YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 1. eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) True (?,1) 2. eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) True (?,1) 3. eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) True (?,1) 4. eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(v_n,v__0_sink,v_1,v_3,v_n) True (?,1) 5. eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb2_in(v__0,v__0,v_1,v_3,v_n) [-1 + v__0 >= 0] (?,1) 6. eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) [0 >= v__0] (?,1) 7. eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb3_in(v__0,v__0_sink,-1 + v__0_sink,v_3,v_n) [-2 + v__0_sink >= 0] (?,1) 8. eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(-1 + v__0_sink,v__0_sink,v_1,v_3,v_n) [0 >= -1 + v__0_sink] (?,1) 9. eval_start_bb3_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) True (?,1) 10. eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_6(v__0,v__0_sink,v_1,nondef_0,v_n) True (?,1) 11. eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(v_1,v__0_sink,v_1,v_3,v_n) [-1 + v_3 >= 0] (?,1) 12. eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb2_in(v__0,v_1,v_1,v_3,v_n) [0 >= v_3] (?,1) 13. eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_stop(v__0,v__0_sink,v_1,v_3,v_n) True (?,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(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->{5,6},5->{7,8},6->{13},7->{9},8->{5,6},9->{10},10->{11,12},11->{5,6} ,12->{7,8},13->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(8,5)] * Step 2: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 1. eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) True (?,1) 2. eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) True (?,1) 3. eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) True (?,1) 4. eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(v_n,v__0_sink,v_1,v_3,v_n) True (?,1) 5. eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb2_in(v__0,v__0,v_1,v_3,v_n) [-1 + v__0 >= 0] (?,1) 6. eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) [0 >= v__0] (?,1) 7. eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb3_in(v__0,v__0_sink,-1 + v__0_sink,v_3,v_n) [-2 + v__0_sink >= 0] (?,1) 8. eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(-1 + v__0_sink,v__0_sink,v_1,v_3,v_n) [0 >= -1 + v__0_sink] (?,1) 9. eval_start_bb3_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) True (?,1) 10. eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_6(v__0,v__0_sink,v_1,nondef_0,v_n) True (?,1) 11. eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(v_1,v__0_sink,v_1,v_3,v_n) [-1 + v_3 >= 0] (?,1) 12. eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb2_in(v__0,v_1,v_1,v_3,v_n) [0 >= v_3] (?,1) 13. eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_stop(v__0,v__0_sink,v_1,v_3,v_n) True (?,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(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->{5,6},5->{7,8},6->{13},7->{9},8->{6},9->{10},10->{11,12},11->{5,6},12->{7 ,8},13->{}] + 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__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 1. eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 2. eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 3. eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 4. eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(v_n,v__0_sink,v_1,v_3,v_n) True (1,1) 5. eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb2_in(v__0,v__0,v_1,v_3,v_n) [-1 + v__0 >= 0] (?,1) 6. eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) [0 >= v__0] (1,1) 7. eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb3_in(v__0,v__0_sink,-1 + v__0_sink,v_3,v_n) [-2 + v__0_sink >= 0] (?,1) 8. eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(-1 + v__0_sink,v__0_sink,v_1,v_3,v_n) [0 >= -1 + v__0_sink] (1,1) 9. eval_start_bb3_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) True (?,1) 10. eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_6(v__0,v__0_sink,v_1,nondef_0,v_n) True (?,1) 11. eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(v_1,v__0_sink,v_1,v_3,v_n) [-1 + v_3 >= 0] (?,1) 12. eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb2_in(v__0,v_1,v_1,v_3,v_n) [0 >= v_3] (?,1) 13. eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_stop(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(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->{5,6},5->{7,8},6->{13},7->{9},8->{6},9->{10},10->{11,12},11->{5,6},12->{7 ,8},13->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_start_0) = x5 p(eval_start_1) = x5 p(eval_start_2) = x5 p(eval_start_5) = x3 p(eval_start_6) = x3 p(eval_start_bb0_in) = x5 p(eval_start_bb1_in) = x1 p(eval_start_bb2_in) = -1 + x2 p(eval_start_bb3_in) = x3 p(eval_start_bb4_in) = x1 p(eval_start_start) = x5 p(eval_start_stop) = x1 Following rules are strictly oriented: [-1 + v__0 >= 0] ==> eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) = v__0 > -1 + v__0 = eval_start_bb2_in(v__0,v__0,v_1,v_3,v_n) Following rules are weakly oriented: True ==> eval_start_start(v__0,v__0_sink,v_1,v_3,v_n) = v_n >= v_n = eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) True ==> eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) = v_n >= v_n = eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) True ==> eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) = v_n >= v_n = eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) True ==> eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) = v_n >= v_n = eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) True ==> eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) = v_n >= v_n = eval_start_bb1_in(v_n,v__0_sink,v_1,v_3,v_n) [0 >= v__0] ==> eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) = v__0 >= v__0 = eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) [-2 + v__0_sink >= 0] ==> eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) = -1 + v__0_sink >= -1 + v__0_sink = eval_start_bb3_in(v__0,v__0_sink,-1 + v__0_sink,v_3,v_n) [0 >= -1 + v__0_sink] ==> eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) = -1 + v__0_sink >= -1 + v__0_sink = eval_start_bb1_in(-1 + v__0_sink,v__0_sink,v_1,v_3,v_n) True ==> eval_start_bb3_in(v__0,v__0_sink,v_1,v_3,v_n) = v_1 >= v_1 = eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) True ==> eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) = v_1 >= v_1 = eval_start_6(v__0,v__0_sink,v_1,nondef_0,v_n) [-1 + v_3 >= 0] ==> eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) = v_1 >= v_1 = eval_start_bb1_in(v_1,v__0_sink,v_1,v_3,v_n) [0 >= v_3] ==> eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) = v_1 >= -1 + v_1 = eval_start_bb2_in(v__0,v_1,v_1,v_3,v_n) True ==> eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) = v__0 >= v__0 = eval_start_stop(v__0,v__0_sink,v_1,v_3,v_n) * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 1. eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 2. eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 3. eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 4. eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(v_n,v__0_sink,v_1,v_3,v_n) True (1,1) 5. eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb2_in(v__0,v__0,v_1,v_3,v_n) [-1 + v__0 >= 0] (v_n,1) 6. eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) [0 >= v__0] (1,1) 7. eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb3_in(v__0,v__0_sink,-1 + v__0_sink,v_3,v_n) [-2 + v__0_sink >= 0] (?,1) 8. eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(-1 + v__0_sink,v__0_sink,v_1,v_3,v_n) [0 >= -1 + v__0_sink] (1,1) 9. eval_start_bb3_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) True (?,1) 10. eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_6(v__0,v__0_sink,v_1,nondef_0,v_n) True (?,1) 11. eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(v_1,v__0_sink,v_1,v_3,v_n) [-1 + v_3 >= 0] (?,1) 12. eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb2_in(v__0,v_1,v_1,v_3,v_n) [0 >= v_3] (?,1) 13. eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_stop(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(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->{5,6},5->{7,8},6->{13},7->{9},8->{6},9->{10},10->{11,12},11->{5,6},12->{7 ,8},13->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_start_0) = 1 + x5 p(eval_start_1) = 1 + x5 p(eval_start_2) = 1 + x5 p(eval_start_5) = 1 + x3 p(eval_start_6) = 1 + x3 p(eval_start_bb0_in) = 1 + x5 p(eval_start_bb1_in) = 1 + x1 p(eval_start_bb2_in) = 1 + x2 p(eval_start_bb3_in) = 1 + x3 p(eval_start_bb4_in) = 1 + x1 p(eval_start_start) = 1 + x5 p(eval_start_stop) = 1 + x1 Following rules are strictly oriented: [-2 + v__0_sink >= 0] ==> eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) = 1 + v__0_sink > v__0_sink = eval_start_bb3_in(v__0,v__0_sink,-1 + v__0_sink,v_3,v_n) Following rules are weakly oriented: True ==> eval_start_start(v__0,v__0_sink,v_1,v_3,v_n) = 1 + v_n >= 1 + v_n = eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) True ==> eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) = 1 + v_n >= 1 + v_n = eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) True ==> eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) = 1 + v_n >= 1 + v_n = eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) True ==> eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) = 1 + v_n >= 1 + v_n = eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) True ==> eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) = 1 + v_n >= 1 + v_n = eval_start_bb1_in(v_n,v__0_sink,v_1,v_3,v_n) [-1 + v__0 >= 0] ==> eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) = 1 + v__0 >= 1 + v__0 = eval_start_bb2_in(v__0,v__0,v_1,v_3,v_n) [0 >= v__0] ==> eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) = 1 + v__0 >= 1 + v__0 = eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) [0 >= -1 + v__0_sink] ==> eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) = 1 + v__0_sink >= v__0_sink = eval_start_bb1_in(-1 + v__0_sink,v__0_sink,v_1,v_3,v_n) True ==> eval_start_bb3_in(v__0,v__0_sink,v_1,v_3,v_n) = 1 + v_1 >= 1 + v_1 = eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) True ==> eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) = 1 + v_1 >= 1 + v_1 = eval_start_6(v__0,v__0_sink,v_1,nondef_0,v_n) [-1 + v_3 >= 0] ==> eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) = 1 + v_1 >= 1 + v_1 = eval_start_bb1_in(v_1,v__0_sink,v_1,v_3,v_n) [0 >= v_3] ==> eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) = 1 + v_1 >= 1 + v_1 = eval_start_bb2_in(v__0,v_1,v_1,v_3,v_n) True ==> eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) = 1 + v__0 >= 1 + v__0 = eval_start_stop(v__0,v__0_sink,v_1,v_3,v_n) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 1. eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 2. eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 3. eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 4. eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(v_n,v__0_sink,v_1,v_3,v_n) True (1,1) 5. eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb2_in(v__0,v__0,v_1,v_3,v_n) [-1 + v__0 >= 0] (v_n,1) 6. eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) [0 >= v__0] (1,1) 7. eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb3_in(v__0,v__0_sink,-1 + v__0_sink,v_3,v_n) [-2 + v__0_sink >= 0] (1 + v_n,1) 8. eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(-1 + v__0_sink,v__0_sink,v_1,v_3,v_n) [0 >= -1 + v__0_sink] (1,1) 9. eval_start_bb3_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) True (?,1) 10. eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_6(v__0,v__0_sink,v_1,nondef_0,v_n) True (?,1) 11. eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(v_1,v__0_sink,v_1,v_3,v_n) [-1 + v_3 >= 0] (?,1) 12. eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb2_in(v__0,v_1,v_1,v_3,v_n) [0 >= v_3] (?,1) 13. eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_stop(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(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->{5,6},5->{7,8},6->{13},7->{9},8->{6},9->{10},10->{11,12},11->{5,6},12->{7 ,8},13->{}] + 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__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 1. eval_start_bb0_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 2. eval_start_0(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 3. eval_start_1(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) 4. eval_start_2(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(v_n,v__0_sink,v_1,v_3,v_n) True (1,1) 5. eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb2_in(v__0,v__0,v_1,v_3,v_n) [-1 + v__0 >= 0] (v_n,1) 6. eval_start_bb1_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) [0 >= v__0] (1,1) 7. eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb3_in(v__0,v__0_sink,-1 + v__0_sink,v_3,v_n) [-2 + v__0_sink >= 0] (1 + v_n,1) 8. eval_start_bb2_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(-1 + v__0_sink,v__0_sink,v_1,v_3,v_n) [0 >= -1 + v__0_sink] (1,1) 9. eval_start_bb3_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) True (1 + v_n,1) 10. eval_start_5(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_6(v__0,v__0_sink,v_1,nondef_0,v_n) True (1 + v_n,1) 11. eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb1_in(v_1,v__0_sink,v_1,v_3,v_n) [-1 + v_3 >= 0] (1 + v_n,1) 12. eval_start_6(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_bb2_in(v__0,v_1,v_1,v_3,v_n) [0 >= v_3] (1 + v_n,1) 13. eval_start_bb4_in(v__0,v__0_sink,v_1,v_3,v_n) -> eval_start_stop(v__0,v__0_sink,v_1,v_3,v_n) True (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(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->{5,6},5->{7,8},6->{13},7->{9},8->{6},9->{10},10->{11,12},11->{5,6},12->{7 ,8},13->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))