YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. eval_speedNestedMultipleDep_start(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb0_in(v_1,v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedNestedMultipleDep_bb0_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_0(v_1,v_m,v_n,v_x_0,v_y_0) True (?,1) 2. eval_speedNestedMultipleDep_0(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_1(v_1,v_m,v_n,v_x_0,v_y_0) True (?,1) 3. eval_speedNestedMultipleDep_1(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_2(v_1,v_m,v_n,v_x_0,v_y_0) True (?,1) 4. eval_speedNestedMultipleDep_2(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_3(v_1,v_m,v_n,v_x_0,v_y_0) True (?,1) 5. eval_speedNestedMultipleDep_3(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_4(v_1,v_m,v_n,v_x_0,v_y_0) True (?,1) 6. eval_speedNestedMultipleDep_4(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_5(v_1,v_m,v_n,v_x_0,v_y_0) True (?,1) 7. eval_speedNestedMultipleDep_5(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_6(v_1,v_m,v_n,v_x_0,v_y_0) True (?,1) 8. eval_speedNestedMultipleDep_6(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb1_in(v_1,v_m,v_n,0,v_y_0) True (?,1) 9. eval_speedNestedMultipleDep_bb1_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb2_in(v_1,v_m,v_n,v_x_0,v_y_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 10. eval_speedNestedMultipleDep_bb1_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb5_in(v_1,v_m,v_n,v_x_0,v_y_0) [v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 11. eval_speedNestedMultipleDep_bb2_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb3_in(1 + v_x_0,v_m,v_n,v_x_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) 12. eval_speedNestedMultipleDep_bb3_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb4_in(v_1,v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 (?,1) && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_1 + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && 1 + -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -2 + v_1 + v_n >= 0 && -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && -1 + v_m >= v_y_0] 13. eval_speedNestedMultipleDep_bb3_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb1_in(v_1,v_m,v_n,v_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_1 + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && 1 + -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -2 + v_1 + v_n >= 0 && -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && v_y_0 >= v_m] 14. eval_speedNestedMultipleDep_bb4_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb3_in(v_1,v_m,v_n,v_x_0,1 + v_y_0) [-1 + v_m + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_m + v_y_0 >= 0 && -1 + v_1 + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_m + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && 1 + -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -2 + v_1 + v_n >= 0 && -1*v_1 + v_n >= 0 && -1 + v_m >= 0 && -2 + v_1 + v_m >= 0 && -1 + v_1 >= 0] 15. eval_speedNestedMultipleDep_bb5_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_stop(v_1,v_m,v_n,v_x_0,v_y_0) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (?,1) Signature: {(eval_speedNestedMultipleDep_0,5) ;(eval_speedNestedMultipleDep_1,5) ;(eval_speedNestedMultipleDep_2,5) ;(eval_speedNestedMultipleDep_3,5) ;(eval_speedNestedMultipleDep_4,5) ;(eval_speedNestedMultipleDep_5,5) ;(eval_speedNestedMultipleDep_6,5) ;(eval_speedNestedMultipleDep_bb0_in,5) ;(eval_speedNestedMultipleDep_bb1_in,5) ;(eval_speedNestedMultipleDep_bb2_in,5) ;(eval_speedNestedMultipleDep_bb3_in,5) ;(eval_speedNestedMultipleDep_bb4_in,5) ;(eval_speedNestedMultipleDep_bb5_in,5) ;(eval_speedNestedMultipleDep_start,5) ;(eval_speedNestedMultipleDep_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{15},11->{12,13},12->{14} ,13->{9,10},14->{12,13},15->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. eval_speedNestedMultipleDep_start(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb0_in(v_1,v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedNestedMultipleDep_bb0_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_0(v_1,v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_speedNestedMultipleDep_0(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_1(v_1,v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_speedNestedMultipleDep_1(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_2(v_1,v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_speedNestedMultipleDep_2(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_3(v_1,v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_speedNestedMultipleDep_3(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_4(v_1,v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_speedNestedMultipleDep_4(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_5(v_1,v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_speedNestedMultipleDep_5(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_6(v_1,v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_speedNestedMultipleDep_6(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb1_in(v_1,v_m,v_n,0,v_y_0) True (1,1) 9. eval_speedNestedMultipleDep_bb1_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb2_in(v_1,v_m,v_n,v_x_0,v_y_0) [v_x_0 >= 0 && -1 + v_n >= v_x_0] (?,1) 10. eval_speedNestedMultipleDep_bb1_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb5_in(v_1,v_m,v_n,v_x_0,v_y_0) [v_x_0 >= 0 && v_x_0 >= v_n] (1,1) 11. eval_speedNestedMultipleDep_bb2_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb3_in(1 + v_x_0,v_m,v_n,v_x_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) 12. eval_speedNestedMultipleDep_bb3_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb4_in(v_1,v_m,v_n,v_x_0,v_y_0) [v_y_0 >= 0 (?,1) && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_1 + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && 1 + -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -2 + v_1 + v_n >= 0 && -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && -1 + v_m >= v_y_0] 13. eval_speedNestedMultipleDep_bb3_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb1_in(v_1,v_m,v_n,v_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_1 + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && 1 + -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -2 + v_1 + v_n >= 0 && -1*v_1 + v_n >= 0 && -1 + v_1 >= 0 && v_y_0 >= v_m] 14. eval_speedNestedMultipleDep_bb4_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_bb3_in(v_1,v_m,v_n,v_x_0,1 + v_y_0) [-1 + v_m + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && -1 + v_m + v_y_0 >= 0 && -1 + v_1 + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && -1 + v_1 + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_m + v_x_0 >= 0 && -1 + v_1 + v_x_0 >= 0 && 1 + -1*v_1 + v_x_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -2 + v_1 + v_n >= 0 && -1*v_1 + v_n >= 0 && -1 + v_m >= 0 && -2 + v_1 + v_m >= 0 && -1 + v_1 >= 0] 15. eval_speedNestedMultipleDep_bb5_in(v_1,v_m,v_n,v_x_0,v_y_0) -> eval_speedNestedMultipleDep_stop(v_1,v_m,v_n,v_x_0,v_y_0) [v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] (1,1) Signature: {(eval_speedNestedMultipleDep_0,5) ;(eval_speedNestedMultipleDep_1,5) ;(eval_speedNestedMultipleDep_2,5) ;(eval_speedNestedMultipleDep_3,5) ;(eval_speedNestedMultipleDep_4,5) ;(eval_speedNestedMultipleDep_5,5) ;(eval_speedNestedMultipleDep_6,5) ;(eval_speedNestedMultipleDep_bb0_in,5) ;(eval_speedNestedMultipleDep_bb1_in,5) ;(eval_speedNestedMultipleDep_bb2_in,5) ;(eval_speedNestedMultipleDep_bb3_in,5) ;(eval_speedNestedMultipleDep_bb4_in,5) ;(eval_speedNestedMultipleDep_bb5_in,5) ;(eval_speedNestedMultipleDep_start,5) ;(eval_speedNestedMultipleDep_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{15},11->{12,13},12->{14} ,13->{9,10},14->{12,13},15->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] | `- p:[9,13,11,14,12] c: [13] | `- p:[12,14] c: [14] YES