YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. eval_speedSimpleMultiple_start(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) True (?,1) 2. eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) True (?,1) 3. eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) True (?,1) 4. eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) True (?,1) 5. eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) True (?,1) 6. eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) True (?,1) 7. eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) True (?,1) 8. eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,0,0) True (?,1) 9. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_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) 10. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_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) 11. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_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] 12. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,1 + 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_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] 13. eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_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_speedSimpleMultiple_0,4) ;(eval_speedSimpleMultiple_1,4) ;(eval_speedSimpleMultiple_2,4) ;(eval_speedSimpleMultiple_3,4) ;(eval_speedSimpleMultiple_4,4) ;(eval_speedSimpleMultiple_5,4) ;(eval_speedSimpleMultiple_6,4) ;(eval_speedSimpleMultiple_bb0_in,4) ;(eval_speedSimpleMultiple_bb1_in,4) ;(eval_speedSimpleMultiple_bb2_in,4) ;(eval_speedSimpleMultiple_bb3_in,4) ;(eval_speedSimpleMultiple_start,4) ;(eval_speedSimpleMultiple_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11,12},10->{13},11->{9,10},12->{9 ,10},13->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. eval_speedSimpleMultiple_start(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,0,0) True (1,1) 9. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_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) 10. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_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) 11. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_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] 12. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,1 + 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_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] 13. eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_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_speedSimpleMultiple_0,4) ;(eval_speedSimpleMultiple_1,4) ;(eval_speedSimpleMultiple_2,4) ;(eval_speedSimpleMultiple_3,4) ;(eval_speedSimpleMultiple_4,4) ;(eval_speedSimpleMultiple_5,4) ;(eval_speedSimpleMultiple_6,4) ;(eval_speedSimpleMultiple_bb0_in,4) ;(eval_speedSimpleMultiple_bb1_in,4) ;(eval_speedSimpleMultiple_bb2_in,4) ;(eval_speedSimpleMultiple_bb3_in,4) ;(eval_speedSimpleMultiple_start,4) ;(eval_speedSimpleMultiple_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11,12},10->{13},11->{9,10},12->{9 ,10},13->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(11,10)] * Step 3: Looptree YES + Considered Problem: Rules: 0. eval_speedSimpleMultiple_start(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_speedSimpleMultiple_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_speedSimpleMultiple_0(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_speedSimpleMultiple_1(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_speedSimpleMultiple_2(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_speedSimpleMultiple_3(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_speedSimpleMultiple_4(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_speedSimpleMultiple_5(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_speedSimpleMultiple_6(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,0,0) True (1,1) 9. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_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) 10. eval_speedSimpleMultiple_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_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) 11. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_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] 12. eval_speedSimpleMultiple_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_bb1_in(v_m,v_n,1 + 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_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] 13. eval_speedSimpleMultiple_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_speedSimpleMultiple_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_speedSimpleMultiple_0,4) ;(eval_speedSimpleMultiple_1,4) ;(eval_speedSimpleMultiple_2,4) ;(eval_speedSimpleMultiple_3,4) ;(eval_speedSimpleMultiple_4,4) ;(eval_speedSimpleMultiple_5,4) ;(eval_speedSimpleMultiple_6,4) ;(eval_speedSimpleMultiple_bb0_in,4) ;(eval_speedSimpleMultiple_bb1_in,4) ;(eval_speedSimpleMultiple_bb2_in,4) ;(eval_speedSimpleMultiple_bb3_in,4) ;(eval_speedSimpleMultiple_start,4) ;(eval_speedSimpleMultiple_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11,12},10->{13},11->{9},12->{9,10} ,13->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[9,11,12] c: [12] | `- p:[9,11] c: [11] YES