YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. eval_loops_start(v_n,v_x_0,v_y_0) -> eval_loops_bb0_in(v_n,v_x_0,v_y_0) True (1,1) 1. eval_loops_bb0_in(v_n,v_x_0,v_y_0) -> eval_loops_0(v_n,v_x_0,v_y_0) True (?,1) 2. eval_loops_0(v_n,v_x_0,v_y_0) -> eval_loops_1(v_n,v_x_0,v_y_0) True (?,1) 3. eval_loops_1(v_n,v_x_0,v_y_0) -> eval_loops_2(v_n,v_x_0,v_y_0) True (?,1) 4. eval_loops_2(v_n,v_x_0,v_y_0) -> eval_loops_bb1_in(v_n,v_n,v_y_0) [v_n >= 0] (?,1) 5. eval_loops_2(v_n,v_x_0,v_y_0) -> eval_loops_bb6_in(v_n,v_x_0,v_y_0) [-1 >= v_n] (?,1) 6. eval_loops_bb1_in(v_n,v_x_0,v_y_0) -> eval_loops_bb2_in(v_n,v_x_0,v_y_0) [v_n + -1*v_x_0 >= 0 && 1 + v_x_0 >= 0 && 1 + v_n + v_x_0 >= 0 && v_n >= 0 && v_x_0 >= 0] (?,1) 7. eval_loops_bb1_in(v_n,v_x_0,v_y_0) -> eval_loops_bb6_in(v_n,v_x_0,v_y_0) [v_n + -1*v_x_0 >= 0 && 1 + v_x_0 >= 0 && 1 + v_n + v_x_0 >= 0 && v_n >= 0 && -1 >= v_x_0] (?,1) 8. eval_loops_bb2_in(v_n,v_x_0,v_y_0) -> eval_loops_bb3_in(v_n,v_x_0,1) [v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_n >= 0 && -1 + v_x_0 >= 1] (?,1) 9. eval_loops_bb2_in(v_n,v_x_0,v_y_0) -> eval_loops_bb5_in(v_n,v_x_0,v_y_0) [v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_n >= 0 && 1 >= v_x_0] (?,1) 10. eval_loops_bb3_in(v_n,v_x_0,v_y_0) -> eval_loops_bb4_in(v_n,v_x_0,v_y_0) [-1 + v_y_0 >= 0 (?,1) && -3 + v_x_0 + v_y_0 >= 0 && -3 + v_n + v_y_0 >= 0 && v_n + -1*v_x_0 >= 0 && -2 + v_x_0 >= 0 && -4 + v_n + v_x_0 >= 0 && -2 + v_n >= 0 && -1 + v_x_0 >= v_y_0] 11. eval_loops_bb3_in(v_n,v_x_0,v_y_0) -> eval_loops_bb5_in(v_n,v_x_0,v_y_0) [-1 + v_y_0 >= 0 (?,1) && -3 + v_x_0 + v_y_0 >= 0 && -3 + v_n + v_y_0 >= 0 && v_n + -1*v_x_0 >= 0 && -2 + v_x_0 >= 0 && -4 + v_n + v_x_0 >= 0 && -2 + v_n >= 0 && v_y_0 >= v_x_0] 12. eval_loops_bb4_in(v_n,v_x_0,v_y_0) -> eval_loops_bb3_in(v_n,v_x_0,2*v_y_0) [-1 + v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_n + -1*v_y_0 >= 0 && -1 + v_y_0 >= 0 && -3 + v_x_0 + v_y_0 >= 0 && -3 + v_n + v_y_0 >= 0 && v_n + -1*v_x_0 >= 0 && -2 + v_x_0 >= 0 && -4 + v_n + v_x_0 >= 0 && -2 + v_n >= 0] 13. eval_loops_bb5_in(v_n,v_x_0,v_y_0) -> eval_loops_bb1_in(v_n,-1 + v_x_0,v_y_0) [v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_n >= 0] (?,1) 14. eval_loops_bb6_in(v_n,v_x_0,v_y_0) -> eval_loops_stop(v_n,v_x_0,v_y_0) True (?,1) Signature: {(eval_loops_0,3) ;(eval_loops_1,3) ;(eval_loops_2,3) ;(eval_loops_bb0_in,3) ;(eval_loops_bb1_in,3) ;(eval_loops_bb2_in,3) ;(eval_loops_bb3_in,3) ;(eval_loops_bb4_in,3) ;(eval_loops_bb5_in,3) ;(eval_loops_bb6_in,3) ;(eval_loops_start,3) ;(eval_loops_stop,3)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{6,7},5->{14},6->{8,9},7->{14},8->{10,11},9->{13},10->{12},11->{13} ,12->{10,11},13->{6,7},14->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. eval_loops_start(v_n,v_x_0,v_y_0) -> eval_loops_bb0_in(v_n,v_x_0,v_y_0) True (1,1) 1. eval_loops_bb0_in(v_n,v_x_0,v_y_0) -> eval_loops_0(v_n,v_x_0,v_y_0) True (1,1) 2. eval_loops_0(v_n,v_x_0,v_y_0) -> eval_loops_1(v_n,v_x_0,v_y_0) True (1,1) 3. eval_loops_1(v_n,v_x_0,v_y_0) -> eval_loops_2(v_n,v_x_0,v_y_0) True (1,1) 4. eval_loops_2(v_n,v_x_0,v_y_0) -> eval_loops_bb1_in(v_n,v_n,v_y_0) [v_n >= 0] (1,1) 5. eval_loops_2(v_n,v_x_0,v_y_0) -> eval_loops_bb6_in(v_n,v_x_0,v_y_0) [-1 >= v_n] (1,1) 6. eval_loops_bb1_in(v_n,v_x_0,v_y_0) -> eval_loops_bb2_in(v_n,v_x_0,v_y_0) [v_n + -1*v_x_0 >= 0 && 1 + v_x_0 >= 0 && 1 + v_n + v_x_0 >= 0 && v_n >= 0 && v_x_0 >= 0] (?,1) 7. eval_loops_bb1_in(v_n,v_x_0,v_y_0) -> eval_loops_bb6_in(v_n,v_x_0,v_y_0) [v_n + -1*v_x_0 >= 0 && 1 + v_x_0 >= 0 && 1 + v_n + v_x_0 >= 0 && v_n >= 0 && -1 >= v_x_0] (1,1) 8. eval_loops_bb2_in(v_n,v_x_0,v_y_0) -> eval_loops_bb3_in(v_n,v_x_0,1) [v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_n >= 0 && -1 + v_x_0 >= 1] (?,1) 9. eval_loops_bb2_in(v_n,v_x_0,v_y_0) -> eval_loops_bb5_in(v_n,v_x_0,v_y_0) [v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_n >= 0 && 1 >= v_x_0] (?,1) 10. eval_loops_bb3_in(v_n,v_x_0,v_y_0) -> eval_loops_bb4_in(v_n,v_x_0,v_y_0) [-1 + v_y_0 >= 0 (?,1) && -3 + v_x_0 + v_y_0 >= 0 && -3 + v_n + v_y_0 >= 0 && v_n + -1*v_x_0 >= 0 && -2 + v_x_0 >= 0 && -4 + v_n + v_x_0 >= 0 && -2 + v_n >= 0 && -1 + v_x_0 >= v_y_0] 11. eval_loops_bb3_in(v_n,v_x_0,v_y_0) -> eval_loops_bb5_in(v_n,v_x_0,v_y_0) [-1 + v_y_0 >= 0 (?,1) && -3 + v_x_0 + v_y_0 >= 0 && -3 + v_n + v_y_0 >= 0 && v_n + -1*v_x_0 >= 0 && -2 + v_x_0 >= 0 && -4 + v_n + v_x_0 >= 0 && -2 + v_n >= 0 && v_y_0 >= v_x_0] 12. eval_loops_bb4_in(v_n,v_x_0,v_y_0) -> eval_loops_bb3_in(v_n,v_x_0,2*v_y_0) [-1 + v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_n + -1*v_y_0 >= 0 && -1 + v_y_0 >= 0 && -3 + v_x_0 + v_y_0 >= 0 && -3 + v_n + v_y_0 >= 0 && v_n + -1*v_x_0 >= 0 && -2 + v_x_0 >= 0 && -4 + v_n + v_x_0 >= 0 && -2 + v_n >= 0] 13. eval_loops_bb5_in(v_n,v_x_0,v_y_0) -> eval_loops_bb1_in(v_n,-1 + v_x_0,v_y_0) [v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_n >= 0] (?,1) 14. eval_loops_bb6_in(v_n,v_x_0,v_y_0) -> eval_loops_stop(v_n,v_x_0,v_y_0) True (1,1) Signature: {(eval_loops_0,3) ;(eval_loops_1,3) ;(eval_loops_2,3) ;(eval_loops_bb0_in,3) ;(eval_loops_bb1_in,3) ;(eval_loops_bb2_in,3) ;(eval_loops_bb3_in,3) ;(eval_loops_bb4_in,3) ;(eval_loops_bb5_in,3) ;(eval_loops_bb6_in,3) ;(eval_loops_start,3) ;(eval_loops_stop,3)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{6,7},5->{14},6->{8,9},7->{14},8->{10,11},9->{13},10->{12},11->{13} ,12->{10,11},13->{6,7},14->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(4,7),(8,11)] * Step 3: Looptree YES + Considered Problem: Rules: 0. eval_loops_start(v_n,v_x_0,v_y_0) -> eval_loops_bb0_in(v_n,v_x_0,v_y_0) True (1,1) 1. eval_loops_bb0_in(v_n,v_x_0,v_y_0) -> eval_loops_0(v_n,v_x_0,v_y_0) True (1,1) 2. eval_loops_0(v_n,v_x_0,v_y_0) -> eval_loops_1(v_n,v_x_0,v_y_0) True (1,1) 3. eval_loops_1(v_n,v_x_0,v_y_0) -> eval_loops_2(v_n,v_x_0,v_y_0) True (1,1) 4. eval_loops_2(v_n,v_x_0,v_y_0) -> eval_loops_bb1_in(v_n,v_n,v_y_0) [v_n >= 0] (1,1) 5. eval_loops_2(v_n,v_x_0,v_y_0) -> eval_loops_bb6_in(v_n,v_x_0,v_y_0) [-1 >= v_n] (1,1) 6. eval_loops_bb1_in(v_n,v_x_0,v_y_0) -> eval_loops_bb2_in(v_n,v_x_0,v_y_0) [v_n + -1*v_x_0 >= 0 && 1 + v_x_0 >= 0 && 1 + v_n + v_x_0 >= 0 && v_n >= 0 && v_x_0 >= 0] (?,1) 7. eval_loops_bb1_in(v_n,v_x_0,v_y_0) -> eval_loops_bb6_in(v_n,v_x_0,v_y_0) [v_n + -1*v_x_0 >= 0 && 1 + v_x_0 >= 0 && 1 + v_n + v_x_0 >= 0 && v_n >= 0 && -1 >= v_x_0] (1,1) 8. eval_loops_bb2_in(v_n,v_x_0,v_y_0) -> eval_loops_bb3_in(v_n,v_x_0,1) [v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_n >= 0 && -1 + v_x_0 >= 1] (?,1) 9. eval_loops_bb2_in(v_n,v_x_0,v_y_0) -> eval_loops_bb5_in(v_n,v_x_0,v_y_0) [v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_n >= 0 && 1 >= v_x_0] (?,1) 10. eval_loops_bb3_in(v_n,v_x_0,v_y_0) -> eval_loops_bb4_in(v_n,v_x_0,v_y_0) [-1 + v_y_0 >= 0 (?,1) && -3 + v_x_0 + v_y_0 >= 0 && -3 + v_n + v_y_0 >= 0 && v_n + -1*v_x_0 >= 0 && -2 + v_x_0 >= 0 && -4 + v_n + v_x_0 >= 0 && -2 + v_n >= 0 && -1 + v_x_0 >= v_y_0] 11. eval_loops_bb3_in(v_n,v_x_0,v_y_0) -> eval_loops_bb5_in(v_n,v_x_0,v_y_0) [-1 + v_y_0 >= 0 (?,1) && -3 + v_x_0 + v_y_0 >= 0 && -3 + v_n + v_y_0 >= 0 && v_n + -1*v_x_0 >= 0 && -2 + v_x_0 >= 0 && -4 + v_n + v_x_0 >= 0 && -2 + v_n >= 0 && v_y_0 >= v_x_0] 12. eval_loops_bb4_in(v_n,v_x_0,v_y_0) -> eval_loops_bb3_in(v_n,v_x_0,2*v_y_0) [-1 + v_x_0 + -1*v_y_0 >= 0 (?,1) && -1 + v_n + -1*v_y_0 >= 0 && -1 + v_y_0 >= 0 && -3 + v_x_0 + v_y_0 >= 0 && -3 + v_n + v_y_0 >= 0 && v_n + -1*v_x_0 >= 0 && -2 + v_x_0 >= 0 && -4 + v_n + v_x_0 >= 0 && -2 + v_n >= 0] 13. eval_loops_bb5_in(v_n,v_x_0,v_y_0) -> eval_loops_bb1_in(v_n,-1 + v_x_0,v_y_0) [v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && v_n + v_x_0 >= 0 && v_n >= 0] (?,1) 14. eval_loops_bb6_in(v_n,v_x_0,v_y_0) -> eval_loops_stop(v_n,v_x_0,v_y_0) True (1,1) Signature: {(eval_loops_0,3) ;(eval_loops_1,3) ;(eval_loops_2,3) ;(eval_loops_bb0_in,3) ;(eval_loops_bb1_in,3) ;(eval_loops_bb2_in,3) ;(eval_loops_bb3_in,3) ;(eval_loops_bb4_in,3) ;(eval_loops_bb5_in,3) ;(eval_loops_bb6_in,3) ;(eval_loops_start,3) ;(eval_loops_stop,3)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{6},5->{14},6->{8,9},7->{14},8->{10},9->{13},10->{12},11->{13},12->{10 ,11},13->{6,7},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:[6,13,9,11,12,10,8] c: [13] | `- p:[10,12] c: [12] YES