YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. eval_speedSingleSingle2_start(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb0_in(v_2,v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedSingleSingle2_bb0_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_0(v_2,v_m,v_n,v_x_0,v_y_0) True (?,1) 2. eval_speedSingleSingle2_0(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_1(v_2,v_m,v_n,v_x_0,v_y_0) True (?,1) 3. eval_speedSingleSingle2_1(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_2(v_2,v_m,v_n,v_x_0,v_y_0) True (?,1) 4. eval_speedSingleSingle2_2(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb6_in(v_2,v_m,v_n,v_x_0,v_y_0) [-1 >= v_n] (?,1) 5. eval_speedSingleSingle2_2(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb6_in(v_2,v_m,v_n,v_x_0,v_y_0) [-1 >= v_m] (?,1) 6. eval_speedSingleSingle2_2(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb1_in(v_2,v_m,v_n,0,0) [v_n >= 0 && v_m >= 0] (?,1) 7. eval_speedSingleSingle2_bb1_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_3(v_2,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && v_m >= 0] 8. eval_speedSingleSingle2_3(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_4(nondef_0,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && v_m >= 0] 9. eval_speedSingleSingle2_4(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb2_in(v_2,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && v_m >= 0 && -1 + v_2 >= 0] 10. eval_speedSingleSingle2_4(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb6_in(v_2,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && v_m >= 0 && 0 >= v_2] 11. eval_speedSingleSingle2_bb2_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb3_in(v_2,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && -1 + v_2 + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && -1 + v_2 + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && -1 + v_2 + v_n >= 0 && v_m >= 0 && -1 + v_2 + v_m >= 0 && -1 + v_2 >= 0 && -1 + v_n >= v_x_0] 12. eval_speedSingleSingle2_bb2_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb4_in(v_2,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && -1 + v_2 + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && -1 + v_2 + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && -1 + v_2 + v_n >= 0 && v_m >= 0 && -1 + v_2 + v_m >= 0 && -1 + v_2 >= 0 && v_x_0 >= v_n] 13. eval_speedSingleSingle2_bb3_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb1_in(v_2,v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && -1 + v_2 + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && -1 + v_2 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_m + v_n >= 0 && -2 + v_2 + v_n >= 0 && v_m >= 0 && -1 + v_2 + v_m >= 0 && -1 + v_2 >= 0] 14. eval_speedSingleSingle2_bb4_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb5_in(v_2,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && -1 + v_2 + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && -1 + v_2 + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && -1 + v_2 + v_n >= 0 && v_m >= 0 && -1 + v_2 + v_m >= 0 && -1 + v_2 >= 0 && -1 + v_m >= v_y_0] 15. eval_speedSingleSingle2_bb4_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb6_in(v_2,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && -1 + v_2 + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && -1 + v_2 + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && -1 + v_2 + v_n >= 0 && v_m >= 0 && -1 + v_2 + v_m >= 0 && -1 + v_2 >= 0 && v_y_0 >= v_m] 16. eval_speedSingleSingle2_bb5_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb1_in(v_2,v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_m + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1 + v_m + v_y_0 >= 0 && -1 + v_2 + v_y_0 >= 0 && -1 + v_m + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m + v_x_0 >= 0 && -1 + v_2 + v_x_0 >= 0 && -1 + v_m + -1*v_n >= 0 && v_n >= 0 && -1 + v_m + v_n >= 0 && -1 + v_2 + v_n >= 0 && -1 + v_m >= 0 && -2 + v_2 + v_m >= 0 && -1 + v_2 >= 0] 17. eval_speedSingleSingle2_bb6_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_stop(v_2,v_m,v_n,v_x_0,v_y_0) True (?,1) Signature: {(eval_speedSingleSingle2_0,5) ;(eval_speedSingleSingle2_1,5) ;(eval_speedSingleSingle2_2,5) ;(eval_speedSingleSingle2_3,5) ;(eval_speedSingleSingle2_4,5) ;(eval_speedSingleSingle2_bb0_in,5) ;(eval_speedSingleSingle2_bb1_in,5) ;(eval_speedSingleSingle2_bb2_in,5) ;(eval_speedSingleSingle2_bb3_in,5) ;(eval_speedSingleSingle2_bb4_in,5) ;(eval_speedSingleSingle2_bb5_in,5) ;(eval_speedSingleSingle2_bb6_in,5) ;(eval_speedSingleSingle2_start,5) ;(eval_speedSingleSingle2_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{17},5->{17},6->{7},7->{8},8->{9,10},9->{11,12},10->{17},11->{13} ,12->{14,15},13->{7},14->{16},15->{17},16->{7},17->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. eval_speedSingleSingle2_start(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb0_in(v_2,v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedSingleSingle2_bb0_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_0(v_2,v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_speedSingleSingle2_0(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_1(v_2,v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_speedSingleSingle2_1(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_2(v_2,v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_speedSingleSingle2_2(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb6_in(v_2,v_m,v_n,v_x_0,v_y_0) [-1 >= v_n] (1,1) 5. eval_speedSingleSingle2_2(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb6_in(v_2,v_m,v_n,v_x_0,v_y_0) [-1 >= v_m] (1,1) 6. eval_speedSingleSingle2_2(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb1_in(v_2,v_m,v_n,0,0) [v_n >= 0 && v_m >= 0] (1,1) 7. eval_speedSingleSingle2_bb1_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_3(v_2,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && v_m >= 0] 8. eval_speedSingleSingle2_3(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_4(nondef_0,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && v_m >= 0] 9. eval_speedSingleSingle2_4(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb2_in(v_2,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && v_m >= 0 && -1 + v_2 >= 0] 10. eval_speedSingleSingle2_4(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb6_in(v_2,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (1,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && v_m >= 0 && 0 >= v_2] 11. eval_speedSingleSingle2_bb2_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb3_in(v_2,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && -1 + v_2 + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && -1 + v_2 + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && -1 + v_2 + v_n >= 0 && v_m >= 0 && -1 + v_2 + v_m >= 0 && -1 + v_2 >= 0 && -1 + v_n >= v_x_0] 12. eval_speedSingleSingle2_bb2_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb4_in(v_2,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && -1 + v_2 + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && -1 + v_2 + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && -1 + v_2 + v_n >= 0 && v_m >= 0 && -1 + v_2 + v_m >= 0 && -1 + v_2 >= 0 && v_x_0 >= v_n] 13. eval_speedSingleSingle2_bb3_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb1_in(v_2,v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_n + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && -1 + v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && -1 + v_2 + v_y_0 >= 0 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && -1 + v_2 + v_x_0 >= 0 && -1 + v_n >= 0 && -1 + v_m + v_n >= 0 && -2 + v_2 + v_n >= 0 && v_m >= 0 && -1 + v_2 + v_m >= 0 && -1 + v_2 >= 0] 14. eval_speedSingleSingle2_bb4_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb5_in(v_2,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && -1 + v_2 + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && -1 + v_2 + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && -1 + v_2 + v_n >= 0 && v_m >= 0 && -1 + v_2 + v_m >= 0 && -1 + v_2 >= 0 && -1 + v_m >= v_y_0] 15. eval_speedSingleSingle2_bb4_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb6_in(v_2,v_m,v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 (1,1) && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && v_m + v_y_0 >= 0 && -1 + v_2 + v_y_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && v_m + v_x_0 >= 0 && -1 + v_2 + v_x_0 >= 0 && v_n >= 0 && v_m + v_n >= 0 && -1 + v_2 + v_n >= 0 && v_m >= 0 && -1 + v_2 + v_m >= 0 && -1 + v_2 >= 0 && v_y_0 >= v_m] 16. eval_speedSingleSingle2_bb5_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_bb1_in(v_2,v_m,v_n,1 + v_x_0,1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_m + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && -1*v_x_0 + v_y_0 >= 0 && v_n + v_y_0 >= 0 && -1*v_n + v_y_0 >= 0 && -1 + v_m + v_y_0 >= 0 && -1 + v_2 + v_y_0 >= 0 && -1 + v_m + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m + v_x_0 >= 0 && -1 + v_2 + v_x_0 >= 0 && -1 + v_m + -1*v_n >= 0 && v_n >= 0 && -1 + v_m + v_n >= 0 && -1 + v_2 + v_n >= 0 && -1 + v_m >= 0 && -2 + v_2 + v_m >= 0 && -1 + v_2 >= 0] 17. eval_speedSingleSingle2_bb6_in(v_2,v_m,v_n,v_x_0,v_y_0) -> eval_speedSingleSingle2_stop(v_2,v_m,v_n,v_x_0,v_y_0) True (1,1) Signature: {(eval_speedSingleSingle2_0,5) ;(eval_speedSingleSingle2_1,5) ;(eval_speedSingleSingle2_2,5) ;(eval_speedSingleSingle2_3,5) ;(eval_speedSingleSingle2_4,5) ;(eval_speedSingleSingle2_bb0_in,5) ;(eval_speedSingleSingle2_bb1_in,5) ;(eval_speedSingleSingle2_bb2_in,5) ;(eval_speedSingleSingle2_bb3_in,5) ;(eval_speedSingleSingle2_bb4_in,5) ;(eval_speedSingleSingle2_bb5_in,5) ;(eval_speedSingleSingle2_bb6_in,5) ;(eval_speedSingleSingle2_start,5) ;(eval_speedSingleSingle2_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5,6},4->{17},5->{17},6->{7},7->{8},8->{9,10},9->{11,12},10->{17},11->{13} ,12->{14,15},13->{7},14->{16},15->{17},16->{7},17->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17] | `- p:[7,13,11,9,8,16,14,12] c: [16] | `- p:[7,13,11,9,8] c: [13] YES