YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. eval_start_start(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v__1,v__2,v_x,v_y) True (1,1) 1. eval_start_bb0_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_0(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) 2. eval_start_0(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_1(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) 3. eval_start_1(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_2(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) 4. eval_start_2(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_3(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) 5. eval_start_3(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_4(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) 6. eval_start_4(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v__1,v__2,v_x,v_y) True (?,1) 7. eval_start_bb1_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v__1,v__2,v_x,v_y) [-1 + v__0 >= 0] (?,1) 8. eval_start_bb1_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v__01,v__2,v_x,v_y) [0 >= v__0] (?,1) 9. eval_start_bb2_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,2 + v__01,v__1,v__2,v_x,v_y) True (?,1) 10. eval_start_bb3_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb4_in(v__0,v__01,v__1,v__2,v_x,v_y) [-1 + v__1 >= 0] (?,1) 11. eval_start_bb3_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb5_in(v__0,v__01,v__1,v__1,v_x,v_y) [0 >= v__1] (?,1) 12. eval_start_bb4_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,-1 + v__1,v__2,v_x,v_y) True (?,1) 13. eval_start_bb5_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb6_in(v__0,v__01,v__1,v__2,v_x,v_y) [-1 + v__2 >= 0] (?,1) 14. eval_start_bb5_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb7_in(v__0,v__01,v__1,v__2,v_x,v_y) [0 >= v__2] (?,1) 15. eval_start_bb6_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb5_in(v__0,v__01,v__1,-1 + v__2,v_x,v_y) True (?,1) 16. eval_start_bb7_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_stop(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) Signature: {(eval_start_0,6) ;(eval_start_1,6) ;(eval_start_2,6) ;(eval_start_3,6) ;(eval_start_4,6) ;(eval_start_bb0_in,6) ;(eval_start_bb1_in,6) ;(eval_start_bb2_in,6) ;(eval_start_bb3_in,6) ;(eval_start_bb4_in,6) ;(eval_start_bb5_in,6) ;(eval_start_bb6_in,6) ;(eval_start_bb7_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->{7,8},7->{9},8->{10,11},9->{7,8},10->{12},11->{13,14} ,12->{10,11},13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(11,13)] * Step 2: UnreachableRules YES + Considered Problem: Rules: 0. eval_start_start(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v__1,v__2,v_x,v_y) True (1,1) 1. eval_start_bb0_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_0(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) 2. eval_start_0(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_1(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) 3. eval_start_1(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_2(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) 4. eval_start_2(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_3(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) 5. eval_start_3(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_4(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) 6. eval_start_4(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v__1,v__2,v_x,v_y) True (?,1) 7. eval_start_bb1_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v__1,v__2,v_x,v_y) [-1 + v__0 >= 0] (?,1) 8. eval_start_bb1_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v__01,v__2,v_x,v_y) [0 >= v__0] (?,1) 9. eval_start_bb2_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,2 + v__01,v__1,v__2,v_x,v_y) True (?,1) 10. eval_start_bb3_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb4_in(v__0,v__01,v__1,v__2,v_x,v_y) [-1 + v__1 >= 0] (?,1) 11. eval_start_bb3_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb5_in(v__0,v__01,v__1,v__1,v_x,v_y) [0 >= v__1] (?,1) 12. eval_start_bb4_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,-1 + v__1,v__2,v_x,v_y) True (?,1) 13. eval_start_bb5_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb6_in(v__0,v__01,v__1,v__2,v_x,v_y) [-1 + v__2 >= 0] (?,1) 14. eval_start_bb5_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb7_in(v__0,v__01,v__1,v__2,v_x,v_y) [0 >= v__2] (?,1) 15. eval_start_bb6_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb5_in(v__0,v__01,v__1,-1 + v__2,v_x,v_y) True (?,1) 16. eval_start_bb7_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_stop(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) Signature: {(eval_start_0,6) ;(eval_start_1,6) ;(eval_start_2,6) ;(eval_start_3,6) ;(eval_start_4,6) ;(eval_start_bb0_in,6) ;(eval_start_bb1_in,6) ;(eval_start_bb2_in,6) ;(eval_start_bb3_in,6) ;(eval_start_bb4_in,6) ;(eval_start_bb5_in,6) ;(eval_start_bb6_in,6) ;(eval_start_bb7_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->{7,8},7->{9},8->{10,11},9->{7,8},10->{12},11->{14},12->{10 ,11},13->{15},14->{16},15->{13,14},16->{}] + Applied Processor: UnreachableRules + Details: Following transitions are not reachable from the starting states and are revomed: [13,15] * Step 3: FromIts YES + Considered Problem: Rules: 0. eval_start_start(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v__1,v__2,v_x,v_y) True (1,1) 1. eval_start_bb0_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_0(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) 2. eval_start_0(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_1(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) 3. eval_start_1(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_2(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) 4. eval_start_2(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_3(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) 5. eval_start_3(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_4(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) 6. eval_start_4(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v__1,v__2,v_x,v_y) True (?,1) 7. eval_start_bb1_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v__1,v__2,v_x,v_y) [-1 + v__0 >= 0] (?,1) 8. eval_start_bb1_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v__01,v__2,v_x,v_y) [0 >= v__0] (?,1) 9. eval_start_bb2_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,2 + v__01,v__1,v__2,v_x,v_y) True (?,1) 10. eval_start_bb3_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb4_in(v__0,v__01,v__1,v__2,v_x,v_y) [-1 + v__1 >= 0] (?,1) 11. eval_start_bb3_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb5_in(v__0,v__01,v__1,v__1,v_x,v_y) [0 >= v__1] (?,1) 12. eval_start_bb4_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,-1 + v__1,v__2,v_x,v_y) True (?,1) 14. eval_start_bb5_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb7_in(v__0,v__01,v__1,v__2,v_x,v_y) [0 >= v__2] (?,1) 16. eval_start_bb7_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_stop(v__0,v__01,v__1,v__2,v_x,v_y) True (?,1) Signature: {(eval_start_0,6) ;(eval_start_1,6) ;(eval_start_2,6) ;(eval_start_3,6) ;(eval_start_4,6) ;(eval_start_bb0_in,6) ;(eval_start_bb1_in,6) ;(eval_start_bb2_in,6) ;(eval_start_bb3_in,6) ;(eval_start_bb4_in,6) ;(eval_start_bb5_in,6) ;(eval_start_bb6_in,6) ;(eval_start_bb7_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->{7,8},7->{9},8->{10,11},9->{7,8},10->{12},11->{14},12->{10 ,11},14->{16},16->{}] + Applied Processor: FromIts + Details: () * Step 4: Decompose YES + Considered Problem: Rules: eval_start_start(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v__1,v__2,v_x ,v_y) True eval_start_bb0_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_0(v__0,v__01,v__1,v__2,v_x ,v_y) True eval_start_0(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_1(v__0,v__01,v__1,v__2,v_x ,v_y) True eval_start_1(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_2(v__0,v__01,v__1,v__2,v_x ,v_y) True eval_start_2(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_3(v__0,v__01,v__1,v__2,v_x ,v_y) True eval_start_3(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_4(v__0,v__01,v__1,v__2,v_x ,v_y) True eval_start_4(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v__1,v__2,v_x ,v_y) True eval_start_bb1_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v__1,v__2,v_x ,v_y) [-1 + v__0 >= 0] eval_start_bb1_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v__01,v__2,v_x ,v_y) [0 >= v__0] eval_start_bb2_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,2 + v__01,v__1,v__2,v_x ,v_y) True eval_start_bb3_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb4_in(v__0,v__01,v__1,v__2,v_x ,v_y) [-1 + v__1 >= 0] eval_start_bb3_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb5_in(v__0,v__01,v__1,v__1,v_x ,v_y) [0 >= v__1] eval_start_bb4_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,-1 + v__1,v__2,v_x ,v_y) True eval_start_bb5_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb7_in(v__0,v__01,v__1,v__2,v_x ,v_y) [0 >= v__2] eval_start_bb7_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_stop(v__0,v__01,v__1,v__2,v_x ,v_y) True Signature: {(eval_start_0,6) ;(eval_start_1,6) ;(eval_start_2,6) ;(eval_start_3,6) ;(eval_start_4,6) ;(eval_start_bb0_in,6) ;(eval_start_bb1_in,6) ;(eval_start_bb2_in,6) ;(eval_start_bb3_in,6) ;(eval_start_bb4_in,6) ;(eval_start_bb5_in,6) ;(eval_start_bb6_in,6) ;(eval_start_bb7_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->{7,8},7->{9},8->{10,11},9->{7,8},10->{12},11->{14},12->{10 ,11},14->{16},16->{}] + Applied Processor: Decompose NoGreedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,14,16] | +- p:[7,9] c: [7,9] | `- p:[10,12] c: [10,12] * Step 5: CloseWith YES + Considered Problem: (Rules: eval_start_start(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb0_in(v__0,v__01,v__1,v__2,v_x ,v_y) True eval_start_bb0_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_0(v__0,v__01,v__1,v__2,v_x ,v_y) True eval_start_0(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_1(v__0,v__01,v__1,v__2,v_x ,v_y) True eval_start_1(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_2(v__0,v__01,v__1,v__2,v_x ,v_y) True eval_start_2(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_3(v__0,v__01,v__1,v__2,v_x ,v_y) True eval_start_3(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_4(v__0,v__01,v__1,v__2,v_x ,v_y) True eval_start_4(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb1_in(v_x,v_y,v__1,v__2,v_x ,v_y) True eval_start_bb1_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb2_in(v__0,v__01,v__1,v__2,v_x ,v_y) [-1 + v__0 >= 0] eval_start_bb1_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,v__01,v__2,v_x ,v_y) [0 >= v__0] eval_start_bb2_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb1_in(-1 + v__0,2 + v__01,v__1,v__2,v_x ,v_y) True eval_start_bb3_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb4_in(v__0,v__01,v__1,v__2,v_x ,v_y) [-1 + v__1 >= 0] eval_start_bb3_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb5_in(v__0,v__01,v__1,v__1,v_x ,v_y) [0 >= v__1] eval_start_bb4_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb3_in(v__0,v__01,-1 + v__1,v__2,v_x ,v_y) True eval_start_bb5_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_bb7_in(v__0,v__01,v__1,v__2,v_x ,v_y) [0 >= v__2] eval_start_bb7_in(v__0,v__01,v__1,v__2,v_x,v_y) -> eval_start_stop(v__0,v__01,v__1,v__2,v_x ,v_y) True Signature: {(eval_start_0,6) ;(eval_start_1,6) ;(eval_start_2,6) ;(eval_start_3,6) ;(eval_start_4,6) ;(eval_start_bb0_in,6) ;(eval_start_bb1_in,6) ;(eval_start_bb2_in,6) ;(eval_start_bb3_in,6) ;(eval_start_bb4_in,6) ;(eval_start_bb5_in,6) ;(eval_start_bb6_in,6) ;(eval_start_bb7_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->{7,8},7->{9},8->{10,11},9->{7,8},10->{12},11->{14},12->{10 ,11},14->{16},16->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,14,16] | +- p:[7,9] c: [7,9] | `- p:[10,12] c: [10,12]) + Applied Processor: CloseWith True + Details: () YES