YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. eval_start_start(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_0(v_m,v_n,v_x_0,v_y_0) True (?,1) 2. eval_start_0(v_m,v_n,v_x_0,v_y_0) -> eval_start_1(v_m,v_n,v_x_0,v_y_0) True (?,1) 3. eval_start_1(v_m,v_n,v_x_0,v_y_0) -> eval_start_2(v_m,v_n,v_x_0,v_y_0) True (?,1) 4. eval_start_2(v_m,v_n,v_x_0,v_y_0) -> eval_start_3(v_m,v_n,v_x_0,v_y_0) True (?,1) 5. eval_start_3(v_m,v_n,v_x_0,v_y_0) -> eval_start_4(v_m,v_n,v_x_0,v_y_0) True (?,1) 6. eval_start_4(v_m,v_n,v_x_0,v_y_0) -> eval_start_5(v_m,v_n,v_x_0,v_y_0) True (?,1) 7. eval_start_5(v_m,v_n,v_x_0,v_y_0) -> eval_start_6(v_m,v_n,v_x_0,v_y_0) True (?,1) 8. eval_start_6(v_m,v_n,v_x_0,v_y_0) -> eval_start_7(v_m,v_n,v_x_0,v_y_0) True (?,1) 9. eval_start_7(v_m,v_n,v_x_0,v_y_0) -> eval_start_8(v_m,v_n,v_x_0,v_y_0) True (?,1) 10. eval_start_8(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,0,0) True (?,1) 11. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb2_in(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_x_0 >= 0 && -1 + v_n >= v_x_0] 12. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb3_in(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_x_0 >= 0 && v_x_0 >= v_n] 13. eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(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 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 14. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb4_in(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 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m >= v_y_0] 15. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb5_in(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 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && v_y_0 >= v_m] 16. eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(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 && -1*v_n + v_y_0 >= 0 && -1 + v_m + v_y_0 >= 0 && -1 + v_m + -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_m + -1*v_n >= 0 && -1 + v_m >= 0] 17. eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_stop(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 && -1*v_n + v_y_0 >= 0 && -1*v_m + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1*v_m + v_x_0 >= 0] Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_5,4) ;(eval_start_6,4) ;(eval_start_7,4) ;(eval_start_8,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11,12},11->{13},12->{14,15} ,13->{11,12},14->{16},15->{17},16->{11,12},17->{}] + 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_m,v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_0(v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_start_0(v_m,v_n,v_x_0,v_y_0) -> eval_start_1(v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_start_1(v_m,v_n,v_x_0,v_y_0) -> eval_start_2(v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_start_2(v_m,v_n,v_x_0,v_y_0) -> eval_start_3(v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_start_3(v_m,v_n,v_x_0,v_y_0) -> eval_start_4(v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_start_4(v_m,v_n,v_x_0,v_y_0) -> eval_start_5(v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_start_5(v_m,v_n,v_x_0,v_y_0) -> eval_start_6(v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_start_6(v_m,v_n,v_x_0,v_y_0) -> eval_start_7(v_m,v_n,v_x_0,v_y_0) True (1,1) 9. eval_start_7(v_m,v_n,v_x_0,v_y_0) -> eval_start_8(v_m,v_n,v_x_0,v_y_0) True (1,1) 10. eval_start_8(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,0,0) True (1,1) 11. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb2_in(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_x_0 >= 0 && -1 + v_n >= v_x_0] 12. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb3_in(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_x_0 >= 0 && v_x_0 >= v_n] 13. eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(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 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 14. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb4_in(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 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m >= v_y_0] 15. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb5_in(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 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && v_y_0 >= v_m] 16. eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(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 && -1*v_n + v_y_0 >= 0 && -1 + v_m + v_y_0 >= 0 && -1 + v_m + -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_m + -1*v_n >= 0 && -1 + v_m >= 0] 17. eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_stop(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 && -1*v_n + v_y_0 >= 0 && -1*v_m + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1*v_m + v_x_0 >= 0] Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_5,4) ;(eval_start_6,4) ;(eval_start_7,4) ;(eval_start_8,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11,12},11->{13},12->{14,15} ,13->{11,12},14->{16},15->{17},16->{11,12},17->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(16,11)] * Step 3: Looptree YES + Considered Problem: Rules: 0. eval_start_start(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_0(v_m,v_n,v_x_0,v_y_0) True (1,1) 2. eval_start_0(v_m,v_n,v_x_0,v_y_0) -> eval_start_1(v_m,v_n,v_x_0,v_y_0) True (1,1) 3. eval_start_1(v_m,v_n,v_x_0,v_y_0) -> eval_start_2(v_m,v_n,v_x_0,v_y_0) True (1,1) 4. eval_start_2(v_m,v_n,v_x_0,v_y_0) -> eval_start_3(v_m,v_n,v_x_0,v_y_0) True (1,1) 5. eval_start_3(v_m,v_n,v_x_0,v_y_0) -> eval_start_4(v_m,v_n,v_x_0,v_y_0) True (1,1) 6. eval_start_4(v_m,v_n,v_x_0,v_y_0) -> eval_start_5(v_m,v_n,v_x_0,v_y_0) True (1,1) 7. eval_start_5(v_m,v_n,v_x_0,v_y_0) -> eval_start_6(v_m,v_n,v_x_0,v_y_0) True (1,1) 8. eval_start_6(v_m,v_n,v_x_0,v_y_0) -> eval_start_7(v_m,v_n,v_x_0,v_y_0) True (1,1) 9. eval_start_7(v_m,v_n,v_x_0,v_y_0) -> eval_start_8(v_m,v_n,v_x_0,v_y_0) True (1,1) 10. eval_start_8(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,0,0) True (1,1) 11. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb2_in(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_x_0 >= 0 && -1 + v_n >= v_x_0] 12. eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb3_in(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_x_0 >= 0 && v_x_0 >= v_n] 13. eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(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 && -1 + v_n + -1*v_x_0 >= 0 && v_x_0 >= 0 && -1 + v_n + v_x_0 >= 0 && -1 + v_n >= 0] 14. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb4_in(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 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1 + v_m >= v_y_0] 15. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb5_in(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 && -1*v_n + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && v_y_0 >= v_m] 16. eval_start_bb4_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(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 && -1*v_n + v_y_0 >= 0 && -1 + v_m + v_y_0 >= 0 && -1 + v_m + -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_m + -1*v_n >= 0 && -1 + v_m >= 0] 17. eval_start_bb5_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_stop(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 && -1*v_n + v_y_0 >= 0 && -1*v_m + v_y_0 >= 0 && v_x_0 >= 0 && -1*v_n + v_x_0 >= 0 && -1*v_m + v_x_0 >= 0] Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_5,4) ;(eval_start_6,4) ;(eval_start_7,4) ;(eval_start_8,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9},9->{10},10->{11,12},11->{13},12->{14,15} ,13->{11,12},14->{16},15->{17},16->{12},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:[11,13] c: [13] | `- p:[12,16,14] c: [16] YES