YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) True (1,1) 1. eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_0(v__0,v__1,v_3,v_i,v_k) True (?,1) 2. eval_start_0(v__0,v__1,v_3,v_i,v_k) -> eval_start_1(v__0,v__1,v_3,v_i,v_k) True (?,1) 3. eval_start_1(v__0,v__1,v_3,v_i,v_k) -> eval_start_2(v__0,v__1,v_3,v_i,v_k) True (?,1) 4. eval_start_2(v__0,v__1,v_3,v_i,v_k) -> eval_start_3(v__0,v__1,v_3,v_i,v_k) True (?,1) 5. eval_start_3(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb1_in(v_i,v__1,v_3,v_i,v_k) True (?,1) 6. eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) [-1 + v__0 >= 100] (?,1) 7. eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) [100 >= v__0] (?,1) 8. eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb1_in(-1 + v__0,v__1,v_3,v_i,v_k) True (?,1) 9. eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_8(v__0,v__1,50 + v__0 + v_k,v_i,v_k) True (?,1) 10. eval_start_8(v__0,v__1,v_3,v_i,v_k) -> eval_start_9(v__0,v__1,v_3,v_i,v_k) True (?,1) 11. eval_start_9(v__0,v__1,v_3,v_i,v_k) -> eval_start_10(v__0,v__1,v_3,v_i,v_k) True (?,1) 12. eval_start_10(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb4_in(v__0,v_3,v_3,v_i,v_k) True (?,1) 13. eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) [v__1 >= 0] (?,1) 14. eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) [-1 >= v__1] (?,1) 15. eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb4_in(v__0,-1 + v__1,v_3,v_i,v_k) True (?,1) 16. eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_stop(v__0,v__1,v_3,v_i,v_k) True (?,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_10,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_8,5) ;(eval_start_9,5) ;(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_bb5_in,5) ;(eval_start_bb6_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},7->{9},8->{6,7},9->{10},10->{11},11->{12},12->{13,14} ,13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) True (1,1) 1. eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_0(v__0,v__1,v_3,v_i,v_k) True (1,1) 2. eval_start_0(v__0,v__1,v_3,v_i,v_k) -> eval_start_1(v__0,v__1,v_3,v_i,v_k) True (1,1) 3. eval_start_1(v__0,v__1,v_3,v_i,v_k) -> eval_start_2(v__0,v__1,v_3,v_i,v_k) True (1,1) 4. eval_start_2(v__0,v__1,v_3,v_i,v_k) -> eval_start_3(v__0,v__1,v_3,v_i,v_k) True (1,1) 5. eval_start_3(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb1_in(v_i,v__1,v_3,v_i,v_k) True (1,1) 6. eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) [-1 + v__0 >= 100] (?,1) 7. eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) [100 >= v__0] (1,1) 8. eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb1_in(-1 + v__0,v__1,v_3,v_i,v_k) True (?,1) 9. eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_8(v__0,v__1,50 + v__0 + v_k,v_i,v_k) True (1,1) 10. eval_start_8(v__0,v__1,v_3,v_i,v_k) -> eval_start_9(v__0,v__1,v_3,v_i,v_k) True (1,1) 11. eval_start_9(v__0,v__1,v_3,v_i,v_k) -> eval_start_10(v__0,v__1,v_3,v_i,v_k) True (1,1) 12. eval_start_10(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb4_in(v__0,v_3,v_3,v_i,v_k) True (1,1) 13. eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) [v__1 >= 0] (?,1) 14. eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) [-1 >= v__1] (1,1) 15. eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb4_in(v__0,-1 + v__1,v_3,v_i,v_k) True (?,1) 16. eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_stop(v__0,v__1,v_3,v_i,v_k) True (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_10,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_8,5) ;(eval_start_9,5) ;(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_bb5_in,5) ;(eval_start_bb6_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},7->{9},8->{6,7},9->{10},10->{11},11->{12},12->{13,14} ,13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_start_0) = 151 + x5 p(eval_start_1) = 151 + x5 p(eval_start_10) = 1 + x3 p(eval_start_2) = 151 + x5 p(eval_start_3) = 151 + x5 p(eval_start_8) = 1 + x3 p(eval_start_9) = 1 + x3 p(eval_start_bb0_in) = 151 + x5 p(eval_start_bb1_in) = 151 + x5 p(eval_start_bb2_in) = 151 + x5 p(eval_start_bb3_in) = 51 + x1 + x5 p(eval_start_bb4_in) = 1 + x2 p(eval_start_bb5_in) = x2 p(eval_start_bb6_in) = 1 + x2 p(eval_start_start) = 151 + x5 p(eval_start_stop) = 1 + x2 Following rules are strictly oriented: [v__1 >= 0] ==> eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) = 1 + v__1 > v__1 = eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) Following rules are weakly oriented: True ==> eval_start_start(v__0,v__1,v_3,v_i,v_k) = 151 + v_k >= 151 + v_k = eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) = 151 + v_k >= 151 + v_k = eval_start_0(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_0(v__0,v__1,v_3,v_i,v_k) = 151 + v_k >= 151 + v_k = eval_start_1(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_1(v__0,v__1,v_3,v_i,v_k) = 151 + v_k >= 151 + v_k = eval_start_2(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_2(v__0,v__1,v_3,v_i,v_k) = 151 + v_k >= 151 + v_k = eval_start_3(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_3(v__0,v__1,v_3,v_i,v_k) = 151 + v_k >= 151 + v_k = eval_start_bb1_in(v_i,v__1,v_3,v_i,v_k) [-1 + v__0 >= 100] ==> eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) = 151 + v_k >= 151 + v_k = eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) [100 >= v__0] ==> eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) = 151 + v_k >= 51 + v__0 + v_k = eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) = 151 + v_k >= 151 + v_k = eval_start_bb1_in(-1 + v__0,v__1,v_3,v_i,v_k) True ==> eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) = 51 + v__0 + v_k >= 51 + v__0 + v_k = eval_start_8(v__0,v__1,50 + v__0 + v_k,v_i,v_k) True ==> eval_start_8(v__0,v__1,v_3,v_i,v_k) = 1 + v_3 >= 1 + v_3 = eval_start_9(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_9(v__0,v__1,v_3,v_i,v_k) = 1 + v_3 >= 1 + v_3 = eval_start_10(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_10(v__0,v__1,v_3,v_i,v_k) = 1 + v_3 >= 1 + v_3 = eval_start_bb4_in(v__0,v_3,v_3,v_i,v_k) [-1 >= v__1] ==> eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) = 1 + v__1 >= 1 + v__1 = eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) = v__1 >= v__1 = eval_start_bb4_in(v__0,-1 + v__1,v_3,v_i,v_k) True ==> eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) = 1 + v__1 >= 1 + v__1 = eval_start_stop(v__0,v__1,v_3,v_i,v_k) * Step 3: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) True (1,1) 1. eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_0(v__0,v__1,v_3,v_i,v_k) True (1,1) 2. eval_start_0(v__0,v__1,v_3,v_i,v_k) -> eval_start_1(v__0,v__1,v_3,v_i,v_k) True (1,1) 3. eval_start_1(v__0,v__1,v_3,v_i,v_k) -> eval_start_2(v__0,v__1,v_3,v_i,v_k) True (1,1) 4. eval_start_2(v__0,v__1,v_3,v_i,v_k) -> eval_start_3(v__0,v__1,v_3,v_i,v_k) True (1,1) 5. eval_start_3(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb1_in(v_i,v__1,v_3,v_i,v_k) True (1,1) 6. eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) [-1 + v__0 >= 100] (?,1) 7. eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) [100 >= v__0] (1,1) 8. eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb1_in(-1 + v__0,v__1,v_3,v_i,v_k) True (?,1) 9. eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_8(v__0,v__1,50 + v__0 + v_k,v_i,v_k) True (1,1) 10. eval_start_8(v__0,v__1,v_3,v_i,v_k) -> eval_start_9(v__0,v__1,v_3,v_i,v_k) True (1,1) 11. eval_start_9(v__0,v__1,v_3,v_i,v_k) -> eval_start_10(v__0,v__1,v_3,v_i,v_k) True (1,1) 12. eval_start_10(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb4_in(v__0,v_3,v_3,v_i,v_k) True (1,1) 13. eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) [v__1 >= 0] (151 + v_k,1) 14. eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) [-1 >= v__1] (1,1) 15. eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb4_in(v__0,-1 + v__1,v_3,v_i,v_k) True (?,1) 16. eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_stop(v__0,v__1,v_3,v_i,v_k) True (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_10,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_8,5) ;(eval_start_9,5) ;(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_bb5_in,5) ;(eval_start_bb6_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},7->{9},8->{6,7},9->{10},10->{11},11->{12},12->{13,14} ,13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) True (1,1) 1. eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_0(v__0,v__1,v_3,v_i,v_k) True (1,1) 2. eval_start_0(v__0,v__1,v_3,v_i,v_k) -> eval_start_1(v__0,v__1,v_3,v_i,v_k) True (1,1) 3. eval_start_1(v__0,v__1,v_3,v_i,v_k) -> eval_start_2(v__0,v__1,v_3,v_i,v_k) True (1,1) 4. eval_start_2(v__0,v__1,v_3,v_i,v_k) -> eval_start_3(v__0,v__1,v_3,v_i,v_k) True (1,1) 5. eval_start_3(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb1_in(v_i,v__1,v_3,v_i,v_k) True (1,1) 6. eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) [-1 + v__0 >= 100] (?,1) 7. eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) [100 >= v__0] (1,1) 8. eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb1_in(-1 + v__0,v__1,v_3,v_i,v_k) True (?,1) 9. eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_8(v__0,v__1,50 + v__0 + v_k,v_i,v_k) True (1,1) 10. eval_start_8(v__0,v__1,v_3,v_i,v_k) -> eval_start_9(v__0,v__1,v_3,v_i,v_k) True (1,1) 11. eval_start_9(v__0,v__1,v_3,v_i,v_k) -> eval_start_10(v__0,v__1,v_3,v_i,v_k) True (1,1) 12. eval_start_10(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb4_in(v__0,v_3,v_3,v_i,v_k) True (1,1) 13. eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) [v__1 >= 0] (151 + v_k,1) 14. eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) [-1 >= v__1] (1,1) 15. eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb4_in(v__0,-1 + v__1,v_3,v_i,v_k) True (151 + v_k,1) 16. eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_stop(v__0,v__1,v_3,v_i,v_k) True (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_10,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_8,5) ;(eval_start_9,5) ;(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_bb5_in,5) ;(eval_start_bb6_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},7->{9},8->{6,7},9->{10},10->{11},11->{12},12->{13,14} ,13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_start_0) = 2 + x4 p(eval_start_1) = 2 + x4 p(eval_start_10) = x1 p(eval_start_2) = 2 + x4 p(eval_start_3) = 2 + x4 p(eval_start_8) = x1 p(eval_start_9) = x1 p(eval_start_bb0_in) = 2 + x4 p(eval_start_bb1_in) = 2 + x1 p(eval_start_bb2_in) = 1 + x1 p(eval_start_bb3_in) = 2 + x1 p(eval_start_bb4_in) = x1 p(eval_start_bb5_in) = x1 p(eval_start_bb6_in) = x1 p(eval_start_start) = 2 + x4 p(eval_start_stop) = x1 Following rules are strictly oriented: [-1 + v__0 >= 100] ==> eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) = 2 + v__0 > 1 + v__0 = eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) Following rules are weakly oriented: True ==> eval_start_start(v__0,v__1,v_3,v_i,v_k) = 2 + v_i >= 2 + v_i = eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) = 2 + v_i >= 2 + v_i = eval_start_0(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_0(v__0,v__1,v_3,v_i,v_k) = 2 + v_i >= 2 + v_i = eval_start_1(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_1(v__0,v__1,v_3,v_i,v_k) = 2 + v_i >= 2 + v_i = eval_start_2(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_2(v__0,v__1,v_3,v_i,v_k) = 2 + v_i >= 2 + v_i = eval_start_3(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_3(v__0,v__1,v_3,v_i,v_k) = 2 + v_i >= 2 + v_i = eval_start_bb1_in(v_i,v__1,v_3,v_i,v_k) [100 >= v__0] ==> eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) = 2 + v__0 >= 2 + v__0 = eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) = 1 + v__0 >= 1 + v__0 = eval_start_bb1_in(-1 + v__0,v__1,v_3,v_i,v_k) True ==> eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) = 2 + v__0 >= v__0 = eval_start_8(v__0,v__1,50 + v__0 + v_k,v_i,v_k) True ==> eval_start_8(v__0,v__1,v_3,v_i,v_k) = v__0 >= v__0 = eval_start_9(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_9(v__0,v__1,v_3,v_i,v_k) = v__0 >= v__0 = eval_start_10(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_10(v__0,v__1,v_3,v_i,v_k) = v__0 >= v__0 = eval_start_bb4_in(v__0,v_3,v_3,v_i,v_k) [v__1 >= 0] ==> eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) = v__0 >= v__0 = eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) [-1 >= v__1] ==> eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) = v__0 >= v__0 = eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) True ==> eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) = v__0 >= v__0 = eval_start_bb4_in(v__0,-1 + v__1,v_3,v_i,v_k) True ==> eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) = v__0 >= v__0 = eval_start_stop(v__0,v__1,v_3,v_i,v_k) * Step 5: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) True (1,1) 1. eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_0(v__0,v__1,v_3,v_i,v_k) True (1,1) 2. eval_start_0(v__0,v__1,v_3,v_i,v_k) -> eval_start_1(v__0,v__1,v_3,v_i,v_k) True (1,1) 3. eval_start_1(v__0,v__1,v_3,v_i,v_k) -> eval_start_2(v__0,v__1,v_3,v_i,v_k) True (1,1) 4. eval_start_2(v__0,v__1,v_3,v_i,v_k) -> eval_start_3(v__0,v__1,v_3,v_i,v_k) True (1,1) 5. eval_start_3(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb1_in(v_i,v__1,v_3,v_i,v_k) True (1,1) 6. eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) [-1 + v__0 >= 100] (2 + v_i,1) 7. eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) [100 >= v__0] (1,1) 8. eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb1_in(-1 + v__0,v__1,v_3,v_i,v_k) True (?,1) 9. eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_8(v__0,v__1,50 + v__0 + v_k,v_i,v_k) True (1,1) 10. eval_start_8(v__0,v__1,v_3,v_i,v_k) -> eval_start_9(v__0,v__1,v_3,v_i,v_k) True (1,1) 11. eval_start_9(v__0,v__1,v_3,v_i,v_k) -> eval_start_10(v__0,v__1,v_3,v_i,v_k) True (1,1) 12. eval_start_10(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb4_in(v__0,v_3,v_3,v_i,v_k) True (1,1) 13. eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) [v__1 >= 0] (151 + v_k,1) 14. eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) [-1 >= v__1] (1,1) 15. eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb4_in(v__0,-1 + v__1,v_3,v_i,v_k) True (151 + v_k,1) 16. eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_stop(v__0,v__1,v_3,v_i,v_k) True (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_10,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_8,5) ;(eval_start_9,5) ;(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_bb5_in,5) ;(eval_start_bb6_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},7->{9},8->{6,7},9->{10},10->{11},11->{12},12->{13,14} ,13->{15},14->{16},15->{13,14},16->{}] + 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__1,v_3,v_i,v_k) -> eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) True (1,1) 1. eval_start_bb0_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_0(v__0,v__1,v_3,v_i,v_k) True (1,1) 2. eval_start_0(v__0,v__1,v_3,v_i,v_k) -> eval_start_1(v__0,v__1,v_3,v_i,v_k) True (1,1) 3. eval_start_1(v__0,v__1,v_3,v_i,v_k) -> eval_start_2(v__0,v__1,v_3,v_i,v_k) True (1,1) 4. eval_start_2(v__0,v__1,v_3,v_i,v_k) -> eval_start_3(v__0,v__1,v_3,v_i,v_k) True (1,1) 5. eval_start_3(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb1_in(v_i,v__1,v_3,v_i,v_k) True (1,1) 6. eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) [-1 + v__0 >= 100] (2 + v_i,1) 7. eval_start_bb1_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) [100 >= v__0] (1,1) 8. eval_start_bb2_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb1_in(-1 + v__0,v__1,v_3,v_i,v_k) True (2 + v_i,1) 9. eval_start_bb3_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_8(v__0,v__1,50 + v__0 + v_k,v_i,v_k) True (1,1) 10. eval_start_8(v__0,v__1,v_3,v_i,v_k) -> eval_start_9(v__0,v__1,v_3,v_i,v_k) True (1,1) 11. eval_start_9(v__0,v__1,v_3,v_i,v_k) -> eval_start_10(v__0,v__1,v_3,v_i,v_k) True (1,1) 12. eval_start_10(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb4_in(v__0,v_3,v_3,v_i,v_k) True (1,1) 13. eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) [v__1 >= 0] (151 + v_k,1) 14. eval_start_bb4_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) [-1 >= v__1] (1,1) 15. eval_start_bb5_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_bb4_in(v__0,-1 + v__1,v_3,v_i,v_k) True (151 + v_k,1) 16. eval_start_bb6_in(v__0,v__1,v_3,v_i,v_k) -> eval_start_stop(v__0,v__1,v_3,v_i,v_k) True (1,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_10,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_8,5) ;(eval_start_9,5) ;(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_bb5_in,5) ;(eval_start_bb6_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},7->{9},8->{6,7},9->{10},10->{11},11->{12},12->{13,14} ,13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))