YES * Step 1: UnsatRules 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_bb1_in(v_m,v_n,0,0) True (?,1) 9. 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) [-1 + v_n >= v_x_0] (?,1) 10. 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 >= v_n] (?,1) 11. eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,v_x_0,1 + v_y_0) [-1 + v_m >= v_y_0 && -1 + v_m >= v_y_0] (?,1) 12. 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) [-1 + v_m >= v_y_0 && v_y_0 >= v_m] (?,1) 13. eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,v_x_0,v_y_0) [v_y_0 >= v_m && -1 + v_m >= v_y_0] (?,1) 14. 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,v_y_0) [v_y_0 >= v_m && v_y_0 >= v_m] (?,1) 15. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_stop(v_m,v_n,v_x_0,v_y_0) True (?,1) 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_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_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->{9,10},9->{11,12,13,14},10->{15},11->{9,10} ,12->{9,10},13->{9,10},14->{9,10},15->{}] + Applied Processor: UnsatRules + Details: Following transitions have unsatisfiable constraints and are removed: [12,13] * Step 2: FromIts 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_bb1_in(v_m,v_n,0,0) True (?,1) 9. 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) [-1 + v_n >= v_x_0] (?,1) 10. 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 >= v_n] (?,1) 11. eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,v_x_0,1 + v_y_0) [-1 + v_m >= v_y_0 && -1 + v_m >= v_y_0] (?,1) 14. 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,v_y_0) [v_y_0 >= v_m && v_y_0 >= v_m] (?,1) 15. eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_stop(v_m,v_n,v_x_0,v_y_0) True (?,1) 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_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_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->{9,10},9->{11,14},10->{15},11->{9,10},14->{9 ,10},15->{}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: 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 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 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 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 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 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 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 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 eval_start_6(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,0,0) True 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) [-1 + v_n >= v_x_0] 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 >= v_n] eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,v_x_0,1 + v_y_0) [-1 + v_m >= v_y_0 && -1 + v_m >= v_y_0] 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,v_y_0) [v_y_0 >= v_m && v_y_0 >= v_m] eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_stop(v_m,v_n,v_x_0,v_y_0) True 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_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11,14},10->{15},11->{9,10},14->{9 ,10},15->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,14,15] | `- p:[9,11,14] c: [11] | `- p:[9,14] c: [9,14] * Step 4: CloseWith YES + Considered Problem: (Rules: 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 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 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 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 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 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 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 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 eval_start_6(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,0,0) True 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) [-1 + v_n >= v_x_0] 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 >= v_n] eval_start_bb2_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_bb1_in(v_m,v_n,v_x_0,1 + v_y_0) [-1 + v_m >= v_y_0 && -1 + v_m >= v_y_0] 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,v_y_0) [v_y_0 >= v_m && v_y_0 >= v_m] eval_start_bb3_in(v_m,v_n,v_x_0,v_y_0) -> eval_start_stop(v_m,v_n,v_x_0,v_y_0) True 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_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8},8->{9,10},9->{11,14},10->{15},11->{9,10},14->{9 ,10},15->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,14,15] | `- p:[9,11,14] c: [11] | `- p:[9,14] c: [9,14]) + Applied Processor: CloseWith True + Details: () YES