YES * Step 1: FromIts YES + Considered Problem: Rules: 0. eval_start_start(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) True (1,1) 1. eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_0(v__0,v__01,v_1,v_x,v_y) True (?,1) 2. eval_start_0(v__0,v__01,v_1,v_x,v_y) -> eval_start_1(v__0,v__01,v_1,v_x,v_y) True (?,1) 3. eval_start_1(v__0,v__01,v_1,v_x,v_y) -> eval_start_2(v__0,v__01,v_1,v_x,v_y) True (?,1) 4. eval_start_2(v__0,v__01,v_1,v_x,v_y) -> eval_start_3(v__0,v__01,v_1,v_x,v_y) True (?,1) 5. eval_start_3(v__0,v__01,v_1,v_x,v_y) -> eval_start_4(v__0,v__01,v_1,v_x,v_y) True (?,1) 6. eval_start_4(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v_1,v_x,v_y) True (?,1) 7. eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v__01] (?,1) 8. eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && v__01 >= v__0] (?,1) 9. eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_5(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] 10. eval_start_5(v__0,v__01,v_1,v_x,v_y) -> eval_start_6(v__0,v__01,nondef_0,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] 11. eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v__0,1 + v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] 12. eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 (?,1) && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && 0 >= v_1] 13. eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_stop(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1*v__0 + v__01 >= 0] (?,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_4,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{13},9->{10},10->{11,12},11->{7,8},12->{7,8} ,13->{}] + Applied Processor: FromIts + Details: () * Step 2: Decompose YES + Considered Problem: Rules: eval_start_start(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) True eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_0(v__0,v__01,v_1,v_x,v_y) True eval_start_0(v__0,v__01,v_1,v_x,v_y) -> eval_start_1(v__0,v__01,v_1,v_x,v_y) True eval_start_1(v__0,v__01,v_1,v_x,v_y) -> eval_start_2(v__0,v__01,v_1,v_x,v_y) True eval_start_2(v__0,v__01,v_1,v_x,v_y) -> eval_start_3(v__0,v__01,v_1,v_x,v_y) True eval_start_3(v__0,v__01,v_1,v_x,v_y) -> eval_start_4(v__0,v__01,v_1,v_x,v_y) True eval_start_4(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v_1,v_x,v_y) True eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v__01] eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && v__01 >= v__0] eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_5(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] eval_start_5(v__0,v__01,v_1,v_x,v_y) -> eval_start_6(v__0,v__01,nondef_0,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v__0,1 + v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && 0 >= v_1] eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_stop(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1*v__0 + v__01 >= 0] Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_4,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{13},9->{10},10->{11,12},11->{7,8},12->{7,8} ,13->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[7,11,10,9,12] c: [12] | `- p:[7,11,10,9] c: [7,9,10,11] * Step 3: CloseWith YES + Considered Problem: (Rules: eval_start_start(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) True eval_start_bb0_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_0(v__0,v__01,v_1,v_x,v_y) True eval_start_0(v__0,v__01,v_1,v_x,v_y) -> eval_start_1(v__0,v__01,v_1,v_x,v_y) True eval_start_1(v__0,v__01,v_1,v_x,v_y) -> eval_start_2(v__0,v__01,v_1,v_x,v_y) True eval_start_2(v__0,v__01,v_1,v_x,v_y) -> eval_start_3(v__0,v__01,v_1,v_x,v_y) True eval_start_3(v__0,v__01,v_1,v_x,v_y) -> eval_start_4(v__0,v__01,v_1,v_x,v_y) True eval_start_4(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v_1,v_x,v_y) True eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 >= v__01] eval_start_bb1_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && v__01 >= v__0] eval_start_bb2_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_5(v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] eval_start_5(v__0,v__01,v_1,v_x,v_y) -> eval_start_6(v__0,v__01,nondef_0,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0] eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(v__0,1 + v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && -1 + v_1 >= 0] eval_start_6(v__0,v__01,v_1,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,v__01,v_1,v_x,v_y) [-1 + v_x + -1*v_y >= 0 && v__01 + -1*v_y >= 0 && -1 + v__0 + -1*v_y >= 0 && -1 + -1*v__01 + v_x >= 0 && -1*v__0 + v_x >= 0 && -1 + v__0 + -1*v__01 >= 0 && 0 >= v_1] eval_start_bb3_in(v__0,v__01,v_1,v_x,v_y) -> eval_start_stop(v__0,v__01,v_1,v_x,v_y) [v__01 + -1*v_y >= 0 && -1*v__0 + v_x >= 0 && -1*v__0 + v__01 >= 0] Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_4,5) ;(eval_start_5,5) ;(eval_start_6,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{13},9->{10},10->{11,12},11->{7,8},12->{7,8} ,13->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13] | `- p:[7,11,10,9,12] c: [12] | `- p:[7,11,10,9] c: [7,9,10,11]) + Applied Processor: CloseWith True + Details: () YES