YES * Step 1: TrivialSCCs YES + Considered Problem: Rules: 0. eval_abc_start(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb0_in(v_3,v_i_0,v_j_0,v_n) True (1,1) 1. eval_abc_bb0_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_0(v_3,v_i_0,v_j_0,v_n) True (?,1) 2. eval_abc_0(v_3,v_i_0,v_j_0,v_n) -> eval_abc_1(v_3,v_i_0,v_j_0,v_n) True (?,1) 3. eval_abc_1(v_3,v_i_0,v_j_0,v_n) -> eval_abc_2(v_3,v_i_0,v_j_0,v_n) True (?,1) 4. eval_abc_2(v_3,v_i_0,v_j_0,v_n) -> eval_abc_3(v_3,v_i_0,v_j_0,v_n) True (?,1) 5. eval_abc_3(v_3,v_i_0,v_j_0,v_n) -> eval_abc_4(v_3,v_i_0,v_j_0,v_n) True (?,1) 6. eval_abc_4(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb1_in(v_3,1,v_j_0,v_n) True (?,1) 7. eval_abc_bb1_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb2_in(v_3,v_i_0,1,v_n) [-1 + v_i_0 >= 0 && v_n >= v_i_0] (?,1) 8. eval_abc_bb1_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb5_in(v_3,v_i_0,v_j_0,v_n) [-1 + v_i_0 >= 0 && -1 + v_i_0 >= v_n] (?,1) 9. eval_abc_bb2_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb3_in(v_3,v_i_0,v_j_0,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*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_n >= v_j_0] 10. eval_abc_bb2_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb4_in(v_3,v_i_0,v_j_0,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*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_j_0 >= v_n] 11. eval_abc_bb3_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb2_in(v_3,v_i_0,1 + v_j_0,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 + v_n >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] 12. eval_abc_bb4_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_8(1 + v_i_0,v_i_0,v_j_0,v_n) [-1 + v_j_0 + -1*v_n >= 0 (?,1) && -1 + v_n >= 0 && -3 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -2 + v_j_0 >= 0 && -3 + v_i_0 + v_j_0 >= 0 && -1 + -1*v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] 13. eval_abc_8(v_3,v_i_0,v_j_0,v_n) -> eval_abc_9(v_3,v_i_0,v_j_0,v_n) [-1 + v_j_0 + -1*v_n >= 0 (?,1) && -1 + v_n >= 0 && -3 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -3 + v_3 + v_n >= 0 && 1 + -1*v_3 + v_n >= 0 && -2 + v_j_0 >= 0 && -3 + v_i_0 + v_j_0 >= 0 && -1 + -1*v_i_0 + v_j_0 >= 0 && -4 + v_3 + v_j_0 >= 0 && -1*v_3 + v_j_0 >= 0 && -1 + v_3 + -1*v_i_0 >= 0 && -1 + v_i_0 >= 0 && -3 + v_3 + v_i_0 >= 0 && 1 + -1*v_3 + v_i_0 >= 0 && -2 + v_3 >= 0] 14. eval_abc_9(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb1_in(v_3,v_3,v_j_0,v_n) [-1 + v_j_0 + -1*v_n >= 0 (?,1) && -1 + v_n >= 0 && -3 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -3 + v_3 + v_n >= 0 && 1 + -1*v_3 + v_n >= 0 && -2 + v_j_0 >= 0 && -3 + v_i_0 + v_j_0 >= 0 && -1 + -1*v_i_0 + v_j_0 >= 0 && -4 + v_3 + v_j_0 >= 0 && -1*v_3 + v_j_0 >= 0 && -1 + v_3 + -1*v_i_0 >= 0 && -1 + v_i_0 >= 0 && -3 + v_3 + v_i_0 >= 0 && 1 + -1*v_3 + v_i_0 >= 0 && -2 + v_3 >= 0] 15. eval_abc_bb5_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_stop(v_3,v_i_0,v_j_0,v_n) [-1 + v_i_0 + -1*v_n >= 0 && -1 + v_i_0 >= 0] (?,1) Signature: {(eval_abc_0,4) ;(eval_abc_1,4) ;(eval_abc_2,4) ;(eval_abc_3,4) ;(eval_abc_4,4) ;(eval_abc_8,4) ;(eval_abc_9,4) ;(eval_abc_bb0_in,4) ;(eval_abc_bb1_in,4) ;(eval_abc_bb2_in,4) ;(eval_abc_bb3_in,4) ;(eval_abc_bb4_in,4) ;(eval_abc_bb5_in,4) ;(eval_abc_start,4) ;(eval_abc_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9,10},8->{15},9->{11},10->{12},11->{9,10},12->{13} ,13->{14},14->{7,8},15->{}] + Applied Processor: TrivialSCCs + Details: All trivial SCCs of the transition graph admit timebound 1. * Step 2: UnsatPaths YES + Considered Problem: Rules: 0. eval_abc_start(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb0_in(v_3,v_i_0,v_j_0,v_n) True (1,1) 1. eval_abc_bb0_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_0(v_3,v_i_0,v_j_0,v_n) True (1,1) 2. eval_abc_0(v_3,v_i_0,v_j_0,v_n) -> eval_abc_1(v_3,v_i_0,v_j_0,v_n) True (1,1) 3. eval_abc_1(v_3,v_i_0,v_j_0,v_n) -> eval_abc_2(v_3,v_i_0,v_j_0,v_n) True (1,1) 4. eval_abc_2(v_3,v_i_0,v_j_0,v_n) -> eval_abc_3(v_3,v_i_0,v_j_0,v_n) True (1,1) 5. eval_abc_3(v_3,v_i_0,v_j_0,v_n) -> eval_abc_4(v_3,v_i_0,v_j_0,v_n) True (1,1) 6. eval_abc_4(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb1_in(v_3,1,v_j_0,v_n) True (1,1) 7. eval_abc_bb1_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb2_in(v_3,v_i_0,1,v_n) [-1 + v_i_0 >= 0 && v_n >= v_i_0] (?,1) 8. eval_abc_bb1_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb5_in(v_3,v_i_0,v_j_0,v_n) [-1 + v_i_0 >= 0 && -1 + v_i_0 >= v_n] (1,1) 9. eval_abc_bb2_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb3_in(v_3,v_i_0,v_j_0,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*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_n >= v_j_0] 10. eval_abc_bb2_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb4_in(v_3,v_i_0,v_j_0,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*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_j_0 >= v_n] 11. eval_abc_bb3_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb2_in(v_3,v_i_0,1 + v_j_0,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 + v_n >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] 12. eval_abc_bb4_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_8(1 + v_i_0,v_i_0,v_j_0,v_n) [-1 + v_j_0 + -1*v_n >= 0 (?,1) && -1 + v_n >= 0 && -3 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -2 + v_j_0 >= 0 && -3 + v_i_0 + v_j_0 >= 0 && -1 + -1*v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] 13. eval_abc_8(v_3,v_i_0,v_j_0,v_n) -> eval_abc_9(v_3,v_i_0,v_j_0,v_n) [-1 + v_j_0 + -1*v_n >= 0 (?,1) && -1 + v_n >= 0 && -3 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -3 + v_3 + v_n >= 0 && 1 + -1*v_3 + v_n >= 0 && -2 + v_j_0 >= 0 && -3 + v_i_0 + v_j_0 >= 0 && -1 + -1*v_i_0 + v_j_0 >= 0 && -4 + v_3 + v_j_0 >= 0 && -1*v_3 + v_j_0 >= 0 && -1 + v_3 + -1*v_i_0 >= 0 && -1 + v_i_0 >= 0 && -3 + v_3 + v_i_0 >= 0 && 1 + -1*v_3 + v_i_0 >= 0 && -2 + v_3 >= 0] 14. eval_abc_9(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb1_in(v_3,v_3,v_j_0,v_n) [-1 + v_j_0 + -1*v_n >= 0 (?,1) && -1 + v_n >= 0 && -3 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -3 + v_3 + v_n >= 0 && 1 + -1*v_3 + v_n >= 0 && -2 + v_j_0 >= 0 && -3 + v_i_0 + v_j_0 >= 0 && -1 + -1*v_i_0 + v_j_0 >= 0 && -4 + v_3 + v_j_0 >= 0 && -1*v_3 + v_j_0 >= 0 && -1 + v_3 + -1*v_i_0 >= 0 && -1 + v_i_0 >= 0 && -3 + v_3 + v_i_0 >= 0 && 1 + -1*v_3 + v_i_0 >= 0 && -2 + v_3 >= 0] 15. eval_abc_bb5_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_stop(v_3,v_i_0,v_j_0,v_n) [-1 + v_i_0 + -1*v_n >= 0 && -1 + v_i_0 >= 0] (1,1) Signature: {(eval_abc_0,4) ;(eval_abc_1,4) ;(eval_abc_2,4) ;(eval_abc_3,4) ;(eval_abc_4,4) ;(eval_abc_8,4) ;(eval_abc_9,4) ;(eval_abc_bb0_in,4) ;(eval_abc_bb1_in,4) ;(eval_abc_bb2_in,4) ;(eval_abc_bb3_in,4) ;(eval_abc_bb4_in,4) ;(eval_abc_bb5_in,4) ;(eval_abc_start,4) ;(eval_abc_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9,10},8->{15},9->{11},10->{12},11->{9,10},12->{13} ,13->{14},14->{7,8},15->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(7,10)] * Step 3: Looptree YES + Considered Problem: Rules: 0. eval_abc_start(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb0_in(v_3,v_i_0,v_j_0,v_n) True (1,1) 1. eval_abc_bb0_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_0(v_3,v_i_0,v_j_0,v_n) True (1,1) 2. eval_abc_0(v_3,v_i_0,v_j_0,v_n) -> eval_abc_1(v_3,v_i_0,v_j_0,v_n) True (1,1) 3. eval_abc_1(v_3,v_i_0,v_j_0,v_n) -> eval_abc_2(v_3,v_i_0,v_j_0,v_n) True (1,1) 4. eval_abc_2(v_3,v_i_0,v_j_0,v_n) -> eval_abc_3(v_3,v_i_0,v_j_0,v_n) True (1,1) 5. eval_abc_3(v_3,v_i_0,v_j_0,v_n) -> eval_abc_4(v_3,v_i_0,v_j_0,v_n) True (1,1) 6. eval_abc_4(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb1_in(v_3,1,v_j_0,v_n) True (1,1) 7. eval_abc_bb1_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb2_in(v_3,v_i_0,1,v_n) [-1 + v_i_0 >= 0 && v_n >= v_i_0] (?,1) 8. eval_abc_bb1_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb5_in(v_3,v_i_0,v_j_0,v_n) [-1 + v_i_0 >= 0 && -1 + v_i_0 >= v_n] (1,1) 9. eval_abc_bb2_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb3_in(v_3,v_i_0,v_j_0,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*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_n >= v_j_0] 10. eval_abc_bb2_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb4_in(v_3,v_i_0,v_j_0,v_n) [-1 + v_n >= 0 (?,1) && -2 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*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_j_0 >= v_n] 11. eval_abc_bb3_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb2_in(v_3,v_i_0,1 + v_j_0,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 + v_n >= 0 && -1 + v_j_0 >= 0 && -2 + v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] 12. eval_abc_bb4_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_8(1 + v_i_0,v_i_0,v_j_0,v_n) [-1 + v_j_0 + -1*v_n >= 0 (?,1) && -1 + v_n >= 0 && -3 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -2 + v_j_0 >= 0 && -3 + v_i_0 + v_j_0 >= 0 && -1 + -1*v_i_0 + v_j_0 >= 0 && -1 + v_i_0 >= 0] 13. eval_abc_8(v_3,v_i_0,v_j_0,v_n) -> eval_abc_9(v_3,v_i_0,v_j_0,v_n) [-1 + v_j_0 + -1*v_n >= 0 (?,1) && -1 + v_n >= 0 && -3 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -3 + v_3 + v_n >= 0 && 1 + -1*v_3 + v_n >= 0 && -2 + v_j_0 >= 0 && -3 + v_i_0 + v_j_0 >= 0 && -1 + -1*v_i_0 + v_j_0 >= 0 && -4 + v_3 + v_j_0 >= 0 && -1*v_3 + v_j_0 >= 0 && -1 + v_3 + -1*v_i_0 >= 0 && -1 + v_i_0 >= 0 && -3 + v_3 + v_i_0 >= 0 && 1 + -1*v_3 + v_i_0 >= 0 && -2 + v_3 >= 0] 14. eval_abc_9(v_3,v_i_0,v_j_0,v_n) -> eval_abc_bb1_in(v_3,v_3,v_j_0,v_n) [-1 + v_j_0 + -1*v_n >= 0 (?,1) && -1 + v_n >= 0 && -3 + v_j_0 + v_n >= 0 && -2 + v_i_0 + v_n >= 0 && -1*v_i_0 + v_n >= 0 && -3 + v_3 + v_n >= 0 && 1 + -1*v_3 + v_n >= 0 && -2 + v_j_0 >= 0 && -3 + v_i_0 + v_j_0 >= 0 && -1 + -1*v_i_0 + v_j_0 >= 0 && -4 + v_3 + v_j_0 >= 0 && -1*v_3 + v_j_0 >= 0 && -1 + v_3 + -1*v_i_0 >= 0 && -1 + v_i_0 >= 0 && -3 + v_3 + v_i_0 >= 0 && 1 + -1*v_3 + v_i_0 >= 0 && -2 + v_3 >= 0] 15. eval_abc_bb5_in(v_3,v_i_0,v_j_0,v_n) -> eval_abc_stop(v_3,v_i_0,v_j_0,v_n) [-1 + v_i_0 + -1*v_n >= 0 && -1 + v_i_0 >= 0] (1,1) Signature: {(eval_abc_0,4) ;(eval_abc_1,4) ;(eval_abc_2,4) ;(eval_abc_3,4) ;(eval_abc_4,4) ;(eval_abc_8,4) ;(eval_abc_9,4) ;(eval_abc_bb0_in,4) ;(eval_abc_bb1_in,4) ;(eval_abc_bb2_in,4) ;(eval_abc_bb3_in,4) ;(eval_abc_bb4_in,4) ;(eval_abc_bb5_in,4) ;(eval_abc_start,4) ;(eval_abc_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6},6->{7,8},7->{9},8->{15},9->{11},10->{12},11->{9,10},12->{13} ,13->{14},14->{7,8},15->{}] + Applied Processor: Looptree + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15] | `- p:[7,14,13,12,10,11,9] c: [14] | `- p:[9,11] c: [11] YES