YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. eval_aaron2_start(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb0_in(v__01,v__02,v_3,v_tx,v_x,v_y) True (1,1) 1. eval_aaron2_bb0_in(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_0(v__01,v__02,v_3,v_tx,v_x,v_y) True (?,1) 2. eval_aaron2_0(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_1(v__01,v__02,v_3,v_tx,v_x,v_y) True (?,1) 3. eval_aaron2_1(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_2(v__01,v__02,v_3,v_tx,v_x,v_y) True (?,1) 4. eval_aaron2_2(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_3(v__01,v__02,v_3,v_tx,v_x,v_y) True (?,1) 5. eval_aaron2_3(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb1_in(v_x,v_y,v_3,v_tx,v_x,v_y) [v_tx >= 0] (?,1) 6. eval_aaron2_3(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb5_in(v__01,v__02,v_3,v_tx,v_x,v_y) [-1 >= v_tx] (?,1) 7. eval_aaron2_bb1_in(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb5_in(v__01,v__02,v_3,v_tx,v_x,v_y) [v__02 + -1*v_y >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && -1 + v__02 >= v__01] (?,1) 8. eval_aaron2_bb1_in(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb2_in(v__01,v__02,v_3,v_tx,v_x,v_y) [v__02 + -1*v_y >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && v__01 >= v__02] (?,1) 9. eval_aaron2_bb2_in(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_4(v__01,v__02,v_3,v_tx,v_x,v_y) [v_x + -1*v_y >= 0 (?,1) && v__02 + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1*v__02 + v_x >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && v__01 + -1*v__02 >= 0] 10. eval_aaron2_4(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_5(v__01,v__02,nondef_0,v_tx,v_x,v_y) [v_x + -1*v_y >= 0 (?,1) && v__02 + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1*v__02 + v_x >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && v__01 + -1*v__02 >= 0] 11. eval_aaron2_5(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb3_in(v__01,v__02,v_3,v_tx,v_x,v_y) [v_x + -1*v_y >= 0 (?,1) && v__02 + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1*v__02 + v_x >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && v__01 + -1*v__02 >= 0 && -1 + v_3 >= 0] 12. eval_aaron2_5(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb4_in(v__01,v__02,v_3,v_tx,v_x,v_y) [v_x + -1*v_y >= 0 (?,1) && v__02 + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1*v__02 + v_x >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && v__01 + -1*v__02 >= 0 && 0 >= v_3] 13. eval_aaron2_bb3_in(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb1_in(-1 + v__01 + -1*v_tx,v__02,v_3,v_tx,v_x,v_y) [v_x + -1*v_y >= 0 (?,1) && v__02 + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1*v__02 + v_x >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && -1 + v_3 + v_tx >= 0 && -1 + v_3 >= 0 && v__01 + -1*v__02 >= 0] 14. eval_aaron2_bb4_in(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb1_in(v__01,1 + v__02 + v_tx,v_3,v_tx,v_x,v_y) [v_x + -1*v_y >= 0 (?,1) && v__02 + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1*v__02 + v_x >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && -1*v_3 + v_tx >= 0 && -1*v_3 >= 0 && v__01 + -1*v__02 >= 0] 15. eval_aaron2_bb5_in(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_stop(v__01,v__02,v_3,v_tx,v_x,v_y) True (?,1) Signature: {(eval_aaron2_0,6) ;(eval_aaron2_1,6) ;(eval_aaron2_2,6) ;(eval_aaron2_3,6) ;(eval_aaron2_4,6) ;(eval_aaron2_5,6) ;(eval_aaron2_bb0_in,6) ;(eval_aaron2_bb1_in,6) ;(eval_aaron2_bb2_in,6) ;(eval_aaron2_bb3_in,6) ;(eval_aaron2_bb4_in,6) ;(eval_aaron2_bb5_in,6) ;(eval_aaron2_start,6) ;(eval_aaron2_stop,6)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5,6},5->{7,8},6->{15},7->{15},8->{9},9->{10},10->{11,12},11->{13} ,12->{14},13->{7,8},14->{7,8},15->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: Looptree YES + Considered Problem: Rules: 0. eval_aaron2_start(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb0_in(v__01,v__02,v_3,v_tx,v_x,v_y) True (1,1) 1. eval_aaron2_bb0_in(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_0(v__01,v__02,v_3,v_tx,v_x,v_y) True (1,1) 2. eval_aaron2_0(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_1(v__01,v__02,v_3,v_tx,v_x,v_y) True (1,1) 3. eval_aaron2_1(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_2(v__01,v__02,v_3,v_tx,v_x,v_y) True (1,1) 4. eval_aaron2_2(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_3(v__01,v__02,v_3,v_tx,v_x,v_y) True (1,1) 5. eval_aaron2_3(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb1_in(v_x,v_y,v_3,v_tx,v_x,v_y) [v_tx >= 0] (1,1) 6. eval_aaron2_3(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb5_in(v__01,v__02,v_3,v_tx,v_x,v_y) [-1 >= v_tx] (1,1) 7. eval_aaron2_bb1_in(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb5_in(v__01,v__02,v_3,v_tx,v_x,v_y) [v__02 + -1*v_y >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && -1 + v__02 >= v__01] (1,1) 8. eval_aaron2_bb1_in(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb2_in(v__01,v__02,v_3,v_tx,v_x,v_y) [v__02 + -1*v_y >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && v__01 >= v__02] (?,1) 9. eval_aaron2_bb2_in(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_4(v__01,v__02,v_3,v_tx,v_x,v_y) [v_x + -1*v_y >= 0 (?,1) && v__02 + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1*v__02 + v_x >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && v__01 + -1*v__02 >= 0] 10. eval_aaron2_4(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_5(v__01,v__02,nondef_0,v_tx,v_x,v_y) [v_x + -1*v_y >= 0 (?,1) && v__02 + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1*v__02 + v_x >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && v__01 + -1*v__02 >= 0] 11. eval_aaron2_5(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb3_in(v__01,v__02,v_3,v_tx,v_x,v_y) [v_x + -1*v_y >= 0 (?,1) && v__02 + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1*v__02 + v_x >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && v__01 + -1*v__02 >= 0 && -1 + v_3 >= 0] 12. eval_aaron2_5(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb4_in(v__01,v__02,v_3,v_tx,v_x,v_y) [v_x + -1*v_y >= 0 (?,1) && v__02 + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1*v__02 + v_x >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && v__01 + -1*v__02 >= 0 && 0 >= v_3] 13. eval_aaron2_bb3_in(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb1_in(-1 + v__01 + -1*v_tx,v__02,v_3,v_tx,v_x,v_y) [v_x + -1*v_y >= 0 (?,1) && v__02 + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1*v__02 + v_x >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && -1 + v_3 + v_tx >= 0 && -1 + v_3 >= 0 && v__01 + -1*v__02 >= 0] 14. eval_aaron2_bb4_in(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_bb1_in(v__01,1 + v__02 + v_tx,v_3,v_tx,v_x,v_y) [v_x + -1*v_y >= 0 (?,1) && v__02 + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1*v__02 + v_x >= 0 && -1*v__01 + v_x >= 0 && v_tx >= 0 && -1*v_3 + v_tx >= 0 && -1*v_3 >= 0 && v__01 + -1*v__02 >= 0] 15. eval_aaron2_bb5_in(v__01,v__02,v_3,v_tx,v_x,v_y) -> eval_aaron2_stop(v__01,v__02,v_3,v_tx,v_x,v_y) True (1,1) Signature: {(eval_aaron2_0,6) ;(eval_aaron2_1,6) ;(eval_aaron2_2,6) ;(eval_aaron2_3,6) ;(eval_aaron2_4,6) ;(eval_aaron2_5,6) ;(eval_aaron2_bb0_in,6) ;(eval_aaron2_bb1_in,6) ;(eval_aaron2_bb2_in,6) ;(eval_aaron2_bb3_in,6) ;(eval_aaron2_bb4_in,6) ;(eval_aaron2_bb5_in,6) ;(eval_aaron2_start,6) ;(eval_aaron2_stop,6)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5,6},5->{7,8},6->{15},7->{15},8->{9},9->{10},10->{11,12},11->{13} ,12->{14},13->{7,8},14->{7,8},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:[8,13,11,10,9,14,12] c: [14] | `- p:[8,13,11,10,9] c: [13] YES