YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. eval_start_start(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) True (1,1) 1. eval_start_bb0_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_0(v__0,v__01,v__1,v_1,v_2,v_x,v_y) True (?,1) 2. eval_start_0(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_1(v__0,v__01,v__1,v_1,v_2,v_x,v_y) True (?,1) 3. eval_start_1(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_2(v__0,v__01,v__1,v_1,v_2,v_x,v_y) True (?,1) 4. eval_start_2(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_3(v__0,v__01,v__1,v_1,v_2,v_x,v_y) True (?,1) 5. eval_start_3(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_4(v__0,v__01,v__1,v_1,v_2,v_x,v_y) True (?,1) 6. eval_start_4(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_5(v__0,v__01,v__1,v_1,v_2,v_x,v_y) True (?,1) 7. eval_start_5(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v__1,v_1,v_2,v_x,v_y) True (?,1) 8. eval_start_bb1_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) [-1*v__0 + v_x >= 0 && -1 + v__0 >= 0] (?,1) 9. eval_start_bb1_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb6_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) [-1*v__0 + v_x >= 0 && 0 >= v__0] (?,1) 10. eval_start_bb2_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_7(v__0,v__01,v__1,-1 + v__0,v_2,v_x,v_y) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0] (?,1) 11. eval_start_7(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_8(v__0,v__01,v__1,v_1,nondef_0,v_x,v_y) [-1 + v_x >= 0 (?,1) && -1 + v_1 + v_x >= 0 && -1 + -1*v_1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_1 + v__0 >= 0 && v_1 >= 0 && -1 + v_1 + v__0 >= 0 && 1 + v_1 + -1*v__0 >= 0 && -1 + v__0 >= 0] 12. eval_start_8(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) [-1 + v_x >= 0 (?,1) && -1 + v_1 + v_x >= 0 && -1 + -1*v_1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_1 + v__0 >= 0 && v_1 >= 0 && -1 + v_1 + v__0 >= 0 && 1 + v_1 + -1*v__0 >= 0 && -1 + v__0 >= 0 && -1 + v_2 >= 0] 13. eval_start_8(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb4_in(v__0,v__01,v__01,v_1,v_2,v_x,v_y) [-1 + v_x >= 0 (?,1) && -1 + v_1 + v_x >= 0 && -1 + -1*v_1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_1 + v__0 >= 0 && v_1 >= 0 && -1 + v_1 + v__0 >= 0 && 1 + v_1 + -1*v__0 >= 0 && -1 + v__0 >= 0 && 0 >= v_2] 14. eval_start_bb3_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb1_in(v_1,1 + v__01,v__1,v_1,v_2,v_x,v_y) [-1 + v_x >= 0 (?,1) && -2 + v_2 + v_x >= 0 && -1 + v_1 + v_x >= 0 && -1 + -1*v_1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v_2 >= 0 && -1 + v_1 + v_2 >= 0 && -2 + v_2 + v__0 >= 0 && -1 + -1*v_1 + v__0 >= 0 && v_1 >= 0 && -1 + v_1 + v__0 >= 0 && 1 + v_1 + -1*v__0 >= 0 && -1 + v__0 >= 0] 15. eval_start_bb4_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb5_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) [-1 + v_x >= 0 (?,1) && -1 + -1*v_2 + v_x >= 0 && -1 + v_1 + v_x >= 0 && -1 + -1*v_1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1*v_2 >= 0 && v_1 + -1*v_2 >= 0 && -1 + -1*v_2 + v__0 >= 0 && -1 + -1*v_1 + v__0 >= 0 && v_1 >= 0 && -1 + v_1 + v__0 >= 0 && 1 + v_1 + -1*v__0 >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__0 >= 0 && -1 + v__1 >= 0] 16. eval_start_bb4_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb1_in(v_1,v__1,v__1,v_1,v_2,v_x,v_y) [-1 + v_x >= 0 (?,1) && -1 + -1*v_2 + v_x >= 0 && -1 + v_1 + v_x >= 0 && -1 + -1*v_1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1*v_2 >= 0 && v_1 + -1*v_2 >= 0 && -1 + -1*v_2 + v__0 >= 0 && -1 + -1*v_1 + v__0 >= 0 && v_1 >= 0 && -1 + v_1 + v__0 >= 0 && 1 + v_1 + -1*v__0 >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__0 >= 0 && 0 >= v__1] 17. eval_start_bb5_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb4_in(v__0,v__01,-1 + v__1,v_1,v_2,v_x,v_y) [-1 + v_x >= 0 (?,1) && -1 + -1*v_2 + v_x >= 0 && -1 + v_1 + v_x >= 0 && -1 + -1*v_1 + v_x >= 0 && -2 + v__1 + v_x >= 0 && -2 + v__01 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1*v_2 >= 0 && v_1 + -1*v_2 >= 0 && -1 + -1*v_2 + v__1 >= 0 && -1 + -1*v_2 + v__01 >= 0 && -1 + -1*v_2 + v__0 >= 0 && -1 + -1*v_1 + v__0 >= 0 && v_1 >= 0 && -1 + v_1 + v__1 >= 0 && -1 + v_1 + v__01 >= 0 && -1 + v_1 + v__0 >= 0 && 1 + v_1 + -1*v__0 >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__1 >= 0 && -2 + v__01 + v__1 >= 0 && -2 + v__0 + v__1 >= 0 && -1 + v__01 >= 0 && -2 + v__0 + v__01 >= 0 && -1 + v__0 >= 0] 18. eval_start_bb6_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_stop(v__0,v__01,v__1,v_1,v_2,v_x,v_y) [-1*v__0 + v_x >= 0 && -1*v__0 >= 0] (?,1) Signature: {(eval_start_0,7) ;(eval_start_1,7) ;(eval_start_2,7) ;(eval_start_3,7) ;(eval_start_4,7) ;(eval_start_5,7) ;(eval_start_7,7) ;(eval_start_8,7) ;(eval_start_bb0_in,7) ;(eval_start_bb1_in,7) ;(eval_start_bb2_in,7) ;(eval_start_bb3_in,7) ;(eval_start_bb4_in,7) ;(eval_start_bb5_in,7) ;(eval_start_bb6_in,7) ;(eval_start_start,7) ;(eval_start_stop,7)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9},8->{10},9->{18},10->{11},11->{12,13},12->{14} ,13->{15,16},14->{8,9},15->{17},16->{8,9},17->{15,16},18->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. eval_start_start(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) True (1,1) 1. eval_start_bb0_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_0(v__0,v__01,v__1,v_1,v_2,v_x,v_y) True (1,1) 2. eval_start_0(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_1(v__0,v__01,v__1,v_1,v_2,v_x,v_y) True (1,1) 3. eval_start_1(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_2(v__0,v__01,v__1,v_1,v_2,v_x,v_y) True (1,1) 4. eval_start_2(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_3(v__0,v__01,v__1,v_1,v_2,v_x,v_y) True (1,1) 5. eval_start_3(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_4(v__0,v__01,v__1,v_1,v_2,v_x,v_y) True (1,1) 6. eval_start_4(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_5(v__0,v__01,v__1,v_1,v_2,v_x,v_y) True (1,1) 7. eval_start_5(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v__1,v_1,v_2,v_x,v_y) True (1,1) 8. eval_start_bb1_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) [-1*v__0 + v_x >= 0 && -1 + v__0 >= 0] (?,1) 9. eval_start_bb1_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb6_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) [-1*v__0 + v_x >= 0 && 0 >= v__0] (1,1) 10. eval_start_bb2_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_7(v__0,v__01,v__1,-1 + v__0,v_2,v_x,v_y) [-1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0] (?,1) 11. eval_start_7(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_8(v__0,v__01,v__1,v_1,nondef_0,v_x,v_y) [-1 + v_x >= 0 (?,1) && -1 + v_1 + v_x >= 0 && -1 + -1*v_1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_1 + v__0 >= 0 && v_1 >= 0 && -1 + v_1 + v__0 >= 0 && 1 + v_1 + -1*v__0 >= 0 && -1 + v__0 >= 0] 12. eval_start_8(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) [-1 + v_x >= 0 (?,1) && -1 + v_1 + v_x >= 0 && -1 + -1*v_1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_1 + v__0 >= 0 && v_1 >= 0 && -1 + v_1 + v__0 >= 0 && 1 + v_1 + -1*v__0 >= 0 && -1 + v__0 >= 0 && -1 + v_2 >= 0] 13. eval_start_8(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb4_in(v__0,v__01,v__01,v_1,v_2,v_x,v_y) [-1 + v_x >= 0 (?,1) && -1 + v_1 + v_x >= 0 && -1 + -1*v_1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_1 + v__0 >= 0 && v_1 >= 0 && -1 + v_1 + v__0 >= 0 && 1 + v_1 + -1*v__0 >= 0 && -1 + v__0 >= 0 && 0 >= v_2] 14. eval_start_bb3_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb1_in(v_1,1 + v__01,v__1,v_1,v_2,v_x,v_y) [-1 + v_x >= 0 (?,1) && -2 + v_2 + v_x >= 0 && -1 + v_1 + v_x >= 0 && -1 + -1*v_1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v_2 >= 0 && -1 + v_1 + v_2 >= 0 && -2 + v_2 + v__0 >= 0 && -1 + -1*v_1 + v__0 >= 0 && v_1 >= 0 && -1 + v_1 + v__0 >= 0 && 1 + v_1 + -1*v__0 >= 0 && -1 + v__0 >= 0] 15. eval_start_bb4_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb5_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) [-1 + v_x >= 0 (?,1) && -1 + -1*v_2 + v_x >= 0 && -1 + v_1 + v_x >= 0 && -1 + -1*v_1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1*v_2 >= 0 && v_1 + -1*v_2 >= 0 && -1 + -1*v_2 + v__0 >= 0 && -1 + -1*v_1 + v__0 >= 0 && v_1 >= 0 && -1 + v_1 + v__0 >= 0 && 1 + v_1 + -1*v__0 >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__0 >= 0 && -1 + v__1 >= 0] 16. eval_start_bb4_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb1_in(v_1,v__1,v__1,v_1,v_2,v_x,v_y) [-1 + v_x >= 0 (?,1) && -1 + -1*v_2 + v_x >= 0 && -1 + v_1 + v_x >= 0 && -1 + -1*v_1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1*v_2 >= 0 && v_1 + -1*v_2 >= 0 && -1 + -1*v_2 + v__0 >= 0 && -1 + -1*v_1 + v__0 >= 0 && v_1 >= 0 && -1 + v_1 + v__0 >= 0 && 1 + v_1 + -1*v__0 >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__0 >= 0 && 0 >= v__1] 17. eval_start_bb5_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_bb4_in(v__0,v__01,-1 + v__1,v_1,v_2,v_x,v_y) [-1 + v_x >= 0 (?,1) && -1 + -1*v_2 + v_x >= 0 && -1 + v_1 + v_x >= 0 && -1 + -1*v_1 + v_x >= 0 && -2 + v__1 + v_x >= 0 && -2 + v__01 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1*v_2 >= 0 && v_1 + -1*v_2 >= 0 && -1 + -1*v_2 + v__1 >= 0 && -1 + -1*v_2 + v__01 >= 0 && -1 + -1*v_2 + v__0 >= 0 && -1 + -1*v_1 + v__0 >= 0 && v_1 >= 0 && -1 + v_1 + v__1 >= 0 && -1 + v_1 + v__01 >= 0 && -1 + v_1 + v__0 >= 0 && 1 + v_1 + -1*v__0 >= 0 && v__01 + -1*v__1 >= 0 && -1 + v__1 >= 0 && -2 + v__01 + v__1 >= 0 && -2 + v__0 + v__1 >= 0 && -1 + v__01 >= 0 && -2 + v__0 + v__01 >= 0 && -1 + v__0 >= 0] 18. eval_start_bb6_in(v__0,v__01,v__1,v_1,v_2,v_x,v_y) -> eval_start_stop(v__0,v__01,v__1,v_1,v_2,v_x,v_y) [-1*v__0 + v_x >= 0 && -1*v__0 >= 0] (1,1) Signature: {(eval_start_0,7) ;(eval_start_1,7) ;(eval_start_2,7) ;(eval_start_3,7) ;(eval_start_4,7) ;(eval_start_5,7) ;(eval_start_7,7) ;(eval_start_8,7) ;(eval_start_bb0_in,7) ;(eval_start_bb1_in,7) ;(eval_start_bb2_in,7) ;(eval_start_bb3_in,7) ;(eval_start_bb4_in,7) ;(eval_start_bb5_in,7) ;(eval_start_bb6_in,7) ;(eval_start_start,7) ;(eval_start_stop,7)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9},8->{10},9->{18},10->{11},11->{12,13},12->{14} ,13->{15,16},14->{8,9},15->{17},16->{8,9},17->{15,16},18->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18] | `- p:[8,14,12,11,10,16,13,17,15] c: [17] | `- p:[8,14,12,11,10,16,13] c: [16] | `- p:[8,14,12,11,10] c: [14] YES