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