YES * Step 1: FromIts YES + Considered Problem: Rules: 0. eval_abc_start(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb0_in(v_3,v_i_0,v_j_0,v_m,v_n) True (1,1) 1. eval_abc_bb0_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_0(v_3,v_i_0,v_j_0,v_m,v_n) True (?,1) 2. eval_abc_0(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_1(v_3,v_i_0,v_j_0,v_m,v_n) True (?,1) 3. eval_abc_1(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_2(v_3,v_i_0,v_j_0,v_m,v_n) True (?,1) 4. eval_abc_2(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_3(v_3,v_i_0,v_j_0,v_m,v_n) True (?,1) 5. eval_abc_3(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_4(v_3,v_i_0,v_j_0,v_m,v_n) True (?,1) 6. eval_abc_4(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_5(v_3,v_i_0,v_j_0,v_m,v_n) True (?,1) 7. eval_abc_5(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb1_in(v_3,v_i_0,1,v_m,v_n) True (?,1) 8. eval_abc_bb1_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb2_in(v_3,1,v_j_0,v_m,v_n) [-1 + v_j_0 >= 0 && v_n >= v_j_0] (?,1) 9. eval_abc_bb1_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb5_in(v_3,v_i_0,v_j_0,v_m,v_n) [-1 + v_j_0 >= 0 && -1 + v_j_0 >= v_n] (?,1) 10. eval_abc_bb2_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb3_in(v_3,v_i_0,v_j_0,v_m,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && v_m >= v_i_0] 11. eval_abc_bb2_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb4_in(v_3,v_i_0,v_j_0,v_m,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && -1 + v_i_0 >= v_m] 12. eval_abc_bb3_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb2_in(v_3,1 + v_i_0,v_j_0,v_m,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -2 + v_j_0 + v_m >= 0 && -2 + v_i_0 + v_m >= 0 && -1*v_i_0 + v_m >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] 13. eval_abc_bb4_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_9(1 + v_j_0,v_i_0,v_j_0,v_m,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_i_0 + -1*v_m >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] 14. eval_abc_9(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_10(v_3,v_i_0,v_j_0,v_m,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -3 + v_3 + v_n >= 0 && 1 + -1*v_3 + v_n >= 0 && -1 + v_i_0 + -1*v_m >= 0 && -1 + v_3 + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -3 + v_3 + v_j_0 >= 0 && 1 + -1*v_3 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && -3 + v_3 + v_i_0 >= 0 && -2 + v_3 >= 0] 15. eval_abc_10(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb1_in(v_3,v_i_0,v_3,v_m,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -3 + v_3 + v_n >= 0 && 1 + -1*v_3 + v_n >= 0 && -1 + v_i_0 + -1*v_m >= 0 && -1 + v_3 + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -3 + v_3 + v_j_0 >= 0 && 1 + -1*v_3 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && -3 + v_3 + v_i_0 >= 0 && -2 + v_3 >= 0] 16. eval_abc_bb5_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_stop(v_3,v_i_0,v_j_0,v_m,v_n) [-1 + v_j_0 + -1*v_n >= 0 && -1 + v_j_0 >= 0] (?,1) Signature: {(eval_abc_0,5) ;(eval_abc_1,5) ;(eval_abc_10,5) ;(eval_abc_2,5) ;(eval_abc_3,5) ;(eval_abc_4,5) ;(eval_abc_5,5) ;(eval_abc_9,5) ;(eval_abc_bb0_in,5) ;(eval_abc_bb1_in,5) ;(eval_abc_bb2_in,5) ;(eval_abc_bb3_in,5) ;(eval_abc_bb4_in,5) ;(eval_abc_bb5_in,5) ;(eval_abc_start,5) ;(eval_abc_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9},8->{10,11},9->{16},10->{12},11->{13},12->{10 ,11},13->{14},14->{15},15->{8,9},16->{}] + Applied Processor: FromIts + Details: () * Step 2: Decompose YES + Considered Problem: Rules: eval_abc_start(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb0_in(v_3,v_i_0,v_j_0,v_m,v_n) True eval_abc_bb0_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_0(v_3,v_i_0,v_j_0,v_m,v_n) True eval_abc_0(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_1(v_3,v_i_0,v_j_0,v_m,v_n) True eval_abc_1(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_2(v_3,v_i_0,v_j_0,v_m,v_n) True eval_abc_2(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_3(v_3,v_i_0,v_j_0,v_m,v_n) True eval_abc_3(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_4(v_3,v_i_0,v_j_0,v_m,v_n) True eval_abc_4(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_5(v_3,v_i_0,v_j_0,v_m,v_n) True eval_abc_5(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb1_in(v_3,v_i_0,1,v_m,v_n) True eval_abc_bb1_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb2_in(v_3,1,v_j_0,v_m,v_n) [-1 + v_j_0 >= 0 && v_n >= v_j_0] eval_abc_bb1_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb5_in(v_3,v_i_0,v_j_0,v_m,v_n) [-1 + v_j_0 >= 0 && -1 + v_j_0 >= v_n] eval_abc_bb2_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb3_in(v_3,v_i_0,v_j_0,v_m,v_n) [-1 + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && v_m >= v_i_0] eval_abc_bb2_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb4_in(v_3,v_i_0,v_j_0,v_m,v_n) [-1 + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && -1 + v_i_0 >= v_m] eval_abc_bb3_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb2_in(v_3,1 + v_i_0,v_j_0,v_m,v_n) [-1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -2 + v_j_0 + v_m >= 0 && -2 + v_i_0 + v_m >= 0 && -1*v_i_0 + v_m >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] eval_abc_bb4_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_9(1 + v_j_0,v_i_0,v_j_0,v_m,v_n) [-1 + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_i_0 + -1*v_m >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] eval_abc_9(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_10(v_3,v_i_0,v_j_0,v_m,v_n) [-1 + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -3 + v_3 + v_n >= 0 && 1 + -1*v_3 + v_n >= 0 && -1 + v_i_0 + -1*v_m >= 0 && -1 + v_3 + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -3 + v_3 + v_j_0 >= 0 && 1 + -1*v_3 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && -3 + v_3 + v_i_0 >= 0 && -2 + v_3 >= 0] eval_abc_10(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb1_in(v_3,v_i_0,v_3,v_m,v_n) [-1 + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -3 + v_3 + v_n >= 0 && 1 + -1*v_3 + v_n >= 0 && -1 + v_i_0 + -1*v_m >= 0 && -1 + v_3 + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -3 + v_3 + v_j_0 >= 0 && 1 + -1*v_3 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && -3 + v_3 + v_i_0 >= 0 && -2 + v_3 >= 0] eval_abc_bb5_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_stop(v_3,v_i_0,v_j_0,v_m,v_n) [-1 + v_j_0 + -1*v_n >= 0 && -1 + v_j_0 >= 0] Signature: {(eval_abc_0,5) ;(eval_abc_1,5) ;(eval_abc_10,5) ;(eval_abc_2,5) ;(eval_abc_3,5) ;(eval_abc_4,5) ;(eval_abc_5,5) ;(eval_abc_9,5) ;(eval_abc_bb0_in,5) ;(eval_abc_bb1_in,5) ;(eval_abc_bb2_in,5) ;(eval_abc_bb3_in,5) ;(eval_abc_bb4_in,5) ;(eval_abc_bb5_in,5) ;(eval_abc_start,5) ;(eval_abc_stop,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9},8->{10,11},9->{16},10->{12},11->{13},12->{10 ,11},13->{14},14->{15},15->{8,9},16->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] | `- p:[8,15,14,13,11,12,10] c: [8,11,13,14,15] | `- p:[10,12] c: [10,12] * Step 3: CloseWith YES + Considered Problem: (Rules: eval_abc_start(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb0_in(v_3,v_i_0,v_j_0,v_m,v_n) True eval_abc_bb0_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_0(v_3,v_i_0,v_j_0,v_m,v_n) True eval_abc_0(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_1(v_3,v_i_0,v_j_0,v_m,v_n) True eval_abc_1(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_2(v_3,v_i_0,v_j_0,v_m,v_n) True eval_abc_2(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_3(v_3,v_i_0,v_j_0,v_m,v_n) True eval_abc_3(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_4(v_3,v_i_0,v_j_0,v_m,v_n) True eval_abc_4(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_5(v_3,v_i_0,v_j_0,v_m,v_n) True eval_abc_5(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb1_in(v_3,v_i_0,1,v_m,v_n) True eval_abc_bb1_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb2_in(v_3,1,v_j_0,v_m,v_n) [-1 + v_j_0 >= 0 && v_n >= v_j_0] eval_abc_bb1_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb5_in(v_3,v_i_0,v_j_0,v_m,v_n) [-1 + v_j_0 >= 0 && -1 + v_j_0 >= v_n] eval_abc_bb2_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb3_in(v_3,v_i_0,v_j_0,v_m,v_n) [-1 + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && v_m >= v_i_0] eval_abc_bb2_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb4_in(v_3,v_i_0,v_j_0,v_m,v_n) [-1 + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && -1 + v_i_0 >= v_m] eval_abc_bb3_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb2_in(v_3,1 + v_i_0,v_j_0,v_m,v_n) [-1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_m >= 0 && -2 + v_j_0 + v_m >= 0 && -2 + v_i_0 + v_m >= 0 && -1*v_i_0 + v_m >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] eval_abc_bb4_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_9(1 + v_j_0,v_i_0,v_j_0,v_m,v_n) [-1 + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1 + v_i_0 + -1*v_m >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] eval_abc_9(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_10(v_3,v_i_0,v_j_0,v_m,v_n) [-1 + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -3 + v_3 + v_n >= 0 && 1 + -1*v_3 + v_n >= 0 && -1 + v_i_0 + -1*v_m >= 0 && -1 + v_3 + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -3 + v_3 + v_j_0 >= 0 && 1 + -1*v_3 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && -3 + v_3 + v_i_0 >= 0 && -2 + v_3 >= 0] eval_abc_10(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_bb1_in(v_3,v_i_0,v_3,v_m,v_n) [-1 + v_n >= 0 && -2 + v_j_0 + v_n >= 0 && -1*v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -3 + v_3 + v_n >= 0 && 1 + -1*v_3 + v_n >= 0 && -1 + v_i_0 + -1*v_m >= 0 && -1 + v_3 + -1*v_j_0 >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -3 + v_3 + v_j_0 >= 0 && 1 + -1*v_3 + v_j_0 >= 0 && -1 + v_i_0 >= 0 && -3 + v_3 + v_i_0 >= 0 && -2 + v_3 >= 0] eval_abc_bb5_in(v_3,v_i_0,v_j_0,v_m,v_n) -> eval_abc_stop(v_3,v_i_0,v_j_0,v_m,v_n) [-1 + v_j_0 + -1*v_n >= 0 && -1 + v_j_0 >= 0] Signature: {(eval_abc_0,5) ;(eval_abc_1,5) ;(eval_abc_10,5) ;(eval_abc_2,5) ;(eval_abc_3,5) ;(eval_abc_4,5) ;(eval_abc_5,5) ;(eval_abc_9,5) ;(eval_abc_bb0_in,5) ;(eval_abc_bb1_in,5) ;(eval_abc_bb2_in,5) ;(eval_abc_bb3_in,5) ;(eval_abc_bb4_in,5) ;(eval_abc_bb5_in,5) ;(eval_abc_start,5) ;(eval_abc_stop,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7},7->{8,9},8->{10,11},9->{16},10->{12},11->{13},12->{10 ,11},13->{14},14->{15},15->{8,9},16->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] | `- p:[8,15,14,13,11,12,10] c: [8,11,13,14,15] | `- p:[10,12] c: [10,12]) + Applied Processor: CloseWith True + Details: () YES