YES * Step 1: UnsatPaths YES + Considered Problem: Rules: 0. eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 1. eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 2. eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 3. eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 4. eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 5. eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,0,v_x_0_sink) True (?,1) 6. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0) [-1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= v_n] (?,1) 8. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0,v_x_0_sink) [-1 + v_n >= 1 + v_x_0_sink] (?,1) 9. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink,v_x_0_sink) [1 + v_x_0_sink >= v_n] (?,1) 10. eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 11. eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_7(v_1,nondef_0,v_n,v_x_0,v_x_0_sink) True (?,1) 12. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,v_1,v_x_0_sink) [-1 + v_3 >= 0] (?,1) 13. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_1) [0 >= v_3] (?,1) 14. eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_stop(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_6,5) ;(eval_start_7,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10},9->{6,7},10->{11},11->{12,13},12->{6 ,7},13->{8,9},14->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(9,6)] * Step 2: FromIts YES + Considered Problem: Rules: 0. eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (1,1) 1. eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 2. eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 3. eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 4. eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 5. eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,0,v_x_0_sink) True (?,1) 6. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0) [-1 + v_n >= v_x_0] (?,1) 7. eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) [v_x_0 >= v_n] (?,1) 8. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0,v_x_0_sink) [-1 + v_n >= 1 + v_x_0_sink] (?,1) 9. eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink,v_x_0_sink) [1 + v_x_0_sink >= v_n] (?,1) 10. eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) 11. eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_7(v_1,nondef_0,v_n,v_x_0,v_x_0_sink) True (?,1) 12. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,v_1,v_x_0_sink) [-1 + v_3 >= 0] (?,1) 13. eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_1) [0 >= v_3] (?,1) 14. eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_stop(v_1,v_3,v_n,v_x_0,v_x_0_sink) True (?,1) Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_6,5) ;(eval_start_7,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10},9->{7},10->{11},11->{12,13},12->{6 ,7},13->{8,9},14->{}] + Applied Processor: FromIts + Details: () * Step 3: Decompose YES + Considered Problem: Rules: eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb0_in(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_0(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_1(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_2(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_3(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,0 ,v_x_0_sink) True eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0 ,v_x_0) [-1 + v_n >= v_x_0] eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb4_in(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) [v_x_0 >= v_n] eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0 ,v_x_0_sink) [-1 + v_n >= 1 + v_x_0_sink] eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink ,v_x_0_sink) [1 + v_x_0_sink >= v_n] eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_6(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_7(v_1,nondef_0,v_n,v_x_0 ,v_x_0_sink) True eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,v_1 ,v_x_0_sink) [-1 + v_3 >= 0] eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0 ,v_1) [0 >= v_3] eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_stop(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_6,5) ;(eval_start_7,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10},9->{7},10->{11},11->{12,13},12->{6 ,7},13->{8,9},14->{}] + 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] | `- p:[6,12,11,10,8,13] c: [6,12] | `- p:[8,13,11,10] c: [8,10,11,13] * Step 4: CloseWith YES + Considered Problem: (Rules: eval_start_start(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb0_in(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_bb0_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_0(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_0(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_1(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_1(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_2(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_2(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_3(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_3(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,0 ,v_x_0_sink) True eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0 ,v_x_0) [-1 + v_n >= v_x_0] eval_start_bb1_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb4_in(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) [v_x_0 >= v_n] eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb3_in(1 + v_x_0_sink,v_3,v_n,v_x_0 ,v_x_0_sink) [-1 + v_n >= 1 + v_x_0_sink] eval_start_bb2_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,1 + v_x_0_sink ,v_x_0_sink) [1 + v_x_0_sink >= v_n] eval_start_bb3_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_6(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True eval_start_6(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_7(v_1,nondef_0,v_n,v_x_0 ,v_x_0_sink) True eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb1_in(v_1,v_3,v_n,v_1 ,v_x_0_sink) [-1 + v_3 >= 0] eval_start_7(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_bb2_in(v_1,v_3,v_n,v_x_0 ,v_1) [0 >= v_3] eval_start_bb4_in(v_1,v_3,v_n,v_x_0,v_x_0_sink) -> eval_start_stop(v_1,v_3,v_n,v_x_0 ,v_x_0_sink) True Signature: {(eval_start_0,5) ;(eval_start_1,5) ;(eval_start_2,5) ;(eval_start_3,5) ;(eval_start_6,5) ;(eval_start_7,5) ;(eval_start_bb0_in,5) ;(eval_start_bb1_in,5) ;(eval_start_bb2_in,5) ;(eval_start_bb3_in,5) ;(eval_start_bb4_in,5) ;(eval_start_start,5) ;(eval_start_stop,5)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10},9->{7},10->{11},11->{12,13},12->{6 ,7},13->{8,9},14->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14] | `- p:[6,12,11,10,8,13] c: [6,12] | `- p:[8,13,11,10] c: [8,10,11,13]) + Applied Processor: CloseWith True + Details: () YES