YES(?,POLY) * Step 1: UnsatPaths WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_start_start(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) True (1,1) 1. eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_0(v_1,v_n,v_x_0,v_x_1) True (?,1) 2. eval_start_0(v_1,v_n,v_x_0,v_x_1) -> eval_start_1(v_1,v_n,v_x_0,v_x_1) True (?,1) 3. eval_start_1(v_1,v_n,v_x_0,v_x_1) -> eval_start_2(v_1,v_n,v_x_0,v_x_1) True (?,1) 4. eval_start_2(v_1,v_n,v_x_0,v_x_1) -> eval_start_3(v_1,v_n,v_x_0,v_x_1) True (?,1) 5. eval_start_3(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,0,v_x_1) True (?,1) 6. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 8. eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_4(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 9. eval_start_4(v_1,v_n,v_x_0,v_x_1) -> eval_start_5(nondef_0,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 10. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_1 >= 0] (?,1) 11. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && 0 >= v_1] (?,1) 12. eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,1 + v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 (?,1) && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1*v_1 >= 0] 13. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_1] (?,1) 14. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && v_x_1 >= v_n] (?,1) 15. eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,1 + v_x_1) [-1 + v_n + -1*v_x_1 >= 0 (?,1) && v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1 + v_n + v_x_1 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 16. eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_stop(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1*v_n + v_x_1 >= 0 && v_x_0 >= 0] (?,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_5,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_bb6_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8},7->{13,14},8->{9},9->{10,11},10->{13,14},11->{12} ,12->{6,7},13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(7,13),(10,14)] * Step 2: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_start_start(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) True (1,1) 1. eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_0(v_1,v_n,v_x_0,v_x_1) True (?,1) 2. eval_start_0(v_1,v_n,v_x_0,v_x_1) -> eval_start_1(v_1,v_n,v_x_0,v_x_1) True (?,1) 3. eval_start_1(v_1,v_n,v_x_0,v_x_1) -> eval_start_2(v_1,v_n,v_x_0,v_x_1) True (?,1) 4. eval_start_2(v_1,v_n,v_x_0,v_x_1) -> eval_start_3(v_1,v_n,v_x_0,v_x_1) True (?,1) 5. eval_start_3(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,0,v_x_1) True (?,1) 6. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 8. eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_4(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 9. eval_start_4(v_1,v_n,v_x_0,v_x_1) -> eval_start_5(nondef_0,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] (?,1) 10. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_1 >= 0] (?,1) 11. eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && 0 >= v_1] (?,1) 12. eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,1 + v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 (?,1) && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1*v_1 >= 0] 13. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_1] (?,1) 14. eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && v_x_1 >= v_n] (?,1) 15. eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,1 + v_x_1) [-1 + v_n + -1*v_x_1 >= 0 (?,1) && v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1 + v_n + v_x_1 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 16. eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_stop(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1*v_n + v_x_1 >= 0 && v_x_0 >= 0] (?,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_5,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_bb6_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8},7->{14},8->{9},9->{10,11},10->{13},11->{12},12->{6,7} ,13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: eval_start_start(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) True eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_0(v_1,v_n,v_x_0,v_x_1) True eval_start_0(v_1,v_n,v_x_0,v_x_1) -> eval_start_1(v_1,v_n,v_x_0,v_x_1) True eval_start_1(v_1,v_n,v_x_0,v_x_1) -> eval_start_2(v_1,v_n,v_x_0,v_x_1) True eval_start_2(v_1,v_n,v_x_0,v_x_1) -> eval_start_3(v_1,v_n,v_x_0,v_x_1) True eval_start_3(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,0,v_x_1) True eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) [v_x_0 >= 0 && -1 + v_n >= v_x_0] eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_4(v_1,v_n,v_x_0,v_x_1) [-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_4(v_1,v_n,v_x_0,v_x_1) -> eval_start_5(nondef_0,v_n,v_x_0,v_x_1) [-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_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_1 >= 0] eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && 0 >= v_1] eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,1 + v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1*v_1 >= 0] eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_1] eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && v_x_1 >= v_n] eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,1 + v_x_1) [-1 + v_n + -1*v_x_1 >= 0 && v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1 + v_n + v_x_1 >= 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_bb6_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_stop(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1*v_n + v_x_1 >= 0 && v_x_0 >= 0] Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_5,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_bb6_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8},7->{14},8->{9},9->{10,11},10->{13},11->{12},12->{6,7} ,13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: AddSinks + Details: () * Step 4: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: eval_start_start(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) True eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_0(v_1,v_n,v_x_0,v_x_1) True eval_start_0(v_1,v_n,v_x_0,v_x_1) -> eval_start_1(v_1,v_n,v_x_0,v_x_1) True eval_start_1(v_1,v_n,v_x_0,v_x_1) -> eval_start_2(v_1,v_n,v_x_0,v_x_1) True eval_start_2(v_1,v_n,v_x_0,v_x_1) -> eval_start_3(v_1,v_n,v_x_0,v_x_1) True eval_start_3(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,0,v_x_1) True eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) [v_x_0 >= 0 && -1 + v_n >= v_x_0] eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_4(v_1,v_n,v_x_0,v_x_1) [-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_4(v_1,v_n,v_x_0,v_x_1) -> eval_start_5(nondef_0,v_n,v_x_0,v_x_1) [-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_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_1 >= 0] eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && 0 >= v_1] eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,1 + v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1*v_1 >= 0] eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_1] eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && v_x_1 >= v_n] eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,1 + v_x_1) [-1 + v_n + -1*v_x_1 >= 0 && v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1 + v_n + v_x_1 >= 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_bb6_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_stop(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1*v_n + v_x_1 >= 0 && v_x_0 >= 0] eval_start_stop(v_1,v_n,v_x_0,v_x_1) -> exitus616(v_1,v_n,v_x_0,v_x_1) True eval_start_stop(v_1,v_n,v_x_0,v_x_1) -> exitus616(v_1,v_n,v_x_0,v_x_1) True Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_5,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_bb6_in,4) ;(eval_start_start,4) ;(eval_start_stop,4) ;(exitus616,4)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8},7->{14},8->{9},9->{10,11},10->{13},11->{12},12->{6,7} ,13->{15},14->{16},15->{13,14},16->{17,18}] + 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] | +- p:[6,12,11,9,8] c: [6,8,9,11,12] | `- p:[13,15] c: [13,15] * Step 5: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: eval_start_start(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) True eval_start_bb0_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_0(v_1,v_n,v_x_0,v_x_1) True eval_start_0(v_1,v_n,v_x_0,v_x_1) -> eval_start_1(v_1,v_n,v_x_0,v_x_1) True eval_start_1(v_1,v_n,v_x_0,v_x_1) -> eval_start_2(v_1,v_n,v_x_0,v_x_1) True eval_start_2(v_1,v_n,v_x_0,v_x_1) -> eval_start_3(v_1,v_n,v_x_0,v_x_1) True eval_start_3(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,0,v_x_1) True eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) [v_x_0 >= 0 && -1 + v_n >= v_x_0] eval_start_bb1_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] eval_start_bb2_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_4(v_1,v_n,v_x_0,v_x_1) [-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_4(v_1,v_n,v_x_0,v_x_1) -> eval_start_5(nondef_0,v_n,v_x_0,v_x_1) [-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_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,v_x_0) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_1 >= 0] eval_start_5(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && 0 >= v_1] eval_start_bb3_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb1_in(v_1,v_n,1 + v_x_0,v_x_1) [-1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1*v_1 >= 0] eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_1] eval_start_bb4_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb6_in(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && v_x_0 >= 0 && v_x_1 >= v_n] eval_start_bb5_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_bb4_in(v_1,v_n,v_x_0,1 + v_x_1) [-1 + v_n + -1*v_x_1 >= 0 && v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1 + v_n + v_x_1 >= 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_bb6_in(v_1,v_n,v_x_0,v_x_1) -> eval_start_stop(v_1,v_n,v_x_0,v_x_1) [v_x_1 >= 0 && v_x_0 + v_x_1 >= 0 && -1*v_x_0 + v_x_1 >= 0 && -1*v_n + v_x_1 >= 0 && v_x_0 >= 0] eval_start_stop(v_1,v_n,v_x_0,v_x_1) -> exitus616(v_1,v_n,v_x_0,v_x_1) True eval_start_stop(v_1,v_n,v_x_0,v_x_1) -> exitus616(v_1,v_n,v_x_0,v_x_1) True Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_5,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_bb6_in,4) ;(eval_start_start,4) ;(eval_start_stop,4) ;(exitus616,4)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8},7->{14},8->{9},9->{10,11},10->{13},11->{12},12->{6,7} ,13->{15},14->{16},15->{13,14},16->{17,18}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] | +- p:[6,12,11,9,8] c: [6,8,9,11,12] | `- p:[13,15] c: [13,15]) + Applied Processor: AbstractSize Minimize + Details: () * Step 6: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [v_1,v_n,v_x_0,v_x_1,0.0,0.1] eval_start_start ~> eval_start_bb0_in [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_bb0_in ~> eval_start_0 [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_0 ~> eval_start_1 [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_1 ~> eval_start_2 [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_2 ~> eval_start_3 [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_3 ~> eval_start_bb1_in [v_1 <= v_1, v_n <= v_n, v_x_0 <= 0*K, v_x_1 <= v_x_1] eval_start_bb1_in ~> eval_start_bb2_in [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_bb1_in ~> eval_start_bb4_in [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_0] eval_start_bb2_in ~> eval_start_4 [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_4 ~> eval_start_5 [v_1 <= unknown, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_5 ~> eval_start_bb4_in [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_0] eval_start_5 ~> eval_start_bb3_in [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_bb3_in ~> eval_start_bb1_in [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_n, v_x_1 <= v_x_1] eval_start_bb4_in ~> eval_start_bb5_in [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_bb4_in ~> eval_start_bb6_in [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_bb5_in ~> eval_start_bb4_in [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_n] eval_start_bb6_in ~> eval_start_stop [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_stop ~> exitus616 [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_stop ~> exitus616 [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] + Loop: [0.0 <= K + v_n + v_x_0] eval_start_bb1_in ~> eval_start_bb2_in [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_bb3_in ~> eval_start_bb1_in [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_n, v_x_1 <= v_x_1] eval_start_5 ~> eval_start_bb3_in [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_4 ~> eval_start_5 [v_1 <= unknown, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_bb2_in ~> eval_start_4 [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] + Loop: [0.1 <= v_n + v_x_1] eval_start_bb4_in ~> eval_start_bb5_in [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_x_1] eval_start_bb5_in ~> eval_start_bb4_in [v_1 <= v_1, v_n <= v_n, v_x_0 <= v_x_0, v_x_1 <= v_n] + Applied Processor: AbstractFlow + Details: () * Step 7: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,v_1,v_n,v_x_0,v_x_1,0.0,0.1] eval_start_start ~> eval_start_bb0_in [] eval_start_bb0_in ~> eval_start_0 [] eval_start_0 ~> eval_start_1 [] eval_start_1 ~> eval_start_2 [] eval_start_2 ~> eval_start_3 [] eval_start_3 ~> eval_start_bb1_in [K ~=> v_x_0] eval_start_bb1_in ~> eval_start_bb2_in [] eval_start_bb1_in ~> eval_start_bb4_in [v_x_0 ~=> v_x_1] eval_start_bb2_in ~> eval_start_4 [] eval_start_4 ~> eval_start_5 [huge ~=> v_1] eval_start_5 ~> eval_start_bb4_in [v_x_0 ~=> v_x_1] eval_start_5 ~> eval_start_bb3_in [] eval_start_bb3_in ~> eval_start_bb1_in [v_n ~=> v_x_0] eval_start_bb4_in ~> eval_start_bb5_in [] eval_start_bb4_in ~> eval_start_bb6_in [] eval_start_bb5_in ~> eval_start_bb4_in [v_n ~=> v_x_1] eval_start_bb6_in ~> eval_start_stop [] eval_start_stop ~> exitus616 [] eval_start_stop ~> exitus616 [] + Loop: [v_n ~+> 0.0,v_x_0 ~+> 0.0,K ~+> 0.0] eval_start_bb1_in ~> eval_start_bb2_in [] eval_start_bb3_in ~> eval_start_bb1_in [v_n ~=> v_x_0] eval_start_5 ~> eval_start_bb3_in [] eval_start_4 ~> eval_start_5 [huge ~=> v_1] eval_start_bb2_in ~> eval_start_4 [] + Loop: [v_n ~+> 0.1,v_x_1 ~+> 0.1] eval_start_bb4_in ~> eval_start_bb5_in [] eval_start_bb5_in ~> eval_start_bb4_in [v_n ~=> v_x_1] + Applied Processor: Lare + Details: eval_start_start ~> exitus616 [v_n ~=> v_x_0 ,v_n ~=> v_x_1 ,K ~=> v_x_0 ,K ~=> v_x_1 ,huge ~=> v_1 ,v_n ~+> 0.0 ,v_n ~+> 0.1 ,v_n ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> 0.1 ,K ~+> tick ,v_n ~*> 0.0 ,v_n ~*> 0.1 ,v_n ~*> tick ,K ~*> 0.0 ,K ~*> tick] + eval_start_bb1_in> [v_n ~=> v_x_0 ,huge ~=> v_1 ,v_n ~+> 0.0 ,v_n ~+> tick ,v_x_0 ~+> 0.0 ,v_x_0 ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick] eval_start_5> [v_n ~=> v_x_0 ,huge ~=> v_1 ,v_n ~+> 0.0 ,v_n ~+> tick ,v_x_0 ~+> 0.0 ,v_x_0 ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick] + eval_start_bb4_in> [v_n ~=> v_x_1 ,v_n ~+> 0.1 ,v_n ~+> tick ,v_x_1 ~+> 0.1 ,v_x_1 ~+> tick ,tick ~+> tick] YES(?,POLY)