YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. eval_start_start(v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_n,v_x_0,v_y_0) -> eval_start_0(v_n,v_x_0,v_y_0) True (?,1) 2. eval_start_0(v_n,v_x_0,v_y_0) -> eval_start_1(v_n,v_x_0,v_y_0) True (?,1) 3. eval_start_1(v_n,v_x_0,v_y_0) -> eval_start_2(v_n,v_x_0,v_y_0) True (?,1) 4. eval_start_2(v_n,v_x_0,v_y_0) -> eval_start_3(v_n,v_x_0,v_y_0) True (?,1) 5. eval_start_3(v_n,v_x_0,v_y_0) -> eval_start_4(v_n,v_x_0,v_y_0) True (?,1) 6. eval_start_4(v_n,v_x_0,v_y_0) -> eval_start_5(v_n,v_x_0,v_y_0) True (?,1) 7. eval_start_5(v_n,v_x_0,v_y_0) -> eval_start_6(v_n,v_x_0,v_y_0) True (?,1) 8. eval_start_6(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,0,0) True (?,1) 9. eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 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_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 11. eval_start_bb2_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(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_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] 12. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb4_in(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 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_y_0 >= 0] 13. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb5_in(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 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && 0 >= v_y_0] 14. eval_start_bb4_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,v_x_0,-1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_y_0 >= 0 && -2 + v_x_0 + v_y_0 >= 0 && -1 + v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] 15. eval_start_bb5_in(v_n,v_x_0,v_y_0) -> eval_start_stop(v_n,v_x_0,v_y_0) [-1*v_y_0 >= 0 (?,1) && v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] Signature: {(eval_start_0,3) ;(eval_start_1,3) ;(eval_start_2,3) ;(eval_start_3,3) ;(eval_start_4,3) ;(eval_start_5,3) ;(eval_start_6,3) ;(eval_start_bb0_in,3) ;(eval_start_bb1_in,3) ;(eval_start_bb2_in,3) ;(eval_start_bb3_in,3) ;(eval_start_bb4_in,3) ;(eval_start_bb5_in,3) ;(eval_start_start,3) ;(eval_start_stop,3)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{12,13},11->{9,10},12->{14} ,13->{15},14->{9,10},15->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. eval_start_start(v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_n,v_x_0,v_y_0) -> eval_start_0(v_n,v_x_0,v_y_0) True (1,1) 2. eval_start_0(v_n,v_x_0,v_y_0) -> eval_start_1(v_n,v_x_0,v_y_0) True (1,1) 3. eval_start_1(v_n,v_x_0,v_y_0) -> eval_start_2(v_n,v_x_0,v_y_0) True (1,1) 4. eval_start_2(v_n,v_x_0,v_y_0) -> eval_start_3(v_n,v_x_0,v_y_0) True (1,1) 5. eval_start_3(v_n,v_x_0,v_y_0) -> eval_start_4(v_n,v_x_0,v_y_0) True (1,1) 6. eval_start_4(v_n,v_x_0,v_y_0) -> eval_start_5(v_n,v_x_0,v_y_0) True (1,1) 7. eval_start_5(v_n,v_x_0,v_y_0) -> eval_start_6(v_n,v_x_0,v_y_0) True (1,1) 8. eval_start_6(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,0,0) True (1,1) 9. eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 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_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 11. eval_start_bb2_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(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_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] 12. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb4_in(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 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_y_0 >= 0] 13. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb5_in(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 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && 0 >= v_y_0] 14. eval_start_bb4_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,v_x_0,-1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_y_0 >= 0 && -2 + v_x_0 + v_y_0 >= 0 && -1 + v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] 15. eval_start_bb5_in(v_n,v_x_0,v_y_0) -> eval_start_stop(v_n,v_x_0,v_y_0) [-1*v_y_0 >= 0 (1,1) && v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] Signature: {(eval_start_0,3) ;(eval_start_1,3) ;(eval_start_2,3) ;(eval_start_3,3) ;(eval_start_4,3) ;(eval_start_5,3) ;(eval_start_6,3) ;(eval_start_bb0_in,3) ;(eval_start_bb1_in,3) ;(eval_start_bb2_in,3) ;(eval_start_bb3_in,3) ;(eval_start_bb4_in,3) ;(eval_start_bb5_in,3) ;(eval_start_start,3) ;(eval_start_stop,3)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{12,13},11->{9,10},12->{14} ,13->{15},14->{9,10},15->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(14,9)] * Step 3: Looptree YES + Considered Problem: Rules: 0. eval_start_start(v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_n,v_x_0,v_y_0) -> eval_start_0(v_n,v_x_0,v_y_0) True (1,1) 2. eval_start_0(v_n,v_x_0,v_y_0) -> eval_start_1(v_n,v_x_0,v_y_0) True (1,1) 3. eval_start_1(v_n,v_x_0,v_y_0) -> eval_start_2(v_n,v_x_0,v_y_0) True (1,1) 4. eval_start_2(v_n,v_x_0,v_y_0) -> eval_start_3(v_n,v_x_0,v_y_0) True (1,1) 5. eval_start_3(v_n,v_x_0,v_y_0) -> eval_start_4(v_n,v_x_0,v_y_0) True (1,1) 6. eval_start_4(v_n,v_x_0,v_y_0) -> eval_start_5(v_n,v_x_0,v_y_0) True (1,1) 7. eval_start_5(v_n,v_x_0,v_y_0) -> eval_start_6(v_n,v_x_0,v_y_0) True (1,1) 8. eval_start_6(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,0,0) True (1,1) 9. eval_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb2_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 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_start_bb1_in(v_n,v_x_0,v_y_0) -> eval_start_bb3_in(v_n,v_x_0,v_y_0) [v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && v_x_0 >= v_n] (?,1) 11. eval_start_bb2_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(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_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] 12. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb4_in(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 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_y_0 >= 0] 13. eval_start_bb3_in(v_n,v_x_0,v_y_0) -> eval_start_bb5_in(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 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && 0 >= v_y_0] 14. eval_start_bb4_in(v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_n,v_x_0,-1 + v_y_0) [v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_y_0 >= 0 && -2 + v_x_0 + v_y_0 >= 0 && -1 + v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] 15. eval_start_bb5_in(v_n,v_x_0,v_y_0) -> eval_start_stop(v_n,v_x_0,v_y_0) [-1*v_y_0 >= 0 (1,1) && v_x_0 + -1*v_y_0 >= 0 && v_y_0 >= 0 && v_x_0 + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0] Signature: {(eval_start_0,3) ;(eval_start_1,3) ;(eval_start_2,3) ;(eval_start_3,3) ;(eval_start_4,3) ;(eval_start_5,3) ;(eval_start_6,3) ;(eval_start_bb0_in,3) ;(eval_start_bb1_in,3) ;(eval_start_bb2_in,3) ;(eval_start_bb3_in,3) ;(eval_start_bb4_in,3) ;(eval_start_bb5_in,3) ;(eval_start_start,3) ;(eval_start_stop,3)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11},10->{12,13},11->{9,10},12->{14} ,13->{15},14->{10},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:[9,11] c: [11] | `- p:[10,14,12] c: [14] YES