YES(?,O(n^1)) * Step 1: TrivialSCCs WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_exmini_start(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb0_in(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 1. eval_exmini_bb0_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_0(v__0,v__01,v__02,v_i,v_j,v_k) True (?,1) 2. eval_exmini_0(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_1(v__0,v__01,v__02,v_i,v_j,v_k) True (?,1) 3. eval_exmini_1(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_2(v__0,v__01,v__02,v_i,v_j,v_k) True (?,1) 4. eval_exmini_2(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_3(v__0,v__01,v__02,v_i,v_j,v_k) True (?,1) 5. eval_exmini_3(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_4(v__0,v__01,v__02,v_i,v_j,v_k) True (?,1) 6. eval_exmini_4(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_5(v__0,v__01,v__02,v_i,v_j,v_k) True (?,1) 7. eval_exmini_5(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_6(v__0,v__01,v__02,v_i,v_j,v_k) True (?,1) 8. eval_exmini_6(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_7(v__0,v__01,v__02,v_i,v_j,v_k) True (?,1) 9. eval_exmini_7(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb1_in(v_i,v_j,v_k,v_i,v_j,v_k) True (?,1) 10. eval_exmini_bb1_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb2_in(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && 100 >= v__0 && v__02 >= v__01] (?,1) 11. eval_exmini_bb1_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb3_in(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && -1 + v__0 >= 100] (?,1) 12. eval_exmini_bb1_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb3_in(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && -1 + v__01 >= v__02] (?,1) 13. eval_exmini_bb2_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb1_in(v__01,1 + v__0,-1 + v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && -1*v__01 + v_k >= 0 && -1*v__01 + v__02 >= 0 && 100 + -1*v__0 >= 0] (?,1) 14. eval_exmini_bb3_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_stop(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0] (?,1) Signature: {(eval_exmini_0,6) ;(eval_exmini_1,6) ;(eval_exmini_2,6) ;(eval_exmini_3,6) ;(eval_exmini_4,6) ;(eval_exmini_5,6) ;(eval_exmini_6,6) ;(eval_exmini_7,6) ;(eval_exmini_bb0_in,6) ;(eval_exmini_bb1_in,6) ;(eval_exmini_bb2_in,6) ;(eval_exmini_bb3_in,6) ;(eval_exmini_start,6) ;(eval_exmini_stop,6)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10,11,12},10->{13},11->{14},12->{14} ,13->{10,11,12},14->{}] + 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_exmini_start(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb0_in(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 1. eval_exmini_bb0_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_0(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 2. eval_exmini_0(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_1(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 3. eval_exmini_1(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_2(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 4. eval_exmini_2(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_3(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 5. eval_exmini_3(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_4(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 6. eval_exmini_4(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_5(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 7. eval_exmini_5(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_6(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 8. eval_exmini_6(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_7(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 9. eval_exmini_7(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb1_in(v_i,v_j,v_k,v_i,v_j,v_k) True (1,1) 10. eval_exmini_bb1_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb2_in(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && 100 >= v__0 && v__02 >= v__01] (?,1) 11. eval_exmini_bb1_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb3_in(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && -1 + v__0 >= 100] (1,1) 12. eval_exmini_bb1_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb3_in(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && -1 + v__01 >= v__02] (1,1) 13. eval_exmini_bb2_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb1_in(v__01,1 + v__0,-1 + v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && -1*v__01 + v_k >= 0 && -1*v__01 + v__02 >= 0 && 100 + -1*v__0 >= 0] (?,1) 14. eval_exmini_bb3_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_stop(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0] (1,1) Signature: {(eval_exmini_0,6) ;(eval_exmini_1,6) ;(eval_exmini_2,6) ;(eval_exmini_3,6) ;(eval_exmini_4,6) ;(eval_exmini_5,6) ;(eval_exmini_6,6) ;(eval_exmini_7,6) ;(eval_exmini_bb0_in,6) ;(eval_exmini_bb1_in,6) ;(eval_exmini_bb2_in,6) ;(eval_exmini_bb3_in,6) ;(eval_exmini_start,6) ;(eval_exmini_stop,6)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10,11,12},10->{13},11->{14},12->{14} ,13->{10,11,12},14->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_exmini_0) = 102 + -1*x4 + -1*x5 + x6 p(eval_exmini_1) = 102 + -1*x4 + -1*x5 + x6 p(eval_exmini_2) = 102 + -1*x4 + -1*x5 + x6 p(eval_exmini_3) = 102 + -1*x4 + -1*x5 + x6 p(eval_exmini_4) = 102 + -1*x4 + -1*x5 + x6 p(eval_exmini_5) = 102 + -1*x4 + -1*x5 + x6 p(eval_exmini_6) = 102 + -1*x4 + -1*x5 + x6 p(eval_exmini_7) = 102 + -1*x4 + -1*x5 + x6 p(eval_exmini_bb0_in) = 102 + -1*x4 + -1*x5 + x6 p(eval_exmini_bb1_in) = 102 + -1*x1 + -1*x2 + x3 p(eval_exmini_bb2_in) = 101 + -1*x1 + -1*x2 + x3 p(eval_exmini_bb3_in) = -1*x1 + -1*x2 + x3 p(eval_exmini_start) = 102 + -1*x4 + -1*x5 + x6 p(eval_exmini_stop) = -1*x1 + -1*x2 + x3 Following rules are strictly oriented: [-1*v__02 + v_k >= 0 && -1*v__01 + v_k >= 0 && -1*v__01 + v__02 >= 0 && 100 + -1*v__0 >= 0] ==> eval_exmini_bb2_in(v__0,v__01,v__02,v_i,v_j,v_k) = 101 + -1*v__0 + -1*v__01 + v__02 > 100 + -1*v__0 + -1*v__01 + v__02 = eval_exmini_bb1_in(v__01,1 + v__0,-1 + v__02,v_i,v_j,v_k) Following rules are weakly oriented: True ==> eval_exmini_start(v__0,v__01,v__02,v_i,v_j,v_k) = 102 + -1*v_i + -1*v_j + v_k >= 102 + -1*v_i + -1*v_j + v_k = eval_exmini_bb0_in(v__0,v__01,v__02,v_i,v_j,v_k) True ==> eval_exmini_bb0_in(v__0,v__01,v__02,v_i,v_j,v_k) = 102 + -1*v_i + -1*v_j + v_k >= 102 + -1*v_i + -1*v_j + v_k = eval_exmini_0(v__0,v__01,v__02,v_i,v_j,v_k) True ==> eval_exmini_0(v__0,v__01,v__02,v_i,v_j,v_k) = 102 + -1*v_i + -1*v_j + v_k >= 102 + -1*v_i + -1*v_j + v_k = eval_exmini_1(v__0,v__01,v__02,v_i,v_j,v_k) True ==> eval_exmini_1(v__0,v__01,v__02,v_i,v_j,v_k) = 102 + -1*v_i + -1*v_j + v_k >= 102 + -1*v_i + -1*v_j + v_k = eval_exmini_2(v__0,v__01,v__02,v_i,v_j,v_k) True ==> eval_exmini_2(v__0,v__01,v__02,v_i,v_j,v_k) = 102 + -1*v_i + -1*v_j + v_k >= 102 + -1*v_i + -1*v_j + v_k = eval_exmini_3(v__0,v__01,v__02,v_i,v_j,v_k) True ==> eval_exmini_3(v__0,v__01,v__02,v_i,v_j,v_k) = 102 + -1*v_i + -1*v_j + v_k >= 102 + -1*v_i + -1*v_j + v_k = eval_exmini_4(v__0,v__01,v__02,v_i,v_j,v_k) True ==> eval_exmini_4(v__0,v__01,v__02,v_i,v_j,v_k) = 102 + -1*v_i + -1*v_j + v_k >= 102 + -1*v_i + -1*v_j + v_k = eval_exmini_5(v__0,v__01,v__02,v_i,v_j,v_k) True ==> eval_exmini_5(v__0,v__01,v__02,v_i,v_j,v_k) = 102 + -1*v_i + -1*v_j + v_k >= 102 + -1*v_i + -1*v_j + v_k = eval_exmini_6(v__0,v__01,v__02,v_i,v_j,v_k) True ==> eval_exmini_6(v__0,v__01,v__02,v_i,v_j,v_k) = 102 + -1*v_i + -1*v_j + v_k >= 102 + -1*v_i + -1*v_j + v_k = eval_exmini_7(v__0,v__01,v__02,v_i,v_j,v_k) True ==> eval_exmini_7(v__0,v__01,v__02,v_i,v_j,v_k) = 102 + -1*v_i + -1*v_j + v_k >= 102 + -1*v_i + -1*v_j + v_k = eval_exmini_bb1_in(v_i,v_j,v_k,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && 100 >= v__0 && v__02 >= v__01] ==> eval_exmini_bb1_in(v__0,v__01,v__02,v_i,v_j,v_k) = 102 + -1*v__0 + -1*v__01 + v__02 >= 101 + -1*v__0 + -1*v__01 + v__02 = eval_exmini_bb2_in(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && -1 + v__0 >= 100] ==> eval_exmini_bb1_in(v__0,v__01,v__02,v_i,v_j,v_k) = 102 + -1*v__0 + -1*v__01 + v__02 >= -1*v__0 + -1*v__01 + v__02 = eval_exmini_bb3_in(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && -1 + v__01 >= v__02] ==> eval_exmini_bb1_in(v__0,v__01,v__02,v_i,v_j,v_k) = 102 + -1*v__0 + -1*v__01 + v__02 >= -1*v__0 + -1*v__01 + v__02 = eval_exmini_bb3_in(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0] ==> eval_exmini_bb3_in(v__0,v__01,v__02,v_i,v_j,v_k) = -1*v__0 + -1*v__01 + v__02 >= -1*v__0 + -1*v__01 + v__02 = eval_exmini_stop(v__0,v__01,v__02,v_i,v_j,v_k) * Step 3: KnowledgePropagation WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_exmini_start(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb0_in(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 1. eval_exmini_bb0_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_0(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 2. eval_exmini_0(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_1(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 3. eval_exmini_1(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_2(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 4. eval_exmini_2(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_3(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 5. eval_exmini_3(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_4(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 6. eval_exmini_4(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_5(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 7. eval_exmini_5(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_6(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 8. eval_exmini_6(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_7(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 9. eval_exmini_7(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb1_in(v_i,v_j,v_k,v_i,v_j,v_k) True (1,1) 10. eval_exmini_bb1_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb2_in(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && 100 >= v__0 && v__02 >= v__01] (?,1) 11. eval_exmini_bb1_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb3_in(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && -1 + v__0 >= 100] (1,1) 12. eval_exmini_bb1_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb3_in(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && -1 + v__01 >= v__02] (1,1) 13. eval_exmini_bb2_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb1_in(v__01,1 + v__0,-1 + v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && -1*v__01 + v_k >= 0 && -1*v__01 + v__02 >= 0 && 100 + -1*v__0 >= 0] (102 + v_i + v_j + v_k,1) 14. eval_exmini_bb3_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_stop(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0] (1,1) Signature: {(eval_exmini_0,6) ;(eval_exmini_1,6) ;(eval_exmini_2,6) ;(eval_exmini_3,6) ;(eval_exmini_4,6) ;(eval_exmini_5,6) ;(eval_exmini_6,6) ;(eval_exmini_7,6) ;(eval_exmini_bb0_in,6) ;(eval_exmini_bb1_in,6) ;(eval_exmini_bb2_in,6) ;(eval_exmini_bb3_in,6) ;(eval_exmini_start,6) ;(eval_exmini_stop,6)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10,11,12},10->{13},11->{14},12->{14} ,13->{10,11,12},14->{}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 4: PolyRank WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_exmini_start(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb0_in(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 1. eval_exmini_bb0_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_0(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 2. eval_exmini_0(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_1(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 3. eval_exmini_1(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_2(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 4. eval_exmini_2(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_3(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 5. eval_exmini_3(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_4(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 6. eval_exmini_4(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_5(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 7. eval_exmini_5(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_6(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 8. eval_exmini_6(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_7(v__0,v__01,v__02,v_i,v_j,v_k) True (1,1) 9. eval_exmini_7(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb1_in(v_i,v_j,v_k,v_i,v_j,v_k) True (1,1) 10. eval_exmini_bb1_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb2_in(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && 100 >= v__0 && v__02 >= v__01] (103 + v_i + v_j + v_k,1) 11. eval_exmini_bb1_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb3_in(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && -1 + v__0 >= 100] (1,1) 12. eval_exmini_bb1_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb3_in(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && -1 + v__01 >= v__02] (1,1) 13. eval_exmini_bb2_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_bb1_in(v__01,1 + v__0,-1 + v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0 && -1*v__01 + v_k >= 0 && -1*v__01 + v__02 >= 0 && 100 + -1*v__0 >= 0] (102 + v_i + v_j + v_k,1) 14. eval_exmini_bb3_in(v__0,v__01,v__02,v_i,v_j,v_k) -> eval_exmini_stop(v__0,v__01,v__02,v_i,v_j,v_k) [-1*v__02 + v_k >= 0] (1,1) Signature: {(eval_exmini_0,6) ;(eval_exmini_1,6) ;(eval_exmini_2,6) ;(eval_exmini_3,6) ;(eval_exmini_4,6) ;(eval_exmini_5,6) ;(eval_exmini_6,6) ;(eval_exmini_7,6) ;(eval_exmini_bb0_in,6) ;(eval_exmini_bb1_in,6) ;(eval_exmini_bb2_in,6) ;(eval_exmini_bb3_in,6) ;(eval_exmini_start,6) ;(eval_exmini_stop,6)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10,11,12},10->{13},11->{14},12->{14} ,13->{10,11,12},14->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(n^1))