YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_start_start(v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_n,v_x_0,v_y_0) -> eval_start_0(v_n,v_x_0,v_y_0) True (?,1) 2. eval_start_0(v_n,v_x_0,v_y_0) -> eval_start_1(v_n,v_x_0,v_y_0) True (?,1) 3. eval_start_1(v_n,v_x_0,v_y_0) -> eval_start_2(v_n,v_x_0,v_y_0) True (?,1) 4. eval_start_2(v_n,v_x_0,v_y_0) -> eval_start_3(v_n,v_x_0,v_y_0) True (?,1) 5. eval_start_3(v_n,v_x_0,v_y_0) -> eval_start_4(v_n,v_x_0,v_y_0) True (?,1) 6. eval_start_4(v_n,v_x_0,v_y_0) -> eval_start_5(v_n,v_x_0,v_y_0) True (?,1) 7. eval_start_5(v_n,v_x_0,v_y_0) -> eval_start_6(v_n,v_x_0,v_y_0) True (?,1) 8. eval_start_6(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,0,0) True (?,1) 9. eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 10. eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 11. eval_start_bb2_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 12. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb4_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_y_0 >= 0] 13. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb5_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && 0 >= v_y_0] 14. eval_start_bb4_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,v_x_0,-1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_y_0 >= 0 && -2 + v_x_0 + v_y_0 >= 0 && -1 + v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] 15. eval_start_bb5_in(v_n,v_x_0,v_y_0) -> eval_start_stop(v_n,v_x_0,v_y_0) [-1*v_y_0 >= 0 (?,1) && v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] Signature: {(eval_start_0,3) ;(eval_start_1,3) ;(eval_start_2,3) ;(eval_start_3,3) ;(eval_start_4,3) ;(eval_start_5,3) ;(eval_start_6,3) ;(eval_start_bb0_in,3) ;(eval_start_bb1_in,3) ;(eval_start_bb2_in,3) ;(eval_start_bb3_in,3) ;(eval_start_bb4_in,3) ;(eval_start_bb5_in,3) ;(eval_start_start,3) ;(eval_start_stop,3)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{12,13},11->{9,10},12->{14} ,13->{15},14->{9,10},15->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(14,9)] * Step 2: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_start_start(v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_n,v_x_0,v_y_0) -> eval_start_0(v_n,v_x_0,v_y_0) True (?,1) 2. eval_start_0(v_n,v_x_0,v_y_0) -> eval_start_1(v_n,v_x_0,v_y_0) True (?,1) 3. eval_start_1(v_n,v_x_0,v_y_0) -> eval_start_2(v_n,v_x_0,v_y_0) True (?,1) 4. eval_start_2(v_n,v_x_0,v_y_0) -> eval_start_3(v_n,v_x_0,v_y_0) True (?,1) 5. eval_start_3(v_n,v_x_0,v_y_0) -> eval_start_4(v_n,v_x_0,v_y_0) True (?,1) 6. eval_start_4(v_n,v_x_0,v_y_0) -> eval_start_5(v_n,v_x_0,v_y_0) True (?,1) 7. eval_start_5(v_n,v_x_0,v_y_0) -> eval_start_6(v_n,v_x_0,v_y_0) True (?,1) 8. eval_start_6(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,0,0) True (?,1) 9. eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 10. eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 11. eval_start_bb2_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 12. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb4_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_y_0 >= 0] 13. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb5_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && 0 >= v_y_0] 14. eval_start_bb4_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,v_x_0,-1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_y_0 >= 0 && -2 + v_x_0 + v_y_0 >= 0 && -1 + v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] 15. eval_start_bb5_in(v_n,v_x_0,v_y_0) -> eval_start_stop(v_n,v_x_0,v_y_0) [-1*v_y_0 >= 0 (?,1) && v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] Signature: {(eval_start_0,3) ;(eval_start_1,3) ;(eval_start_2,3) ;(eval_start_3,3) ;(eval_start_4,3) ;(eval_start_5,3) ;(eval_start_6,3) ;(eval_start_bb0_in,3) ;(eval_start_bb1_in,3) ;(eval_start_bb2_in,3) ;(eval_start_bb3_in,3) ;(eval_start_bb4_in,3) ;(eval_start_bb5_in,3) ;(eval_start_start,3) ;(eval_start_stop,3)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{12,13},11->{9,10},12->{14} ,13->{15},14->{10},15->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: eval_start_start(v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_n,v_x_0,v_y_0) True eval_start_bb0_in(v_n,v_x_0,v_y_0) -> eval_start_0(v_n,v_x_0,v_y_0) True eval_start_0(v_n,v_x_0,v_y_0) -> eval_start_1(v_n,v_x_0,v_y_0) True eval_start_1(v_n,v_x_0,v_y_0) -> eval_start_2(v_n,v_x_0,v_y_0) True eval_start_2(v_n,v_x_0,v_y_0) -> eval_start_3(v_n,v_x_0,v_y_0) True eval_start_3(v_n,v_x_0,v_y_0) -> eval_start_4(v_n,v_x_0,v_y_0) True eval_start_4(v_n,v_x_0,v_y_0) -> eval_start_5(v_n,v_x_0,v_y_0) True eval_start_5(v_n,v_x_0,v_y_0) -> eval_start_6(v_n,v_x_0,v_y_0) True eval_start_6(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,0,0) True eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb2_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb4_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_y_0 >= 0] eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb5_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && 0 >= v_y_0] eval_start_bb4_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,v_x_0,-1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 && -1 + v_y_0 >= 0 && -2 + v_x_0 + v_y_0 >= 0 && -1 + v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] eval_start_bb5_in(v_n,v_x_0,v_y_0) -> eval_start_stop(v_n,v_x_0,v_y_0) [-1*v_y_0 >= 0 && v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] Signature: {(eval_start_0,3) ;(eval_start_1,3) ;(eval_start_2,3) ;(eval_start_3,3) ;(eval_start_4,3) ;(eval_start_5,3) ;(eval_start_6,3) ;(eval_start_bb0_in,3) ;(eval_start_bb1_in,3) ;(eval_start_bb2_in,3) ;(eval_start_bb3_in,3) ;(eval_start_bb4_in,3) ;(eval_start_bb5_in,3) ;(eval_start_start,3) ;(eval_start_stop,3)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{12,13},11->{9,10},12->{14} ,13->{15},14->{10},15->{}] + Applied Processor: AddSinks + Details: () * Step 4: Unfold WORST_CASE(?,POLY) + Considered Problem: Rules: eval_start_start(v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_n,v_x_0,v_y_0) True eval_start_bb0_in(v_n,v_x_0,v_y_0) -> eval_start_0(v_n,v_x_0,v_y_0) True eval_start_0(v_n,v_x_0,v_y_0) -> eval_start_1(v_n,v_x_0,v_y_0) True eval_start_1(v_n,v_x_0,v_y_0) -> eval_start_2(v_n,v_x_0,v_y_0) True eval_start_2(v_n,v_x_0,v_y_0) -> eval_start_3(v_n,v_x_0,v_y_0) True eval_start_3(v_n,v_x_0,v_y_0) -> eval_start_4(v_n,v_x_0,v_y_0) True eval_start_4(v_n,v_x_0,v_y_0) -> eval_start_5(v_n,v_x_0,v_y_0) True eval_start_5(v_n,v_x_0,v_y_0) -> eval_start_6(v_n,v_x_0,v_y_0) True eval_start_6(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,0,0) True eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb2_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb4_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_y_0 >= 0] eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb5_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && 0 >= v_y_0] eval_start_bb4_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,v_x_0,-1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 && -1 + v_y_0 >= 0 && -2 + v_x_0 + v_y_0 >= 0 && -1 + v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] eval_start_bb5_in(v_n,v_x_0,v_y_0) -> eval_start_stop(v_n,v_x_0,v_y_0) [-1*v_y_0 >= 0 && v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] eval_start_stop(v_n,v_x_0,v_y_0) -> exitus616(v_n,v_x_0,v_y_0) True Signature: {(eval_start_0,3) ;(eval_start_1,3) ;(eval_start_2,3) ;(eval_start_3,3) ;(eval_start_4,3) ;(eval_start_5,3) ;(eval_start_6,3) ;(eval_start_bb0_in,3) ;(eval_start_bb1_in,3) ;(eval_start_bb2_in,3) ;(eval_start_bb3_in,3) ;(eval_start_bb4_in,3) ;(eval_start_bb5_in,3) ;(eval_start_start,3) ;(eval_start_stop,3) ;(exitus616,3)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{12,13},11->{9,10},12->{14} ,13->{15},14->{10},15->{16}] + Applied Processor: Unfold + Details: () * Step 5: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: eval_start_start.0(v_n,v_x_0,v_y_0) -> eval_start_bb0_in.1(v_n,v_x_0,v_y_0) True eval_start_bb0_in.1(v_n,v_x_0,v_y_0) -> eval_start_0.2(v_n,v_x_0,v_y_0) True eval_start_0.2(v_n,v_x_0,v_y_0) -> eval_start_1.3(v_n,v_x_0,v_y_0) True eval_start_1.3(v_n,v_x_0,v_y_0) -> eval_start_2.4(v_n,v_x_0,v_y_0) True eval_start_2.4(v_n,v_x_0,v_y_0) -> eval_start_3.5(v_n,v_x_0,v_y_0) True eval_start_3.5(v_n,v_x_0,v_y_0) -> eval_start_4.6(v_n,v_x_0,v_y_0) True eval_start_4.6(v_n,v_x_0,v_y_0) -> eval_start_5.7(v_n,v_x_0,v_y_0) True eval_start_5.7(v_n,v_x_0,v_y_0) -> eval_start_6.8(v_n,v_x_0,v_y_0) True eval_start_6.8(v_n,v_x_0,v_y_0) -> eval_start_bb1_in.9(v_n,0,0) True eval_start_6.8(v_n,v_x_0,v_y_0) -> eval_start_bb1_in.10(v_n,0,0) True eval_start_bb1_in.9(v_n,v_x_0,v_y_0) -> eval_start_bb2_in.11(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] eval_start_bb1_in.10(v_n,v_x_0,v_y_0) -> eval_start_bb3_in.12(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb1_in.10(v_n,v_x_0,v_y_0) -> eval_start_bb3_in.13(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb2_in.11(v_n,v_x_0,v_y_0) -> eval_start_bb1_in.9(v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_bb2_in.11(v_n,v_x_0,v_y_0) -> eval_start_bb1_in.10(v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_bb3_in.12(v_n,v_x_0,v_y_0) -> eval_start_bb4_in.14(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_y_0 >= 0] eval_start_bb3_in.13(v_n,v_x_0,v_y_0) -> eval_start_bb5_in.15(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && 0 >= v_y_0] eval_start_bb4_in.14(v_n,v_x_0,v_y_0) -> eval_start_bb1_in.10(v_n,v_x_0,-1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 && -1 + v_y_0 >= 0 && -2 + v_x_0 + v_y_0 >= 0 && -1 + v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] eval_start_bb5_in.15(v_n,v_x_0,v_y_0) -> eval_start_stop.16(v_n,v_x_0,v_y_0) [-1*v_y_0 >= 0 && v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] eval_start_stop.16(v_n,v_x_0,v_y_0) -> exitus616.17(v_n,v_x_0,v_y_0) True Signature: {(eval_start_0.2,3) ;(eval_start_1.3,3) ;(eval_start_2.4,3) ;(eval_start_3.5,3) ;(eval_start_4.6,3) ;(eval_start_5.7,3) ;(eval_start_6.8,3) ;(eval_start_bb0_in.1,3) ;(eval_start_bb1_in.10,3) ;(eval_start_bb1_in.9,3) ;(eval_start_bb2_in.11,3) ;(eval_start_bb3_in.12,3) ;(eval_start_bb3_in.13,3) ;(eval_start_bb4_in.14,3) ;(eval_start_bb5_in.15,3) ;(eval_start_start.0,3) ;(eval_start_stop.16,3) ;(exitus616.17,3)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9},8->{10},9->{11,12},10->{13,14},11->{15} ,12->{16},13->{10},14->{11,12},15->{17},16->{18},17->{11,12},18->{19},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:[10,13] c: [10,13] | `- p:[11,17,15] c: [11,15,17] * Step 6: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: eval_start_start.0(v_n,v_x_0,v_y_0) -> eval_start_bb0_in.1(v_n,v_x_0,v_y_0) True eval_start_bb0_in.1(v_n,v_x_0,v_y_0) -> eval_start_0.2(v_n,v_x_0,v_y_0) True eval_start_0.2(v_n,v_x_0,v_y_0) -> eval_start_1.3(v_n,v_x_0,v_y_0) True eval_start_1.3(v_n,v_x_0,v_y_0) -> eval_start_2.4(v_n,v_x_0,v_y_0) True eval_start_2.4(v_n,v_x_0,v_y_0) -> eval_start_3.5(v_n,v_x_0,v_y_0) True eval_start_3.5(v_n,v_x_0,v_y_0) -> eval_start_4.6(v_n,v_x_0,v_y_0) True eval_start_4.6(v_n,v_x_0,v_y_0) -> eval_start_5.7(v_n,v_x_0,v_y_0) True eval_start_5.7(v_n,v_x_0,v_y_0) -> eval_start_6.8(v_n,v_x_0,v_y_0) True eval_start_6.8(v_n,v_x_0,v_y_0) -> eval_start_bb1_in.9(v_n,0,0) True eval_start_6.8(v_n,v_x_0,v_y_0) -> eval_start_bb1_in.10(v_n,0,0) True eval_start_bb1_in.9(v_n,v_x_0,v_y_0) -> eval_start_bb2_in.11(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] eval_start_bb1_in.10(v_n,v_x_0,v_y_0) -> eval_start_bb3_in.12(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb1_in.10(v_n,v_x_0,v_y_0) -> eval_start_bb3_in.13(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb2_in.11(v_n,v_x_0,v_y_0) -> eval_start_bb1_in.9(v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_bb2_in.11(v_n,v_x_0,v_y_0) -> eval_start_bb1_in.10(v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] eval_start_bb3_in.12(v_n,v_x_0,v_y_0) -> eval_start_bb4_in.14(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_y_0 >= 0] eval_start_bb3_in.13(v_n,v_x_0,v_y_0) -> eval_start_bb5_in.15(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && 0 >= v_y_0] eval_start_bb4_in.14(v_n,v_x_0,v_y_0) -> eval_start_bb1_in.10(v_n,v_x_0,-1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 && -1 + v_y_0 >= 0 && -2 + v_x_0 + v_y_0 >= 0 && -1 + v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] eval_start_bb5_in.15(v_n,v_x_0,v_y_0) -> eval_start_stop.16(v_n,v_x_0,v_y_0) [-1*v_y_0 >= 0 && v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] eval_start_stop.16(v_n,v_x_0,v_y_0) -> exitus616.17(v_n,v_x_0,v_y_0) True Signature: {(eval_start_0.2,3) ;(eval_start_1.3,3) ;(eval_start_2.4,3) ;(eval_start_3.5,3) ;(eval_start_4.6,3) ;(eval_start_5.7,3) ;(eval_start_6.8,3) ;(eval_start_bb0_in.1,3) ;(eval_start_bb1_in.10,3) ;(eval_start_bb1_in.9,3) ;(eval_start_bb2_in.11,3) ;(eval_start_bb3_in.12,3) ;(eval_start_bb3_in.13,3) ;(eval_start_bb4_in.14,3) ;(eval_start_bb5_in.15,3) ;(eval_start_start.0,3) ;(eval_start_stop.16,3) ;(exitus616.17,3)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9},8->{10},9->{11,12},10->{13,14},11->{15} ,12->{16},13->{10},14->{11,12},15->{17},16->{18},17->{11,12},18->{19},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:[10,13] c: [10,13] | `- p:[11,17,15] c: [11,15,17]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [v_n,v_x_0,v_y_0,0.0,0.1] eval_start_start.0 ~> eval_start_bb0_in.1 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb0_in.1 ~> eval_start_0.2 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_0.2 ~> eval_start_1.3 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_1.3 ~> eval_start_2.4 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_2.4 ~> eval_start_3.5 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_3.5 ~> eval_start_4.6 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_4.6 ~> eval_start_5.7 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_5.7 ~> eval_start_6.8 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_6.8 ~> eval_start_bb1_in.9 [v_n <= v_n, v_x_0 <= 0*K, v_y_0 <= 0*K] eval_start_6.8 ~> eval_start_bb1_in.10 [v_n <= v_n, v_x_0 <= 0*K, v_y_0 <= 0*K] eval_start_bb1_in.9 ~> eval_start_bb2_in.11 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb1_in.10 ~> eval_start_bb3_in.12 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb1_in.10 ~> eval_start_bb3_in.13 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb2_in.11 ~> eval_start_bb1_in.9 [v_n <= v_n, v_x_0 <= v_n, v_y_0 <= v_n] eval_start_bb2_in.11 ~> eval_start_bb1_in.10 [v_n <= v_n, v_x_0 <= v_n, v_y_0 <= v_n] eval_start_bb3_in.12 ~> eval_start_bb4_in.14 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb3_in.13 ~> eval_start_bb5_in.15 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb4_in.14 ~> eval_start_bb1_in.10 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb5_in.15 ~> eval_start_stop.16 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_stop.16 ~> exitus616.17 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] + Loop: [0.0 <= v_n + v_y_0] eval_start_bb1_in.9 ~> eval_start_bb2_in.11 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb2_in.11 ~> eval_start_bb1_in.9 [v_n <= v_n, v_x_0 <= v_n, v_y_0 <= v_n] + Loop: [0.1 <= K + v_y_0] eval_start_bb1_in.10 ~> eval_start_bb3_in.12 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb4_in.14 ~> eval_start_bb1_in.10 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] eval_start_bb3_in.12 ~> eval_start_bb4_in.14 [v_n <= v_n, v_x_0 <= v_x_0, v_y_0 <= v_y_0] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,v_n,v_x_0,v_y_0,0.0,0.1] eval_start_start.0 ~> eval_start_bb0_in.1 [] eval_start_bb0_in.1 ~> eval_start_0.2 [] eval_start_0.2 ~> eval_start_1.3 [] eval_start_1.3 ~> eval_start_2.4 [] eval_start_2.4 ~> eval_start_3.5 [] eval_start_3.5 ~> eval_start_4.6 [] eval_start_4.6 ~> eval_start_5.7 [] eval_start_5.7 ~> eval_start_6.8 [] eval_start_6.8 ~> eval_start_bb1_in.9 [K ~=> v_x_0,K ~=> v_y_0] eval_start_6.8 ~> eval_start_bb1_in.10 [K ~=> v_x_0,K ~=> v_y_0] eval_start_bb1_in.9 ~> eval_start_bb2_in.11 [] eval_start_bb1_in.10 ~> eval_start_bb3_in.12 [] eval_start_bb1_in.10 ~> eval_start_bb3_in.13 [] eval_start_bb2_in.11 ~> eval_start_bb1_in.9 [v_n ~=> v_x_0,v_n ~=> v_y_0] eval_start_bb2_in.11 ~> eval_start_bb1_in.10 [v_n ~=> v_x_0,v_n ~=> v_y_0] eval_start_bb3_in.12 ~> eval_start_bb4_in.14 [] eval_start_bb3_in.13 ~> eval_start_bb5_in.15 [] eval_start_bb4_in.14 ~> eval_start_bb1_in.10 [] eval_start_bb5_in.15 ~> eval_start_stop.16 [] eval_start_stop.16 ~> exitus616.17 [] + Loop: [v_n ~+> 0.0,v_y_0 ~+> 0.0] eval_start_bb1_in.9 ~> eval_start_bb2_in.11 [] eval_start_bb2_in.11 ~> eval_start_bb1_in.9 [v_n ~=> v_x_0,v_n ~=> v_y_0] + Loop: [v_y_0 ~+> 0.1,K ~+> 0.1] eval_start_bb1_in.10 ~> eval_start_bb3_in.12 [] eval_start_bb4_in.14 ~> eval_start_bb1_in.10 [] eval_start_bb3_in.12 ~> eval_start_bb4_in.14 [] + Applied Processor: Lare + Details: eval_start_start.0 ~> exitus616.17 [v_n ~=> v_x_0 ,v_n ~=> v_y_0 ,K ~=> v_x_0 ,K ~=> v_y_0 ,v_n ~+> 0.0 ,v_n ~+> 0.1 ,v_n ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,v_n ~*> tick ,K ~*> 0.1 ,K ~*> tick] + eval_start_bb2_in.11> [v_n ~=> v_x_0 ,v_n ~=> v_y_0 ,v_n ~+> 0.0 ,v_n ~+> tick ,v_y_0 ~+> 0.0 ,v_y_0 ~+> tick ,tick ~+> tick] + eval_start_bb1_in.10> [v_y_0 ~+> 0.1 ,v_y_0 ~+> tick ,tick ~+> tick ,K ~+> 0.1 ,K ~+> tick] YES(?,POLY)