bb0_in,3) ;(eval_random1d_bb1_in,3) ;(eval_random1d_bb2_in,3) ;(eval_random1d_bb3_in,3) ;(eval_random1d_start,3) ;(eval_random1d_stop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2},2->{3,4},3->{5},4->{11},5->{7},6->{11},7->{8},8->{9,10},9->{5,6},10->{5,6},11->{12,13}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[5,9,8,7,10] c: [5,7,8,9,10]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [v_2,v_max,v_x_0,0.0] eval_random1d_start ~> eval_random1d_bb0_in [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_x_0] eval_random1d_bb0_in ~> eval_random1d_0 [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_x_0] eval_random1d_0 ~> eval_random1d_1 [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_x_0] eval_random1d_1 ~> eval_random1d_bb1_in [v_2 <= v_2, v_max <= v_max, v_x_0 <= K] eval_random1d_1 ~> eval_random1d_bb3_in [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_x_0] eval_random1d_bb1_in ~> eval_random1d_bb2_in [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_x_0] eval_random1d_bb1_in ~> eval_random1d_bb3_in [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_x_0] eval_random1d_bb2_in ~> eval_random1d_2 [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_x_0] eval_random1d_2 ~> eval_random1d_3 [v_2 <= unknown, v_max <= v_max, v_x_0 <= v_x_0] eval_random1d_3 ~> eval_random1d_bb1_in [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_max + v_x_0] eval_random1d_3 ~> eval_random1d_bb1_in [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_max + v_x_0] eval_random1d_bb3_in ~> eval_random1d_stop [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_x_0] eval_random1d_stop ~> exitus616 [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_x_0] eval_random1d_stop ~> exitus616 [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_x_0] + Loop: [0.0 <= v_max + v_x_0] eval_random1d_bb1_in ~> eval_random1d_bb2_in [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_x_0] eval_random1d_3 ~> eval_random1d_bb1_in [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_max + v_x_0] eval_random1d_2 ~> eval_random1d_3 [v_2 <= unknown, v_max <= v_max, v_x_0 <= v_x_0] eval_random1d_bb2_in ~> eval_random1d_2 [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_x_0] eval_random1d_3 ~> eval_random1d_bb1_in [v_2 <= v_2, v_max <= v_max, v_x_0 <= v_max + v_x_0] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,v_2,v_max,v_x_0,0.0] eval_random1d_start ~> eval_random1d_bb0_in [] eval_random1d_bb0_in ~> eval_random1d_0 [] eval_random1d_0 ~> eval_random1d_1 [] eval_random1d_1 ~> eval_random1d_bb1_in [K ~=> v_x_0] eval_random1d_1 ~> eval_random1d_bb3_in [] eval_random1d_bb1_in ~> eval_random1d_bb2_in [] eval_random1d_bb1_in ~> eval_random1d_bb3_in [] eval_random1d_bb2_in ~> eval_random1d_2 [] eval_random1d_2 ~> eval_random1d_3 [huge ~=> v_2] eval_random1d_3 ~> eval_random1d_bb1_in [v_max ~+> v_x_0,v_x_0 ~+> v_x_0] eval_random1d_3 ~> eval_random1d_bb1_in [v_max ~+> v_x_0,v_x_0 ~+> v_x_0] eval_random1d_bb3_in ~> eval_random1d_stop [] eval_random1d_stop ~> exitus616 [] eval_random1d_stop ~> exitus616 [] + Loop: [v_max ~+> 0.0,v_x_0 ~+> 0.0] eval_random1d_bb1_in ~> eval_random1d_bb2_in [] eval_random1d_3 ~> eval_random1d_bb1_in [v_max ~+> v_x_0,v_x_0 ~+> v_x_0] eval_random1d_2 ~> eval_random1d_3 [huge ~=> v_2] eval_random1d_bb2_in ~> eval_random1d_2 [] eval_random1d_3 ~> eval_random1d_bb1_in [v_max ~+> v_x_0,v_x_0 ~+> v_x_0] + Applied Processor: Lare + Details: eval_random1d_start ~> exitus616 [K ~=> v_x_0 ,huge ~=> v_2 ,v_max ~+> v_x_0 ,v_max ~+> 0.0 ,v_max ~+> tick ,tick ~+> tick ,K ~+> v_x_0 ,K ~+> 0.0 ,K ~+> tick ,v_max ~*> v_x_0 ,K ~*> v_x_0] + eval_random1d_bb1_in> [huge ~=> v_2 ,v_max ~+> v_x_0 ,v_max ~+> 0.0 ,v_max ~+> tick ,v_x_0 ~+> v_x_0 ,v_x_0 ~+> 0.0 ,v_x_0 ~+> tick ,tick ~+> tick ,v_max ~*> v_x_0 ,v_x_0 ~*> v_x_0] YES(?,O(n^1))