YES(?,O(n^1)) * Step 1: UnsatPaths WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_0(v_m,v_n,v_va_0,v_vb_0) True (?,1) 2. eval_start_0(v_m,v_n,v_va_0,v_vb_0) -> eval_start_1(v_m,v_n,v_va_0,v_vb_0) True (?,1) 3. eval_start_1(v_m,v_n,v_va_0,v_vb_0) -> eval_start_2(v_m,v_n,v_va_0,v_vb_0) True (?,1) 4. eval_start_2(v_m,v_n,v_va_0,v_vb_0) -> eval_start_3(v_m,v_n,v_va_0,v_vb_0) True (?,1) 5. eval_start_3(v_m,v_n,v_va_0,v_vb_0) -> eval_start_4(v_m,v_n,v_va_0,v_vb_0) True (?,1) 6. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_n,0) [-1 + v_m >= 0] (?,1) 7. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) [0 >= v_m] (?,1) 8. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && -1 + v_va_0 >= 0] (?,1) 9. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && 0 >= v_va_0] (?,1) 10. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_vb_0] 11. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_va_0,0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_vb_0 >= v_m] 12. eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,-1 + v_va_0,1 + v_vb_0) [-1 + v_m + -1*v_vb_0 >= 0 (?,1) && v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] 13. eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (?,1) && -1*v_va_0 + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && -1*v_va_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m + -1*v_va_0 >= 0 && -1 + v_m >= 0] 14. eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_8(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) 15. eval_start_8(v_m,v_n,v_va_0,v_vb_0) -> eval_start_9(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) 16. eval_start_9(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_8,4) ;(eval_start_9,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10,11},9->{13},10->{12},11->{8,9},12->{8 ,9},13->{},14->{15},15->{16},16->{}] + Applied Processor: UnsatPaths + Details: We remove following edges from the transition graph: [(11,9)] * Step 2: FromIts WORST_CASE(?,O(n^1)) + Considered Problem: Rules: 0. eval_start_start(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) True (1,1) 1. eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_0(v_m,v_n,v_va_0,v_vb_0) True (?,1) 2. eval_start_0(v_m,v_n,v_va_0,v_vb_0) -> eval_start_1(v_m,v_n,v_va_0,v_vb_0) True (?,1) 3. eval_start_1(v_m,v_n,v_va_0,v_vb_0) -> eval_start_2(v_m,v_n,v_va_0,v_vb_0) True (?,1) 4. eval_start_2(v_m,v_n,v_va_0,v_vb_0) -> eval_start_3(v_m,v_n,v_va_0,v_vb_0) True (?,1) 5. eval_start_3(v_m,v_n,v_va_0,v_vb_0) -> eval_start_4(v_m,v_n,v_va_0,v_vb_0) True (?,1) 6. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_n,0) [-1 + v_m >= 0] (?,1) 7. eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) [0 >= v_m] (?,1) 8. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && -1 + v_va_0 >= 0] (?,1) 9. eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && 0 >= v_va_0] (?,1) 10. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_vb_0] 11. eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_va_0,0) [v_vb_0 >= 0 (?,1) && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_vb_0 >= v_m] 12. eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,-1 + v_va_0,1 + v_vb_0) [-1 + v_m + -1*v_vb_0 >= 0 (?,1) && v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] 13. eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 (?,1) && -1*v_va_0 + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && -1*v_va_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m + -1*v_va_0 >= 0 && -1 + v_m >= 0] 14. eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_8(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) 15. eval_start_8(v_m,v_n,v_va_0,v_vb_0) -> eval_start_9(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) 16. eval_start_9(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] (?,1) Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_8,4) ;(eval_start_9,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Flow Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10,11},9->{13},10->{12},11->{8},12->{8 ,9},13->{},14->{15},15->{16},16->{}] + Applied Processor: FromIts + Details: () * Step 3: AddSinks WORST_CASE(?,O(n^1)) + Considered Problem: Rules: eval_start_start(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) True eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_0(v_m,v_n,v_va_0,v_vb_0) True eval_start_0(v_m,v_n,v_va_0,v_vb_0) -> eval_start_1(v_m,v_n,v_va_0,v_vb_0) True eval_start_1(v_m,v_n,v_va_0,v_vb_0) -> eval_start_2(v_m,v_n,v_va_0,v_vb_0) True eval_start_2(v_m,v_n,v_va_0,v_vb_0) -> eval_start_3(v_m,v_n,v_va_0,v_vb_0) True eval_start_3(v_m,v_n,v_va_0,v_vb_0) -> eval_start_4(v_m,v_n,v_va_0,v_vb_0) True eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_n,0) [-1 + v_m >= 0] eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) [0 >= v_m] eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && -1 + v_va_0 >= 0] eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && 0 >= v_va_0] eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_vb_0] eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_va_0,0) [v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_vb_0 >= v_m] eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,-1 + v_va_0,1 + v_vb_0) [-1 + v_m + -1*v_vb_0 >= 0 && v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1*v_va_0 + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && -1*v_va_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m + -1*v_va_0 >= 0 && -1 + v_m >= 0] eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_8(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] eval_start_8(v_m,v_n,v_va_0,v_vb_0) -> eval_start_9(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] eval_start_9(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_8,4) ;(eval_start_9,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_start,4) ;(eval_start_stop,4)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10,11},9->{13},10->{12},11->{8},12->{8 ,9},13->{},14->{15},15->{16},16->{}] + Applied Processor: AddSinks + Details: () * Step 4: Unfold WORST_CASE(?,O(n^1)) + Considered Problem: Rules: eval_start_start(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) True eval_start_bb0_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_0(v_m,v_n,v_va_0,v_vb_0) True eval_start_0(v_m,v_n,v_va_0,v_vb_0) -> eval_start_1(v_m,v_n,v_va_0,v_vb_0) True eval_start_1(v_m,v_n,v_va_0,v_vb_0) -> eval_start_2(v_m,v_n,v_va_0,v_vb_0) True eval_start_2(v_m,v_n,v_va_0,v_vb_0) -> eval_start_3(v_m,v_n,v_va_0,v_vb_0) True eval_start_3(v_m,v_n,v_va_0,v_vb_0) -> eval_start_4(v_m,v_n,v_va_0,v_vb_0) True eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_n,0) [-1 + v_m >= 0] eval_start_4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) [0 >= v_m] eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && -1 + v_va_0 >= 0] eval_start_bb1_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && 0 >= v_va_0] eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_vb_0] eval_start_bb2_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,v_va_0,0) [v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_vb_0 >= v_m] eval_start_bb3_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in(v_m,v_n,-1 + v_va_0,1 + v_vb_0) [-1 + v_m + -1*v_vb_0 >= 0 && v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] eval_start_bb4_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1*v_va_0 + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && -1*v_va_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m + -1*v_va_0 >= 0 && -1 + v_m >= 0] eval_start_bb5_in(v_m,v_n,v_va_0,v_vb_0) -> eval_start_8(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] eval_start_8(v_m,v_n,v_va_0,v_vb_0) -> eval_start_9(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] eval_start_9(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] eval_start_stop(v_m,v_n,v_va_0,v_vb_0) -> exitus616(v_m,v_n,v_va_0,v_vb_0) True eval_start_stop(v_m,v_n,v_va_0,v_vb_0) -> exitus616(v_m,v_n,v_va_0,v_vb_0) True Signature: {(eval_start_0,4) ;(eval_start_1,4) ;(eval_start_2,4) ;(eval_start_3,4) ;(eval_start_4,4) ;(eval_start_8,4) ;(eval_start_9,4) ;(eval_start_bb0_in,4) ;(eval_start_bb1_in,4) ;(eval_start_bb2_in,4) ;(eval_start_bb3_in,4) ;(eval_start_bb4_in,4) ;(eval_start_bb5_in,4) ;(eval_start_start,4) ;(eval_start_stop,4) ;(exitus616,4)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5},5->{6,7},6->{8,9},7->{14},8->{10,11},9->{13},10->{12},11->{8},12->{8 ,9},13->{18},14->{15},15->{16},16->{17}] + Applied Processor: Unfold + Details: () * Step 5: Decompose WORST_CASE(?,O(n^1)) + Considered Problem: Rules: eval_start_start.0(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb0_in.1(v_m,v_n,v_va_0,v_vb_0) True eval_start_bb0_in.1(v_m,v_n,v_va_0,v_vb_0) -> eval_start_0.2(v_m,v_n,v_va_0,v_vb_0) True eval_start_0.2(v_m,v_n,v_va_0,v_vb_0) -> eval_start_1.3(v_m,v_n,v_va_0,v_vb_0) True eval_start_1.3(v_m,v_n,v_va_0,v_vb_0) -> eval_start_2.4(v_m,v_n,v_va_0,v_vb_0) True eval_start_2.4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_3.5(v_m,v_n,v_va_0,v_vb_0) True eval_start_3.5(v_m,v_n,v_va_0,v_vb_0) -> eval_start_4.6(v_m,v_n,v_va_0,v_vb_0) True eval_start_3.5(v_m,v_n,v_va_0,v_vb_0) -> eval_start_4.7(v_m,v_n,v_va_0,v_vb_0) True eval_start_4.6(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in.8(v_m,v_n,v_n,0) [-1 + v_m >= 0] eval_start_4.6(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in.9(v_m,v_n,v_n,0) [-1 + v_m >= 0] eval_start_4.7(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb5_in.14(v_m,v_n,v_va_0,v_vb_0) [0 >= v_m] eval_start_bb1_in.8(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb2_in.10(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && -1 + v_va_0 >= 0] eval_start_bb1_in.8(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb2_in.11(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && -1 + v_va_0 >= 0] eval_start_bb1_in.9(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb4_in.13(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && 0 >= v_va_0] eval_start_bb2_in.10(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb3_in.12(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_vb_0] eval_start_bb2_in.11(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in.8(v_m,v_n,v_va_0,0) [v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_vb_0 >= v_m] eval_start_bb3_in.12(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in.8(v_m,v_n,-1 + v_va_0,1 + v_vb_0) [-1 + v_m + -1*v_vb_0 >= 0 && v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] eval_start_bb3_in.12(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in.9(v_m,v_n,-1 + v_va_0,1 + v_vb_0) [-1 + v_m + -1*v_vb_0 >= 0 && v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] eval_start_bb4_in.13(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop.18(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1*v_va_0 + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && -1*v_va_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m + -1*v_va_0 >= 0 && -1 + v_m >= 0] eval_start_bb5_in.14(v_m,v_n,v_va_0,v_vb_0) -> eval_start_8.15(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] eval_start_8.15(v_m,v_n,v_va_0,v_vb_0) -> eval_start_9.16(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] eval_start_9.16(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop.17(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] eval_start_stop.17(v_m,v_n,v_va_0,v_vb_0) -> exitus616.19(v_m,v_n,v_va_0,v_vb_0) True eval_start_stop.18(v_m,v_n,v_va_0,v_vb_0) -> exitus616.19(v_m,v_n,v_va_0,v_vb_0) True Signature: {(eval_start_0.2,4) ;(eval_start_1.3,4) ;(eval_start_2.4,4) ;(eval_start_3.5,4) ;(eval_start_4.6,4) ;(eval_start_4.7,4) ;(eval_start_8.15,4) ;(eval_start_9.16,4) ;(eval_start_bb0_in.1,4) ;(eval_start_bb1_in.8,4) ;(eval_start_bb1_in.9,4) ;(eval_start_bb2_in.10,4) ;(eval_start_bb2_in.11,4) ;(eval_start_bb3_in.12,4) ;(eval_start_bb4_in.13,4) ;(eval_start_bb5_in.14,4) ;(eval_start_start.0,4) ;(eval_start_stop.17,4) ;(eval_start_stop.18,4) ;(exitus616.19,4)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5,6},5->{7,8},6->{9},7->{10,11},8->{12},9->{18},10->{13},11->{14} ,12->{17},13->{15,16},14->{10,11},15->{10,11},16->{12},17->{22},18->{19},19->{20},20->{21},21->{},22->{}] + Applied Processor: Decompose Greedy + Details: We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22] | `- p:[10,14,11,15,13] c: [10,11,13,14,15] * Step 6: AbstractSize WORST_CASE(?,O(n^1)) + Considered Problem: (Rules: eval_start_start.0(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb0_in.1(v_m,v_n,v_va_0,v_vb_0) True eval_start_bb0_in.1(v_m,v_n,v_va_0,v_vb_0) -> eval_start_0.2(v_m,v_n,v_va_0,v_vb_0) True eval_start_0.2(v_m,v_n,v_va_0,v_vb_0) -> eval_start_1.3(v_m,v_n,v_va_0,v_vb_0) True eval_start_1.3(v_m,v_n,v_va_0,v_vb_0) -> eval_start_2.4(v_m,v_n,v_va_0,v_vb_0) True eval_start_2.4(v_m,v_n,v_va_0,v_vb_0) -> eval_start_3.5(v_m,v_n,v_va_0,v_vb_0) True eval_start_3.5(v_m,v_n,v_va_0,v_vb_0) -> eval_start_4.6(v_m,v_n,v_va_0,v_vb_0) True eval_start_3.5(v_m,v_n,v_va_0,v_vb_0) -> eval_start_4.7(v_m,v_n,v_va_0,v_vb_0) True eval_start_4.6(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in.8(v_m,v_n,v_n,0) [-1 + v_m >= 0] eval_start_4.6(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in.9(v_m,v_n,v_n,0) [-1 + v_m >= 0] eval_start_4.7(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb5_in.14(v_m,v_n,v_va_0,v_vb_0) [0 >= v_m] eval_start_bb1_in.8(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb2_in.10(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && -1 + v_va_0 >= 0] eval_start_bb1_in.8(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb2_in.11(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && -1 + v_va_0 >= 0] eval_start_bb1_in.9(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb4_in.13(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m >= 0 && 0 >= v_va_0] eval_start_bb2_in.10(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb3_in.12(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && -1 + v_m >= v_vb_0] eval_start_bb2_in.11(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in.8(v_m,v_n,v_va_0,0) [v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0 && v_vb_0 >= v_m] eval_start_bb3_in.12(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in.8(v_m,v_n,-1 + v_va_0,1 + v_vb_0) [-1 + v_m + -1*v_vb_0 >= 0 && v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] eval_start_bb3_in.12(v_m,v_n,v_va_0,v_vb_0) -> eval_start_bb1_in.9(v_m,v_n,-1 + v_va_0,1 + v_vb_0) [-1 + v_m + -1*v_vb_0 >= 0 && v_vb_0 >= 0 && -1 + v_va_0 + v_vb_0 >= 0 && -1 + v_n + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_va_0 >= 0 && -2 + v_n + v_va_0 >= 0 && -2 + v_m + v_va_0 >= 0 && -1 + v_n >= 0 && -2 + v_m + v_n >= 0 && -1 + v_m >= 0] eval_start_bb4_in.13(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop.18(v_m,v_n,v_va_0,v_vb_0) [v_vb_0 >= 0 && -1*v_va_0 + v_vb_0 >= 0 && -1 + v_m + v_vb_0 >= 0 && -1*v_va_0 >= 0 && v_n + -1*v_va_0 >= 0 && -1 + v_m + -1*v_va_0 >= 0 && -1 + v_m >= 0] eval_start_bb5_in.14(v_m,v_n,v_va_0,v_vb_0) -> eval_start_8.15(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] eval_start_8.15(v_m,v_n,v_va_0,v_vb_0) -> eval_start_9.16(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] eval_start_9.16(v_m,v_n,v_va_0,v_vb_0) -> eval_start_stop.17(v_m,v_n,v_va_0,v_vb_0) [-1*v_m >= 0] eval_start_stop.17(v_m,v_n,v_va_0,v_vb_0) -> exitus616.19(v_m,v_n,v_va_0,v_vb_0) True eval_start_stop.18(v_m,v_n,v_va_0,v_vb_0) -> exitus616.19(v_m,v_n,v_va_0,v_vb_0) True Signature: {(eval_start_0.2,4) ;(eval_start_1.3,4) ;(eval_start_2.4,4) ;(eval_start_3.5,4) ;(eval_start_4.6,4) ;(eval_start_4.7,4) ;(eval_start_8.15,4) ;(eval_start_9.16,4) ;(eval_start_bb0_in.1,4) ;(eval_start_bb1_in.8,4) ;(eval_start_bb1_in.9,4) ;(eval_start_bb2_in.10,4) ;(eval_start_bb2_in.11,4) ;(eval_start_bb3_in.12,4) ;(eval_start_bb4_in.13,4) ;(eval_start_bb5_in.14,4) ;(eval_start_start.0,4) ;(eval_start_stop.17,4) ;(eval_start_stop.18,4) ;(exitus616.19,4)} Rule Graph: [0->{1},1->{2},2->{3},3->{4},4->{5,6},5->{7,8},6->{9},7->{10,11},8->{12},9->{18},10->{13},11->{14} ,12->{17},13->{15,16},14->{10,11},15->{10,11},16->{12},17->{22},18->{19},19->{20},20->{21},21->{},22->{}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22] | `- p:[10,14,11,15,13] c: [10,11,13,14,15]) + Applied Processor: AbstractSize Minimize + Details: () * Step 7: AbstractFlow WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [v_m,v_n,v_va_0,v_vb_0,0.0] eval_start_start.0 ~> eval_start_bb0_in.1 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb0_in.1 ~> eval_start_0.2 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_0.2 ~> eval_start_1.3 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_1.3 ~> eval_start_2.4 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_2.4 ~> eval_start_3.5 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_3.5 ~> eval_start_4.6 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_3.5 ~> eval_start_4.7 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_4.6 ~> eval_start_bb1_in.8 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_n, v_vb_0 <= 0*K] eval_start_4.6 ~> eval_start_bb1_in.9 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_n, v_vb_0 <= 0*K] eval_start_4.7 ~> eval_start_bb5_in.14 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb1_in.8 ~> eval_start_bb2_in.10 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb1_in.8 ~> eval_start_bb2_in.11 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb1_in.9 ~> eval_start_bb4_in.13 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb2_in.10 ~> eval_start_bb3_in.12 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb2_in.11 ~> eval_start_bb1_in.8 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= 0*K] eval_start_bb3_in.12 ~> eval_start_bb1_in.8 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_m] eval_start_bb3_in.12 ~> eval_start_bb1_in.9 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_m] eval_start_bb4_in.13 ~> eval_start_stop.18 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb5_in.14 ~> eval_start_8.15 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_8.15 ~> eval_start_9.16 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_9.16 ~> eval_start_stop.17 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_stop.17 ~> exitus616.19 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_stop.18 ~> exitus616.19 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] + Loop: [0.0 <= K + v_va_0 + v_vb_0] eval_start_bb1_in.8 ~> eval_start_bb2_in.10 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb2_in.11 ~> eval_start_bb1_in.8 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= 0*K] eval_start_bb1_in.8 ~> eval_start_bb2_in.11 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] eval_start_bb3_in.12 ~> eval_start_bb1_in.8 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_m] eval_start_bb2_in.10 ~> eval_start_bb3_in.12 [v_m <= v_m, v_n <= v_n, v_va_0 <= v_va_0, v_vb_0 <= v_vb_0] + Applied Processor: AbstractFlow + Details: () * Step 8: Lare WORST_CASE(?,O(n^1)) + Considered Problem: Program: Domain: [tick,huge,K,v_m,v_n,v_va_0,v_vb_0,0.0] eval_start_start.0 ~> eval_start_bb0_in.1 [] eval_start_bb0_in.1 ~> eval_start_0.2 [] eval_start_0.2 ~> eval_start_1.3 [] eval_start_1.3 ~> eval_start_2.4 [] eval_start_2.4 ~> eval_start_3.5 [] eval_start_3.5 ~> eval_start_4.6 [] eval_start_3.5 ~> eval_start_4.7 [] eval_start_4.6 ~> eval_start_bb1_in.8 [v_n ~=> v_va_0,K ~=> v_vb_0] eval_start_4.6 ~> eval_start_bb1_in.9 [v_n ~=> v_va_0,K ~=> v_vb_0] eval_start_4.7 ~> eval_start_bb5_in.14 [] eval_start_bb1_in.8 ~> eval_start_bb2_in.10 [] eval_start_bb1_in.8 ~> eval_start_bb2_in.11 [] eval_start_bb1_in.9 ~> eval_start_bb4_in.13 [] eval_start_bb2_in.10 ~> eval_start_bb3_in.12 [] eval_start_bb2_in.11 ~> eval_start_bb1_in.8 [K ~=> v_vb_0] eval_start_bb3_in.12 ~> eval_start_bb1_in.8 [v_m ~=> v_vb_0] eval_start_bb3_in.12 ~> eval_start_bb1_in.9 [v_m ~=> v_vb_0] eval_start_bb4_in.13 ~> eval_start_stop.18 [] eval_start_bb5_in.14 ~> eval_start_8.15 [] eval_start_8.15 ~> eval_start_9.16 [] eval_start_9.16 ~> eval_start_stop.17 [] eval_start_stop.17 ~> exitus616.19 [] eval_start_stop.18 ~> exitus616.19 [] + Loop: [v_va_0 ~+> 0.0,v_vb_0 ~+> 0.0,K ~+> 0.0] eval_start_bb1_in.8 ~> eval_start_bb2_in.10 [] eval_start_bb2_in.11 ~> eval_start_bb1_in.8 [K ~=> v_vb_0] eval_start_bb1_in.8 ~> eval_start_bb2_in.11 [] eval_start_bb3_in.12 ~> eval_start_bb1_in.8 [v_m ~=> v_vb_0] eval_start_bb2_in.10 ~> eval_start_bb3_in.12 [] + Applied Processor: Lare + Details: eval_start_start.0 ~> exitus616.19 [v_m ~=> v_vb_0 ,v_n ~=> v_va_0 ,K ~=> v_vb_0 ,v_n ~+> 0.0 ,v_n ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick ,K ~*> 0.0 ,K ~*> tick] + eval_start_bb3_in.12> [v_m ~=> v_vb_0 ,K ~=> v_vb_0 ,v_va_0 ~+> 0.0 ,v_va_0 ~+> tick ,v_vb_0 ~+> 0.0 ,v_vb_0 ~+> tick ,tick ~+> tick ,K ~+> 0.0 ,K ~+> tick] YES(?,O(n^1))