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