YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. eval_speedSimpleMultipleDep_start(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedSimpleMultipleDep_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_0(v_m,v_n,v_x_0,v_y_0) True (?,1) 2. eval_speedSimpleMultipleDep_0(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_1(v_m,v_n,v_x_0,v_y_0) True (?,1) 3. eval_speedSimpleMultipleDep_1(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_2(v_m,v_n,v_x_0,v_y_0) True (?,1) 4. eval_speedSimpleMultipleDep_2(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_3(v_m,v_n,v_x_0,v_y_0) True (?,1) 5. eval_speedSimpleMultipleDep_3(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_4(v_m,v_n,v_x_0,v_y_0) True (?,1) 6. eval_speedSimpleMultipleDep_4(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_5(v_m,v_n,v_x_0,v_y_0) True (?,1) 7. eval_speedSimpleMultipleDep_5(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_6(v_m,v_n,v_x_0,v_y_0) True (?,1) 8. eval_speedSimpleMultipleDep_6(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_7(v_m,v_n,v_x_0,v_y_0) True (?,1) 9. eval_speedSimpleMultipleDep_7(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb1_in(v_m,v_n,0,0) True (?,1) 10. eval_speedSimpleMultipleDep_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 11. eval_speedSimpleMultipleDep_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 12. eval_speedSimpleMultipleDep_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb1_in(v_m,v_n,v_x_0,1 + v_y_0) [v_y_0 >= 0 (?,1) && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 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_m >= v_y_0] 13. eval_speedSimpleMultipleDep_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb1_in(v_m,v_n,1 + v_x_0,0) [v_y_0 >= 0 (?,1) && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && v_y_0 >= v_m] 14. eval_speedSimpleMultipleDep_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_stop(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (?,1) Signature: {(eval_speedSimpleMultipleDep_0,4) ;(eval_speedSimpleMultipleDep_1,4) ;(eval_speedSimpleMultipleDep_2,4) ;(eval_speedSimpleMultipleDep_3,4) ;(eval_speedSimpleMultipleDep_4,4) ;(eval_speedSimpleMultipleDep_5,4) ;(eval_speedSimpleMultipleDep_6,4) ;(eval_speedSimpleMultipleDep_7,4) ;(eval_speedSimpleMultipleDep_bb0_in,4) ;(eval_speedSimpleMultipleDep_bb1_in,4) ;(eval_speedSimpleMultipleDep_bb2_in,4) ;(eval_speedSimpleMultipleDep_bb3_in,4) ;(eval_speedSimpleMultipleDep_start,4) ;(eval_speedSimpleMultipleDep_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10,11},10->{12,13},11->{14},12->{10 ,11},13->{10,11},14->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. eval_speedSimpleMultipleDep_start(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedSimpleMultipleDep_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_0(v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_speedSimpleMultipleDep_0(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_1(v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_speedSimpleMultipleDep_1(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_2(v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_speedSimpleMultipleDep_2(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_3(v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_speedSimpleMultipleDep_3(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_4(v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_speedSimpleMultipleDep_4(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_5(v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_speedSimpleMultipleDep_5(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_6(v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_speedSimpleMultipleDep_6(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_7(v_m,v_n,v_x_0,v_y_0) True (1,1) 9. eval_speedSimpleMultipleDep_7(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb1_in(v_m,v_n,0,0) True (1,1) 10. eval_speedSimpleMultipleDep_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 11. eval_speedSimpleMultipleDep_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 12. eval_speedSimpleMultipleDep_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb1_in(v_m,v_n,v_x_0,1 + v_y_0) [v_y_0 >= 0 (?,1) && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 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_m >= v_y_0] 13. eval_speedSimpleMultipleDep_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb1_in(v_m,v_n,1 + v_x_0,0) [v_y_0 >= 0 (?,1) && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && v_y_0 >= v_m] 14. eval_speedSimpleMultipleDep_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_stop(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (1,1) Signature: {(eval_speedSimpleMultipleDep_0,4) ;(eval_speedSimpleMultipleDep_1,4) ;(eval_speedSimpleMultipleDep_2,4) ;(eval_speedSimpleMultipleDep_3,4) ;(eval_speedSimpleMultipleDep_4,4) ;(eval_speedSimpleMultipleDep_5,4) ;(eval_speedSimpleMultipleDep_6,4) ;(eval_speedSimpleMultipleDep_7,4) ;(eval_speedSimpleMultipleDep_bb0_in,4) ;(eval_speedSimpleMultipleDep_bb1_in,4) ;(eval_speedSimpleMultipleDep_bb2_in,4) ;(eval_speedSimpleMultipleDep_bb3_in,4) ;(eval_speedSimpleMultipleDep_start,4) ;(eval_speedSimpleMultipleDep_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10,11},10->{12,13},11->{14},12->{10 ,11},13->{10,11},14->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(12,11)] * Step 3: Looptree YES + Considered Problem: Rules: 0. eval_speedSimpleMultipleDep_start(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedSimpleMultipleDep_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_0(v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_speedSimpleMultipleDep_0(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_1(v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_speedSimpleMultipleDep_1(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_2(v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_speedSimpleMultipleDep_2(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_3(v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_speedSimpleMultipleDep_3(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_4(v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_speedSimpleMultipleDep_4(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_5(v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_speedSimpleMultipleDep_5(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_6(v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_speedSimpleMultipleDep_6(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_7(v_m,v_n,v_x_0,v_y_0) True (1,1) 9. eval_speedSimpleMultipleDep_7(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb1_in(v_m,v_n,0,0) True (1,1) 10. eval_speedSimpleMultipleDep_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb2_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 11. eval_speedSimpleMultipleDep_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb3_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 12. eval_speedSimpleMultipleDep_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb1_in(v_m,v_n,v_x_0,1 + v_y_0) [v_y_0 >= 0 (?,1) && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 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_m >= v_y_0] 13. eval_speedSimpleMultipleDep_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_bb1_in(v_m,v_n,1 + v_x_0,0) [v_y_0 >= 0 (?,1) && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0 && v_y_0 >= v_m] 14. eval_speedSimpleMultipleDep_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultipleDep_stop(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (1,1) Signature: {(eval_speedSimpleMultipleDep_0,4) ;(eval_speedSimpleMultipleDep_1,4) ;(eval_speedSimpleMultipleDep_2,4) ;(eval_speedSimpleMultipleDep_3,4) ;(eval_speedSimpleMultipleDep_4,4) ;(eval_speedSimpleMultipleDep_5,4) ;(eval_speedSimpleMultipleDep_6,4) ;(eval_speedSimpleMultipleDep_7,4) ;(eval_speedSimpleMultipleDep_bb0_in,4) ;(eval_speedSimpleMultipleDep_bb1_in,4) ;(eval_speedSimpleMultipleDep_bb2_in,4) ;(eval_speedSimpleMultipleDep_bb3_in,4) ;(eval_speedSimpleMultipleDep_start,4) ;(eval_speedSimpleMultipleDep_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10,11},10->{12,13},11->{14},12->{10} ,13->{10,11},14->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14] | `- p:[10,12,13] c: [13] | `- p:[10,12] c: [12] YES