YES(?,O(1)) * Step 1: TrivialSCCs WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. eval_easy1_start(v_0,v_x_0) -> eval_easy1_bb0_in(v_0,v_x_0) True (1,1) 1. eval_easy1_bb0_in(v_0,v_x_0) -> eval_easy1_1(nondef_0,v_x_0) True (?,1) 2. eval_easy1_1(v_0,v_x_0) -> eval_easy1_2(v_0,v_x_0) True (?,1) 3. eval_easy1_2(v_0,v_x_0) -> eval_easy1_3(v_0,v_x_0) True (?,1) 4. eval_easy1_3(v_0,v_x_0) -> eval_easy1_4(v_0,v_x_0) True (?,1) 5. eval_easy1_4(v_0,v_x_0) -> eval_easy1_5(v_0,v_x_0) True (?,1) 6. eval_easy1_5(v_0,v_x_0) -> eval_easy1_6(v_0,v_x_0) True (?,1) 7. eval_easy1_6(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,0) True (?,1) 8. eval_easy1_bb1_in(v_0,v_x_0) -> eval_easy1_bb2_in(v_0,v_x_0) [v_x_0 >= 0 && 39 >= v_x_0] (?,1) 9. eval_easy1_bb1_in(v_0,v_x_0) -> eval_easy1_bb3_in(v_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= 40] (?,1) 10. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,1 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_0 = 0] (?,1) 11. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 >= v_0] (?,1) 12. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_0 >= 0] (?,1) 13. eval_easy1_bb3_in(v_0,v_x_0) -> eval_easy1_stop(v_0,v_x_0) [-40 + v_x_0 >= 0] (?,1) Signature: {(eval_easy1_1,2) ;(eval_easy1_2,2) ;(eval_easy1_3,2) ;(eval_easy1_4,2) ;(eval_easy1_5,2) ;(eval_easy1_6,2) ;(eval_easy1_bb0_in,2) ;(eval_easy1_bb1_in,2) ;(eval_easy1_bb2_in,2) ;(eval_easy1_bb3_in,2) ;(eval_easy1_start,2) ;(eval_easy1_stop,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9},8->{10,11,12},9->{13},10->{8,9},11->{8,9} ,12->{8,9},13->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. eval_easy1_start(v_0,v_x_0) -> eval_easy1_bb0_in(v_0,v_x_0) True (1,1) 1. eval_easy1_bb0_in(v_0,v_x_0) -> eval_easy1_1(nondef_0,v_x_0) True (1,1) 2. eval_easy1_1(v_0,v_x_0) -> eval_easy1_2(v_0,v_x_0) True (1,1) 3. eval_easy1_2(v_0,v_x_0) -> eval_easy1_3(v_0,v_x_0) True (1,1) 4. eval_easy1_3(v_0,v_x_0) -> eval_easy1_4(v_0,v_x_0) True (1,1) 5. eval_easy1_4(v_0,v_x_0) -> eval_easy1_5(v_0,v_x_0) True (1,1) 6. eval_easy1_5(v_0,v_x_0) -> eval_easy1_6(v_0,v_x_0) True (1,1) 7. eval_easy1_6(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,0) True (1,1) 8. eval_easy1_bb1_in(v_0,v_x_0) -> eval_easy1_bb2_in(v_0,v_x_0) [v_x_0 >= 0 && 39 >= v_x_0] (?,1) 9. eval_easy1_bb1_in(v_0,v_x_0) -> eval_easy1_bb3_in(v_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= 40] (1,1) 10. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,1 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_0 = 0] (?,1) 11. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 >= v_0] (?,1) 12. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_0 >= 0] (?,1) 13. eval_easy1_bb3_in(v_0,v_x_0) -> eval_easy1_stop(v_0,v_x_0) [-40 + v_x_0 >= 0] (1,1) Signature: {(eval_easy1_1,2) ;(eval_easy1_2,2) ;(eval_easy1_3,2) ;(eval_easy1_4,2) ;(eval_easy1_5,2) ;(eval_easy1_6,2) ;(eval_easy1_bb0_in,2) ;(eval_easy1_bb1_in,2) ;(eval_easy1_bb2_in,2) ;(eval_easy1_bb3_in,2) ;(eval_easy1_start,2) ;(eval_easy1_stop,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9},8->{10,11,12},9->{13},10->{8,9},11->{8,9} ,12->{8,9},13->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(7,9)] * Step 3: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. eval_easy1_start(v_0,v_x_0) -> eval_easy1_bb0_in(v_0,v_x_0) True (1,1) 1. eval_easy1_bb0_in(v_0,v_x_0) -> eval_easy1_1(nondef_0,v_x_0) True (1,1) 2. eval_easy1_1(v_0,v_x_0) -> eval_easy1_2(v_0,v_x_0) True (1,1) 3. eval_easy1_2(v_0,v_x_0) -> eval_easy1_3(v_0,v_x_0) True (1,1) 4. eval_easy1_3(v_0,v_x_0) -> eval_easy1_4(v_0,v_x_0) True (1,1) 5. eval_easy1_4(v_0,v_x_0) -> eval_easy1_5(v_0,v_x_0) True (1,1) 6. eval_easy1_5(v_0,v_x_0) -> eval_easy1_6(v_0,v_x_0) True (1,1) 7. eval_easy1_6(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,0) True (1,1) 8. eval_easy1_bb1_in(v_0,v_x_0) -> eval_easy1_bb2_in(v_0,v_x_0) [v_x_0 >= 0 && 39 >= v_x_0] (?,1) 9. eval_easy1_bb1_in(v_0,v_x_0) -> eval_easy1_bb3_in(v_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= 40] (1,1) 10. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,1 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_0 = 0] (?,1) 11. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 >= v_0] (?,1) 12. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_0 >= 0] (?,1) 13. eval_easy1_bb3_in(v_0,v_x_0) -> eval_easy1_stop(v_0,v_x_0) [-40 + v_x_0 >= 0] (1,1) Signature: {(eval_easy1_1,2) ;(eval_easy1_2,2) ;(eval_easy1_3,2) ;(eval_easy1_4,2) ;(eval_easy1_5,2) ;(eval_easy1_6,2) ;(eval_easy1_bb0_in,2) ;(eval_easy1_bb1_in,2) ;(eval_easy1_bb2_in,2) ;(eval_easy1_bb3_in,2) ;(eval_easy1_start,2) ;(eval_easy1_stop,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{10,11,12},9->{13},10->{8,9},11->{8,9},12->{8 ,9},13->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_easy1_1) = 1563 p(eval_easy1_2) = 1563 p(eval_easy1_3) = 1562 p(eval_easy1_4) = 1562 p(eval_easy1_5) = 1561 p(eval_easy1_6) = 1561 p(eval_easy1_bb0_in) = 1564 p(eval_easy1_bb1_in) = 1561 + -39*x2 p(eval_easy1_bb2_in) = 1522 + -39*x2 p(eval_easy1_bb3_in) = 1561 + -39*x2 p(eval_easy1_start) = 1564 p(eval_easy1_stop) = 1561 + -39*x2 Following rules are strictly oriented: True ==> eval_easy1_bb0_in(v_0,v_x_0) = 1564 > 1563 = eval_easy1_1(nondef_0,v_x_0) True ==> eval_easy1_2(v_0,v_x_0) = 1563 > 1562 = eval_easy1_3(v_0,v_x_0) True ==> eval_easy1_4(v_0,v_x_0) = 1562 > 1561 = eval_easy1_5(v_0,v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_0 >= 0] ==> eval_easy1_bb2_in(v_0,v_x_0) = 1522 + -39*v_x_0 > 1483 + -39*v_x_0 = eval_easy1_bb1_in(v_0,2 + v_x_0) Following rules are weakly oriented: True ==> eval_easy1_start(v_0,v_x_0) = 1564 >= 1564 = eval_easy1_bb0_in(v_0,v_x_0) True ==> eval_easy1_1(v_0,v_x_0) = 1563 >= 1563 = eval_easy1_2(v_0,v_x_0) True ==> eval_easy1_3(v_0,v_x_0) = 1562 >= 1562 = eval_easy1_4(v_0,v_x_0) True ==> eval_easy1_5(v_0,v_x_0) = 1561 >= 1561 = eval_easy1_6(v_0,v_x_0) True ==> eval_easy1_6(v_0,v_x_0) = 1561 >= 1561 = eval_easy1_bb1_in(v_0,0) [v_x_0 >= 0 && 39 >= v_x_0] ==> eval_easy1_bb1_in(v_0,v_x_0) = 1561 + -39*v_x_0 >= 1522 + -39*v_x_0 = eval_easy1_bb2_in(v_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= 40] ==> eval_easy1_bb1_in(v_0,v_x_0) = 1561 + -39*v_x_0 >= 1561 + -39*v_x_0 = eval_easy1_bb3_in(v_0,v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_0 = 0] ==> eval_easy1_bb2_in(v_0,v_x_0) = 1522 + -39*v_x_0 >= 1522 + -39*v_x_0 = eval_easy1_bb1_in(v_0,1 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 >= v_0] ==> eval_easy1_bb2_in(v_0,v_x_0) = 1522 + -39*v_x_0 >= 1483 + -39*v_x_0 = eval_easy1_bb1_in(v_0,2 + v_x_0) [-40 + v_x_0 >= 0] ==> eval_easy1_bb3_in(v_0,v_x_0) = 1561 + -39*v_x_0 >= 1561 + -39*v_x_0 = eval_easy1_stop(v_0,v_x_0) * Step 4: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. eval_easy1_start(v_0,v_x_0) -> eval_easy1_bb0_in(v_0,v_x_0) True (1,1) 1. eval_easy1_bb0_in(v_0,v_x_0) -> eval_easy1_1(nondef_0,v_x_0) True (1,1) 2. eval_easy1_1(v_0,v_x_0) -> eval_easy1_2(v_0,v_x_0) True (1,1) 3. eval_easy1_2(v_0,v_x_0) -> eval_easy1_3(v_0,v_x_0) True (1,1) 4. eval_easy1_3(v_0,v_x_0) -> eval_easy1_4(v_0,v_x_0) True (1,1) 5. eval_easy1_4(v_0,v_x_0) -> eval_easy1_5(v_0,v_x_0) True (1,1) 6. eval_easy1_5(v_0,v_x_0) -> eval_easy1_6(v_0,v_x_0) True (1,1) 7. eval_easy1_6(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,0) True (1,1) 8. eval_easy1_bb1_in(v_0,v_x_0) -> eval_easy1_bb2_in(v_0,v_x_0) [v_x_0 >= 0 && 39 >= v_x_0] (?,1) 9. eval_easy1_bb1_in(v_0,v_x_0) -> eval_easy1_bb3_in(v_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= 40] (1,1) 10. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,1 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_0 = 0] (?,1) 11. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 >= v_0] (?,1) 12. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_0 >= 0] (1564,1) 13. eval_easy1_bb3_in(v_0,v_x_0) -> eval_easy1_stop(v_0,v_x_0) [-40 + v_x_0 >= 0] (1,1) Signature: {(eval_easy1_1,2) ;(eval_easy1_2,2) ;(eval_easy1_3,2) ;(eval_easy1_4,2) ;(eval_easy1_5,2) ;(eval_easy1_6,2) ;(eval_easy1_bb0_in,2) ;(eval_easy1_bb1_in,2) ;(eval_easy1_bb2_in,2) ;(eval_easy1_bb3_in,2) ;(eval_easy1_start,2) ;(eval_easy1_stop,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{10,11,12},9->{13},10->{8,9},11->{8,9},12->{8 ,9},13->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_easy1_1) = 1563 p(eval_easy1_2) = 1563 p(eval_easy1_3) = 1562 p(eval_easy1_4) = 1562 p(eval_easy1_5) = 1561 p(eval_easy1_6) = 1561 p(eval_easy1_bb0_in) = 1564 p(eval_easy1_bb1_in) = 1561 + -39*x2 p(eval_easy1_bb2_in) = 1522 + -39*x2 p(eval_easy1_bb3_in) = 1561 + -39*x2 p(eval_easy1_start) = 1564 p(eval_easy1_stop) = 1561 + -39*x2 Following rules are strictly oriented: True ==> eval_easy1_bb0_in(v_0,v_x_0) = 1564 > 1563 = eval_easy1_1(nondef_0,v_x_0) True ==> eval_easy1_2(v_0,v_x_0) = 1563 > 1562 = eval_easy1_3(v_0,v_x_0) True ==> eval_easy1_4(v_0,v_x_0) = 1562 > 1561 = eval_easy1_5(v_0,v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 >= v_0] ==> eval_easy1_bb2_in(v_0,v_x_0) = 1522 + -39*v_x_0 > 1483 + -39*v_x_0 = eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_0 >= 0] ==> eval_easy1_bb2_in(v_0,v_x_0) = 1522 + -39*v_x_0 > 1483 + -39*v_x_0 = eval_easy1_bb1_in(v_0,2 + v_x_0) Following rules are weakly oriented: True ==> eval_easy1_start(v_0,v_x_0) = 1564 >= 1564 = eval_easy1_bb0_in(v_0,v_x_0) True ==> eval_easy1_1(v_0,v_x_0) = 1563 >= 1563 = eval_easy1_2(v_0,v_x_0) True ==> eval_easy1_3(v_0,v_x_0) = 1562 >= 1562 = eval_easy1_4(v_0,v_x_0) True ==> eval_easy1_5(v_0,v_x_0) = 1561 >= 1561 = eval_easy1_6(v_0,v_x_0) True ==> eval_easy1_6(v_0,v_x_0) = 1561 >= 1561 = eval_easy1_bb1_in(v_0,0) [v_x_0 >= 0 && 39 >= v_x_0] ==> eval_easy1_bb1_in(v_0,v_x_0) = 1561 + -39*v_x_0 >= 1522 + -39*v_x_0 = eval_easy1_bb2_in(v_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= 40] ==> eval_easy1_bb1_in(v_0,v_x_0) = 1561 + -39*v_x_0 >= 1561 + -39*v_x_0 = eval_easy1_bb3_in(v_0,v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_0 = 0] ==> eval_easy1_bb2_in(v_0,v_x_0) = 1522 + -39*v_x_0 >= 1522 + -39*v_x_0 = eval_easy1_bb1_in(v_0,1 + v_x_0) [-40 + v_x_0 >= 0] ==> eval_easy1_bb3_in(v_0,v_x_0) = 1561 + -39*v_x_0 >= 1561 + -39*v_x_0 = eval_easy1_stop(v_0,v_x_0) * Step 5: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. eval_easy1_start(v_0,v_x_0) -> eval_easy1_bb0_in(v_0,v_x_0) True (1,1) 1. eval_easy1_bb0_in(v_0,v_x_0) -> eval_easy1_1(nondef_0,v_x_0) True (1,1) 2. eval_easy1_1(v_0,v_x_0) -> eval_easy1_2(v_0,v_x_0) True (1,1) 3. eval_easy1_2(v_0,v_x_0) -> eval_easy1_3(v_0,v_x_0) True (1,1) 4. eval_easy1_3(v_0,v_x_0) -> eval_easy1_4(v_0,v_x_0) True (1,1) 5. eval_easy1_4(v_0,v_x_0) -> eval_easy1_5(v_0,v_x_0) True (1,1) 6. eval_easy1_5(v_0,v_x_0) -> eval_easy1_6(v_0,v_x_0) True (1,1) 7. eval_easy1_6(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,0) True (1,1) 8. eval_easy1_bb1_in(v_0,v_x_0) -> eval_easy1_bb2_in(v_0,v_x_0) [v_x_0 >= 0 && 39 >= v_x_0] (?,1) 9. eval_easy1_bb1_in(v_0,v_x_0) -> eval_easy1_bb3_in(v_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= 40] (1,1) 10. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,1 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_0 = 0] (?,1) 11. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 >= v_0] (1564,1) 12. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_0 >= 0] (1564,1) 13. eval_easy1_bb3_in(v_0,v_x_0) -> eval_easy1_stop(v_0,v_x_0) [-40 + v_x_0 >= 0] (1,1) Signature: {(eval_easy1_1,2) ;(eval_easy1_2,2) ;(eval_easy1_3,2) ;(eval_easy1_4,2) ;(eval_easy1_5,2) ;(eval_easy1_6,2) ;(eval_easy1_bb0_in,2) ;(eval_easy1_bb1_in,2) ;(eval_easy1_bb2_in,2) ;(eval_easy1_bb3_in,2) ;(eval_easy1_start,2) ;(eval_easy1_stop,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{10,11,12},9->{13},10->{8,9},11->{8,9},12->{8 ,9},13->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: We apply a polynomial interpretation of shape linear: p(eval_easy1_1) = 42 p(eval_easy1_2) = 42 p(eval_easy1_3) = 41 p(eval_easy1_4) = 41 p(eval_easy1_5) = 40 p(eval_easy1_6) = 40 p(eval_easy1_bb0_in) = 43 p(eval_easy1_bb1_in) = 40 + -1*x2 p(eval_easy1_bb2_in) = 40 + -1*x2 p(eval_easy1_bb3_in) = 40 + -1*x2 p(eval_easy1_start) = 43 p(eval_easy1_stop) = 40 + -1*x2 Following rules are strictly oriented: True ==> eval_easy1_bb0_in(v_0,v_x_0) = 43 > 42 = eval_easy1_1(nondef_0,v_x_0) True ==> eval_easy1_2(v_0,v_x_0) = 42 > 41 = eval_easy1_3(v_0,v_x_0) True ==> eval_easy1_4(v_0,v_x_0) = 41 > 40 = eval_easy1_5(v_0,v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_0 = 0] ==> eval_easy1_bb2_in(v_0,v_x_0) = 40 + -1*v_x_0 > 39 + -1*v_x_0 = eval_easy1_bb1_in(v_0,1 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 >= v_0] ==> eval_easy1_bb2_in(v_0,v_x_0) = 40 + -1*v_x_0 > 38 + -1*v_x_0 = eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_0 >= 0] ==> eval_easy1_bb2_in(v_0,v_x_0) = 40 + -1*v_x_0 > 38 + -1*v_x_0 = eval_easy1_bb1_in(v_0,2 + v_x_0) Following rules are weakly oriented: True ==> eval_easy1_start(v_0,v_x_0) = 43 >= 43 = eval_easy1_bb0_in(v_0,v_x_0) True ==> eval_easy1_1(v_0,v_x_0) = 42 >= 42 = eval_easy1_2(v_0,v_x_0) True ==> eval_easy1_3(v_0,v_x_0) = 41 >= 41 = eval_easy1_4(v_0,v_x_0) True ==> eval_easy1_5(v_0,v_x_0) = 40 >= 40 = eval_easy1_6(v_0,v_x_0) True ==> eval_easy1_6(v_0,v_x_0) = 40 >= 40 = eval_easy1_bb1_in(v_0,0) [v_x_0 >= 0 && 39 >= v_x_0] ==> eval_easy1_bb1_in(v_0,v_x_0) = 40 + -1*v_x_0 >= 40 + -1*v_x_0 = eval_easy1_bb2_in(v_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= 40] ==> eval_easy1_bb1_in(v_0,v_x_0) = 40 + -1*v_x_0 >= 40 + -1*v_x_0 = eval_easy1_bb3_in(v_0,v_x_0) [-40 + v_x_0 >= 0] ==> eval_easy1_bb3_in(v_0,v_x_0) = 40 + -1*v_x_0 >= 40 + -1*v_x_0 = eval_easy1_stop(v_0,v_x_0) * Step 6: KnowledgePropagation WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. eval_easy1_start(v_0,v_x_0) -> eval_easy1_bb0_in(v_0,v_x_0) True (1,1) 1. eval_easy1_bb0_in(v_0,v_x_0) -> eval_easy1_1(nondef_0,v_x_0) True (1,1) 2. eval_easy1_1(v_0,v_x_0) -> eval_easy1_2(v_0,v_x_0) True (1,1) 3. eval_easy1_2(v_0,v_x_0) -> eval_easy1_3(v_0,v_x_0) True (1,1) 4. eval_easy1_3(v_0,v_x_0) -> eval_easy1_4(v_0,v_x_0) True (1,1) 5. eval_easy1_4(v_0,v_x_0) -> eval_easy1_5(v_0,v_x_0) True (1,1) 6. eval_easy1_5(v_0,v_x_0) -> eval_easy1_6(v_0,v_x_0) True (1,1) 7. eval_easy1_6(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,0) True (1,1) 8. eval_easy1_bb1_in(v_0,v_x_0) -> eval_easy1_bb2_in(v_0,v_x_0) [v_x_0 >= 0 && 39 >= v_x_0] (?,1) 9. eval_easy1_bb1_in(v_0,v_x_0) -> eval_easy1_bb3_in(v_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= 40] (1,1) 10. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,1 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_0 = 0] (43,1) 11. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 >= v_0] (1564,1) 12. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_0 >= 0] (1564,1) 13. eval_easy1_bb3_in(v_0,v_x_0) -> eval_easy1_stop(v_0,v_x_0) [-40 + v_x_0 >= 0] (1,1) Signature: {(eval_easy1_1,2) ;(eval_easy1_2,2) ;(eval_easy1_3,2) ;(eval_easy1_4,2) ;(eval_easy1_5,2) ;(eval_easy1_6,2) ;(eval_easy1_bb0_in,2) ;(eval_easy1_bb1_in,2) ;(eval_easy1_bb2_in,2) ;(eval_easy1_bb3_in,2) ;(eval_easy1_start,2) ;(eval_easy1_stop,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{10,11,12},9->{13},10->{8,9},11->{8,9},12->{8 ,9},13->{}] + Applied Processor: KnowledgePropagation + Details: We propagate bounds from predecessors. * Step 7: PolyRank WORST_CASE(?,O(1)) + Considered Problem: Rules: 0. eval_easy1_start(v_0,v_x_0) -> eval_easy1_bb0_in(v_0,v_x_0) True (1,1) 1. eval_easy1_bb0_in(v_0,v_x_0) -> eval_easy1_1(nondef_0,v_x_0) True (1,1) 2. eval_easy1_1(v_0,v_x_0) -> eval_easy1_2(v_0,v_x_0) True (1,1) 3. eval_easy1_2(v_0,v_x_0) -> eval_easy1_3(v_0,v_x_0) True (1,1) 4. eval_easy1_3(v_0,v_x_0) -> eval_easy1_4(v_0,v_x_0) True (1,1) 5. eval_easy1_4(v_0,v_x_0) -> eval_easy1_5(v_0,v_x_0) True (1,1) 6. eval_easy1_5(v_0,v_x_0) -> eval_easy1_6(v_0,v_x_0) True (1,1) 7. eval_easy1_6(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,0) True (1,1) 8. eval_easy1_bb1_in(v_0,v_x_0) -> eval_easy1_bb2_in(v_0,v_x_0) [v_x_0 >= 0 && 39 >= v_x_0] (3172,1) 9. eval_easy1_bb1_in(v_0,v_x_0) -> eval_easy1_bb3_in(v_0,v_x_0) [v_x_0 >= 0 && v_x_0 >= 40] (1,1) 10. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,1 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_0 = 0] (43,1) 11. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 >= v_0] (1564,1) 12. eval_easy1_bb2_in(v_0,v_x_0) -> eval_easy1_bb1_in(v_0,2 + v_x_0) [39 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_0 >= 0] (1564,1) 13. eval_easy1_bb3_in(v_0,v_x_0) -> eval_easy1_stop(v_0,v_x_0) [-40 + v_x_0 >= 0] (1,1) Signature: {(eval_easy1_1,2) ;(eval_easy1_2,2) ;(eval_easy1_3,2) ;(eval_easy1_4,2) ;(eval_easy1_5,2) ;(eval_easy1_6,2) ;(eval_easy1_bb0_in,2) ;(eval_easy1_bb1_in,2) ;(eval_easy1_bb2_in,2) ;(eval_easy1_bb3_in,2) ;(eval_easy1_start,2) ;(eval_easy1_stop,2)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{10,11,12},9->{13},10->{8,9},11->{8,9},12->{8 ,9},13->{}] + Applied Processor: PolyRank {useFarkas = True, withSizebounds = [], shape = Linear} + Details: The problem is already solved. YES(?,O(1))