YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 1. eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 2. eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 3. eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 4. eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 5. eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,0,v_x_0_sink) True (?,1) 6. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 8. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (?,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_n >= 1 + v_x_0_sink] 9. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (?,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_x_0_sink >= v_n] 10. eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 11. eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_7(v_1,nondef_0,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 12. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,v_1,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && -1 + v_3 >= 0] 13. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_1) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && 0 >= v_3] 14. eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_stop(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (?,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_6,5) ;(eval_start_7,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10},9->{6,7},10->{11},11->{12,13},12->{6 ,7},13->{8,9},14->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(9,6),(12,7)] * Step 2: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 1. eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 2. eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 3. eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 4. eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 5. eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,0,v_x_0_sink) True (?,1) 6. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 8. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (?,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_n >= 1 + v_x_0_sink] 9. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (?,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_x_0_sink >= v_n] 10. eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 11. eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_7(v_1,nondef_0,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 12. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,v_1,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && -1 + v_3 >= 0] 13. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_1) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && 0 >= v_3] 14. eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_stop(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (?,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_6,5) ;(eval_start_7,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10},9->{7},10->{11},11->{12,13},12->{6} ,13->{8,9},14->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 3: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 1. eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 2. eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 3. eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 4. eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 5. eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,0,v_x_0_sink) True (1,1) 6. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 8. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (?,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_n >= 1 + v_x_0_sink] 9. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (1,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_x_0_sink >= v_n] 10. eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 11. eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_7(v_1,nondef_0,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 12. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,v_1,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && -1 + v_3 >= 0] 13. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_1) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && 0 >= v_3] 14. eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_stop(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_6,5) ;(eval_start_7,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10},9->{7},10->{11},11->{12,13},12->{6} ,13->{8,9},14->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_start_0) = x3 p(eval_start_1) = x3 p(eval_start_2) = x3 p(eval_start_3) = x3 p(eval_start_6) = 1 + -1*x1 + x3 p(eval_start_7) = 1 + -1*x1 + x3 p(eval_start_bb0_in) = x3 p(eval_start_bb1_in) = x3 + -1*x4 p(eval_start_bb2_in) = x3 + -1*x5 p(eval_start_bb3_in) = 1 + -1*x1 + x3 p(eval_start_bb4_in) = x3 + -1*x4 p(eval_start_start) = x3 p(eval_start_stop) = x3 + -1*x4 Following rules are strictly oriented: [-1 + v_n + -1*v_x_0_sink >= 0 ==> && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_x_0_sink >= v_n] eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n + -1*v_x_0_sink > -1 + v_n + -1*v_x_0_sink = eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 ==> && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && 0 >= v_3] eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) = 1 + -1*v_1 + v_n > -1*v_1 + v_n = eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_1) Following rules are weakly oriented: True ==> eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n >= v_n = eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) True ==> eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n >= v_n = eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) True ==> eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n >= v_n = eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) True ==> eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n >= v_n = eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) True ==> eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n >= v_n = eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) True ==> eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n >= v_n = eval_start_bb1_in(v_1,v_3,v_n,0,v_x_0_sink) [v_x_0 >= 0 && -1 + v_n >= v_x_0] ==> eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] ==> eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 ==> && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_n >= 1 + v_x_0_sink] eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n + -1*v_x_0_sink >= v_n + -1*v_x_0_sink = eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 ==> && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) = 1 + -1*v_1 + v_n >= 1 + -1*v_1 + v_n = eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 ==> && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) = 1 + -1*v_1 + v_n >= 1 + -1*v_1 + v_n = eval_start_7(v_1,nondef_0,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 ==> && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && -1 + v_3 >= 0] eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) = 1 + -1*v_1 + v_n >= -1*v_1 + v_n = eval_start_bb1_in(v_1,v_3,v_n,v_1,v_x_0_sink) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] ==> eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_start_stop(v_1,v_3,v_n,v_x_0,v_x_0_sink) * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 1. eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 2. eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 3. eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 4. eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 5. eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,0,v_x_0_sink) True (1,1) 6. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 8. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (?,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_n >= 1 + v_x_0_sink] 9. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (1,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_x_0_sink >= v_n] 10. eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 11. eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_7(v_1,nondef_0,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 12. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,v_1,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && -1 + v_3 >= 0] 13. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_1) [-2 + v_n + -1*v_x_0_sink >= 0 (v_n,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && 0 >= v_3] 14. eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_stop(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_6,5) ;(eval_start_7,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10},9->{7},10->{11},11->{12,13},12->{6} ,13->{8,9},14->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_start_0) = x3 p(eval_start_1) = x3 p(eval_start_2) = x3 p(eval_start_3) = x3 p(eval_start_6) = 1 + -1*x1 + x3 p(eval_start_7) = 1 + -1*x1 + x3 p(eval_start_bb0_in) = x3 p(eval_start_bb1_in) = x3 + -1*x4 p(eval_start_bb2_in) = x3 + -1*x5 p(eval_start_bb3_in) = 1 + -1*x1 + x3 p(eval_start_bb4_in) = x3 + -1*x4 p(eval_start_start) = x3 p(eval_start_stop) = x3 + -1*x4 Following rules are strictly oriented: [-1 + v_n + -1*v_x_0_sink >= 0 ==> && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_x_0_sink >= v_n] eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n + -1*v_x_0_sink > -1 + v_n + -1*v_x_0_sink = eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 ==> && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && -1 + v_3 >= 0] eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) = 1 + -1*v_1 + v_n > -1*v_1 + v_n = eval_start_bb1_in(v_1,v_3,v_n,v_1,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 ==> && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && 0 >= v_3] eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) = 1 + -1*v_1 + v_n > -1*v_1 + v_n = eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_1) Following rules are weakly oriented: True ==> eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n >= v_n = eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) True ==> eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n >= v_n = eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) True ==> eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n >= v_n = eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) True ==> eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n >= v_n = eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) True ==> eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n >= v_n = eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) True ==> eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n >= v_n = eval_start_bb1_in(v_1,v_3,v_n,0,v_x_0_sink) [v_x_0 >= 0 && -1 + v_n >= v_x_0] ==> eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= v_n] ==> eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 ==> && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_n >= 1 + v_x_0_sink] eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n + -1*v_x_0_sink >= v_n + -1*v_x_0_sink = eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 ==> && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) = 1 + -1*v_1 + v_n >= 1 + -1*v_1 + v_n = eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 ==> && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) = 1 + -1*v_1 + v_n >= 1 + -1*v_1 + v_n = eval_start_7(v_1,nondef_0,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] ==> eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) = v_n + -1*v_x_0 >= v_n + -1*v_x_0 = eval_start_stop(v_1,v_3,v_n,v_x_0,v_x_0_sink) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 1. eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 2. eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 3. eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 4. eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 5. eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,0,v_x_0_sink) True (1,1) 6. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 8. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (?,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_n >= 1 + v_x_0_sink] 9. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (1,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_x_0_sink >= v_n] 10. eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 11. eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_7(v_1,nondef_0,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (?,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 12. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,v_1,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (v_n,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && -1 + v_3 >= 0] 13. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_1) [-2 + v_n + -1*v_x_0_sink >= 0 (v_n,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && 0 >= v_3] 14. eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_stop(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_6,5) ;(eval_start_7,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10},9->{7},10->{11},11->{12,13},12->{6} ,13->{8,9},14->{}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 6: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 1. eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 2. eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 3. eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 4. eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 5. eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,0,v_x_0_sink) True (1,1) 6. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (1 + v_n,1) 7. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 8. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (1 + 2*v_n,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_n >= 1 + v_x_0_sink] 9. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink,v_x_0_sink) [-1 + v_n + -1*v_x_0_sink >= 0 (1,1) && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -1 + v_n + v_x_0_sink >= 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_x_0_sink >= v_n] 10. eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (1 + 2*v_n,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 11. eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_7(v_1,nondef_0,v_n,v_x_0,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (1 + 2*v_n,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0] 12. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,v_1,v_x_0_sink) [-2 + v_n + -1*v_x_0_sink >= 0 (v_n,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && -1 + v_3 >= 0] 13. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_1) [-2 + v_n + -1*v_x_0_sink >= 0 (v_n,1) && -1 + v_1 + -1*v_x_0_sink >= 0 && v_x_0_sink >= 0 && v_x_0 + v_x_0_sink >= 0 && -1*v_x_0 + v_x_0_sink >= 0 && -2 + v_n + v_x_0_sink >= 0 && -1 + v_1 + v_x_0_sink >= 0 && 1 + -1*v_1 + v_x_0_sink >= 0 && -2 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -2 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && -2 + v_n >= 0 && -3 + v_1 + v_n >= 0 && -1 + -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && 0 >= v_3] 14. eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_stop(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_6,5) ;(eval_start_7,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10},9->{7},10->{11},11->{12,13},12->{6} ,13->{8,9},14->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))