YES * Step 1: FromIts YES + Considered Problem: Rules: 0. eval_start_start(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb0_in(v__0,v_3,v_x,v_y,v_z_0) True (1,1) 1. eval_start_bb0_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_0(v__0,v_3,v_x,v_y,v_z_0) True (?,1) 2. eval_start_0(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_1(v__0,v_3,v_x,v_y,v_z_0) True (?,1) 3. eval_start_1(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_2(v__0,v_3,v_x,v_y,v_z_0) True (?,1) 4. eval_start_2(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb1_in(v_x,v_3,v_x,v_y,v_z_0) [v_y >= 0] (?,1) 5. eval_start_2(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb6_in(v__0,v_3,v_x,v_y,v_z_0) [-1 >= v_y] (?,1) 6. eval_start_bb1_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb2_in(v__0,v_3,v_x,v_y,v_z_0) [v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v_y] (?,1) 7. eval_start_bb1_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb5_in(v__0,v_3,v_x,v_y,v_z_0) [v_y >= 0 && -1*v__0 + v_x >= 0 && v_y >= v__0] (?,1) 8. eval_start_bb2_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb3_in(v__0,-1 + v__0 + -1*v_y,v_x,v_y,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && -1 + v__0 + -1*v_y >= 0 && v_y >= 0 && -1 + v_x + v_y >= 0 && -1 + v__0 + v_y >= 0 && -1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0] 9. eval_start_bb3_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb4_in(v__0,v_3,v_x,v_y,v_z_0) [v_y + -1*v_z_0 >= 0 (?,1) && -1 + v_x + -1*v_z_0 >= 0 && -1 + v__0 + -1*v_z_0 >= 0 && v_z_0 >= 0 && v_y + v_z_0 >= 0 && -1 + v_x + v_z_0 >= 0 && -1 + v__0 + v_z_0 >= 0 && -1 + v_x + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && v_y >= 0 && -1 + v_x + v_y >= 0 && v_3 + v_y >= 0 && -1 + v__0 + v_y >= 0 && -1 + v_x >= 0 && -1 + v_3 + v_x >= 0 && -1 + -1*v_3 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_3 + v__0 >= 0 && -1 + v_3 + v__0 >= 0 && -1 + v__0 >= 0 && -1 + v_z_0 >= 0] 10. eval_start_bb3_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb1_in(v_3,v_3,v_x,v_y,v_z_0) [v_y + -1*v_z_0 >= 0 (?,1) && -1 + v_x + -1*v_z_0 >= 0 && -1 + v__0 + -1*v_z_0 >= 0 && v_z_0 >= 0 && v_y + v_z_0 >= 0 && -1 + v_x + v_z_0 >= 0 && -1 + v__0 + v_z_0 >= 0 && -1 + v_x + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && v_y >= 0 && -1 + v_x + v_y >= 0 && v_3 + v_y >= 0 && -1 + v__0 + v_y >= 0 && -1 + v_x >= 0 && -1 + v_3 + v_x >= 0 && -1 + -1*v_3 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_3 + v__0 >= 0 && -1 + v_3 + v__0 >= 0 && -1 + v__0 >= 0 && 0 >= v_z_0] 11. eval_start_bb4_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb3_in(v__0,v_3,v_x,v_y,-1 + v_z_0) [v_y + -1*v_z_0 >= 0 (?,1) && -1 + v_x + -1*v_z_0 >= 0 && -1 + v__0 + -1*v_z_0 >= 0 && -1 + v_z_0 >= 0 && -2 + v_y + v_z_0 >= 0 && -3 + v_x + v_z_0 >= 0 && -3 + v__0 + v_z_0 >= 0 && -1 + v_x + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + v_y >= 0 && -3 + v_x + v_y >= 0 && v_3 + v_y >= 0 && -3 + v__0 + v_y >= 0 && -2 + v_x >= 0 && -1 + v_3 + v_x >= 0 && -1 + -1*v_3 + v_x >= 0 && -4 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_3 + v__0 >= 0 && -1 + v_3 + v__0 >= 0 && -2 + v__0 >= 0] 12. eval_start_bb5_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_stop(v__0,v_3,v_x,v_y,v_z_0) [v_y >= 0 && -1*v__0 + v_y >= 0 && -1*v__0 + v_x >= 0] (?,1) 13. eval_start_bb6_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_8(v__0,v_3,v_x,v_y,v_z_0) [-1 + -1*v_y >= 0] (?,1) 14. eval_start_8(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_9(v__0,v_3,v_x,v_y,v_z_0) [-1 + -1*v_y >= 0] (?,1) 15. eval_start_9(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_stop(v__0,v_3,v_x,v_y,v_z_0) [-1 + -1*v_y >= 0] (?,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_8,5) ;(eval_start_9,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_bb5_in,5) ;(eval_start_bb6_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{6,7},5->{13},6->{8},7->{12},8->{9,10},9->{11},10->{6,7},11->{9,10} ,12->{},13->{14},14->{15},15->{}] + Applied Processor: FromIts + Details: () * Step 2: Decompose YES + Considered Problem: Rules: eval_start_start(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb0_in(v__0,v_3,v_x,v_y,v_z_0) True eval_start_bb0_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_0(v__0,v_3,v_x,v_y,v_z_0) True eval_start_0(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_1(v__0,v_3,v_x,v_y,v_z_0) True eval_start_1(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_2(v__0,v_3,v_x,v_y,v_z_0) True eval_start_2(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb1_in(v_x,v_3,v_x,v_y,v_z_0) [v_y >= 0] eval_start_2(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb6_in(v__0,v_3,v_x,v_y,v_z_0) [-1 >= v_y] eval_start_bb1_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb2_in(v__0,v_3,v_x,v_y,v_z_0) [v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v_y] eval_start_bb1_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb5_in(v__0,v_3,v_x,v_y,v_z_0) [v_y >= 0 && -1*v__0 + v_x >= 0 && v_y >= v__0] eval_start_bb2_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb3_in(v__0,-1 + v__0 + -1*v_y,v_x,v_y,v_y) [-1 + v_x + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && v_y >= 0 && -1 + v_x + v_y >= 0 && -1 + v__0 + v_y >= 0 && -1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0] eval_start_bb3_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb4_in(v__0,v_3,v_x,v_y,v_z_0) [v_y + -1*v_z_0 >= 0 && -1 + v_x + -1*v_z_0 >= 0 && -1 + v__0 + -1*v_z_0 >= 0 && v_z_0 >= 0 && v_y + v_z_0 >= 0 && -1 + v_x + v_z_0 >= 0 && -1 + v__0 + v_z_0 >= 0 && -1 + v_x + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && v_y >= 0 && -1 + v_x + v_y >= 0 && v_3 + v_y >= 0 && -1 + v__0 + v_y >= 0 && -1 + v_x >= 0 && -1 + v_3 + v_x >= 0 && -1 + -1*v_3 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_3 + v__0 >= 0 && -1 + v_3 + v__0 >= 0 && -1 + v__0 >= 0 && -1 + v_z_0 >= 0] eval_start_bb3_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb1_in(v_3,v_3,v_x,v_y,v_z_0) [v_y + -1*v_z_0 >= 0 && -1 + v_x + -1*v_z_0 >= 0 && -1 + v__0 + -1*v_z_0 >= 0 && v_z_0 >= 0 && v_y + v_z_0 >= 0 && -1 + v_x + v_z_0 >= 0 && -1 + v__0 + v_z_0 >= 0 && -1 + v_x + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && v_y >= 0 && -1 + v_x + v_y >= 0 && v_3 + v_y >= 0 && -1 + v__0 + v_y >= 0 && -1 + v_x >= 0 && -1 + v_3 + v_x >= 0 && -1 + -1*v_3 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_3 + v__0 >= 0 && -1 + v_3 + v__0 >= 0 && -1 + v__0 >= 0 && 0 >= v_z_0] eval_start_bb4_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb3_in(v__0,v_3,v_x,v_y,-1 + v_z_0) [v_y + -1*v_z_0 >= 0 && -1 + v_x + -1*v_z_0 >= 0 && -1 + v__0 + -1*v_z_0 >= 0 && -1 + v_z_0 >= 0 && -2 + v_y + v_z_0 >= 0 && -3 + v_x + v_z_0 >= 0 && -3 + v__0 + v_z_0 >= 0 && -1 + v_x + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + v_y >= 0 && -3 + v_x + v_y >= 0 && v_3 + v_y >= 0 && -3 + v__0 + v_y >= 0 && -2 + v_x >= 0 && -1 + v_3 + v_x >= 0 && -1 + -1*v_3 + v_x >= 0 && -4 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_3 + v__0 >= 0 && -1 + v_3 + v__0 >= 0 && -2 + v__0 >= 0] eval_start_bb5_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_stop(v__0,v_3,v_x,v_y,v_z_0) [v_y >= 0 && -1*v__0 + v_y >= 0 && -1*v__0 + v_x >= 0] eval_start_bb6_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_8(v__0,v_3,v_x,v_y,v_z_0) [-1 + -1*v_y >= 0] eval_start_8(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_9(v__0,v_3,v_x,v_y,v_z_0) [-1 + -1*v_y >= 0] eval_start_9(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_stop(v__0,v_3,v_x,v_y,v_z_0) [-1 + -1*v_y >= 0] Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_8,5) ;(eval_start_9,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_bb5_in,5) ;(eval_start_bb6_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{6,7},5->{13},6->{8},7->{12},8->{9,10},9->{11},10->{6,7},11->{9,10} ,12->{},13->{14},14->{15},15->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] | `- p:[6,10,8,11,9] c: [9,11] | `- p:[6,10,8] c: [6,8,10] * Step 3: CloseWith YES + Considered Problem: (Rules: eval_start_start(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb0_in(v__0,v_3,v_x,v_y,v_z_0) True eval_start_bb0_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_0(v__0,v_3,v_x,v_y,v_z_0) True eval_start_0(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_1(v__0,v_3,v_x,v_y,v_z_0) True eval_start_1(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_2(v__0,v_3,v_x,v_y,v_z_0) True eval_start_2(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb1_in(v_x,v_3,v_x,v_y,v_z_0) [v_y >= 0] eval_start_2(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb6_in(v__0,v_3,v_x,v_y,v_z_0) [-1 >= v_y] eval_start_bb1_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb2_in(v__0,v_3,v_x,v_y,v_z_0) [v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v_y] eval_start_bb1_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb5_in(v__0,v_3,v_x,v_y,v_z_0) [v_y >= 0 && -1*v__0 + v_x >= 0 && v_y >= v__0] eval_start_bb2_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb3_in(v__0,-1 + v__0 + -1*v_y,v_x,v_y,v_y) [-1 + v_x + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && v_y >= 0 && -1 + v_x + v_y >= 0 && -1 + v__0 + v_y >= 0 && -1 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= 0] eval_start_bb3_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb4_in(v__0,v_3,v_x,v_y,v_z_0) [v_y + -1*v_z_0 >= 0 && -1 + v_x + -1*v_z_0 >= 0 && -1 + v__0 + -1*v_z_0 >= 0 && v_z_0 >= 0 && v_y + v_z_0 >= 0 && -1 + v_x + v_z_0 >= 0 && -1 + v__0 + v_z_0 >= 0 && -1 + v_x + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && v_y >= 0 && -1 + v_x + v_y >= 0 && v_3 + v_y >= 0 && -1 + v__0 + v_y >= 0 && -1 + v_x >= 0 && -1 + v_3 + v_x >= 0 && -1 + -1*v_3 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_3 + v__0 >= 0 && -1 + v_3 + v__0 >= 0 && -1 + v__0 >= 0 && -1 + v_z_0 >= 0] eval_start_bb3_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb1_in(v_3,v_3,v_x,v_y,v_z_0) [v_y + -1*v_z_0 >= 0 && -1 + v_x + -1*v_z_0 >= 0 && -1 + v__0 + -1*v_z_0 >= 0 && v_z_0 >= 0 && v_y + v_z_0 >= 0 && -1 + v_x + v_z_0 >= 0 && -1 + v__0 + v_z_0 >= 0 && -1 + v_x + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && v_y >= 0 && -1 + v_x + v_y >= 0 && v_3 + v_y >= 0 && -1 + v__0 + v_y >= 0 && -1 + v_x >= 0 && -1 + v_3 + v_x >= 0 && -1 + -1*v_3 + v_x >= 0 && -2 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_3 + v__0 >= 0 && -1 + v_3 + v__0 >= 0 && -1 + v__0 >= 0 && 0 >= v_z_0] eval_start_bb4_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_bb3_in(v__0,v_3,v_x,v_y,-1 + v_z_0) [v_y + -1*v_z_0 >= 0 && -1 + v_x + -1*v_z_0 >= 0 && -1 + v__0 + -1*v_z_0 >= 0 && -1 + v_z_0 >= 0 && -2 + v_y + v_z_0 >= 0 && -3 + v_x + v_z_0 >= 0 && -3 + v__0 + v_z_0 >= 0 && -1 + v_x + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + v_y >= 0 && -3 + v_x + v_y >= 0 && v_3 + v_y >= 0 && -3 + v__0 + v_y >= 0 && -2 + v_x >= 0 && -1 + v_3 + v_x >= 0 && -1 + -1*v_3 + v_x >= 0 && -4 + v__0 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + -1*v_3 + v__0 >= 0 && -1 + v_3 + v__0 >= 0 && -2 + v__0 >= 0] eval_start_bb5_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_stop(v__0,v_3,v_x,v_y,v_z_0) [v_y >= 0 && -1*v__0 + v_y >= 0 && -1*v__0 + v_x >= 0] eval_start_bb6_in(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_8(v__0,v_3,v_x,v_y,v_z_0) [-1 + -1*v_y >= 0] eval_start_8(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_9(v__0,v_3,v_x,v_y,v_z_0) [-1 + -1*v_y >= 0] eval_start_9(v__0,v_3,v_x,v_y,v_z_0) -> eval_start_stop(v__0,v_3,v_x,v_y,v_z_0) [-1 + -1*v_y >= 0] Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_8,5) ;(eval_start_9,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_bb5_in,5) ;(eval_start_bb6_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4,5},4->{6,7},5->{13},6->{8},7->{12},8->{9,10},9->{11},10->{6,7},11->{9,10} ,12->{},13->{14},14->{15},15->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] | `- p:[6,10,8,11,9] c: [9,11] | `- p:[6,10,8] c: [6,8,10]) + Applied Processor: CloseWith True + Details: () YES