YES(?,POLY) * Step 1: FromIts WORST_CASE(?,POLY) + Considered Problem: Rules: 0. eval_while2_start(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb0_in(v_3,v_N,v_i_0,v_j_0) True (1,1) 1. eval_while2_bb0_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_0(v_3,v_N,v_i_0,v_j_0) True (?,1) 2. eval_while2_0(v_3,v_N,v_i_0,v_j_0) -> eval_while2_1(v_3,v_N,v_i_0,v_j_0) True (?,1) 3. eval_while2_1(v_3,v_N,v_i_0,v_j_0) -> eval_while2_2(v_3,v_N,v_i_0,v_j_0) True (?,1) 4. eval_while2_2(v_3,v_N,v_i_0,v_j_0) -> eval_while2_3(v_3,v_N,v_i_0,v_j_0) True (?,1) 5. eval_while2_3(v_3,v_N,v_i_0,v_j_0) -> eval_while2_4(v_3,v_N,v_i_0,v_j_0) True (?,1) 6. eval_while2_4(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb1_in(v_3,v_N,v_N,v_j_0) True (?,1) 7. eval_while2_bb1_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb2_in(v_3,v_N,v_i_0,v_N) [-1 + v_i_0 >= 0] (?,1) 8. eval_while2_bb1_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb5_in(v_3,v_N,v_i_0,v_j_0) [0 >= v_i_0] (?,1) 9. eval_while2_bb2_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb3_in(v_3,v_N,v_i_0,v_j_0) [-1 + v_j_0 >= 0] (?,1) 10. eval_while2_bb2_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb4_in(v_3,v_N,v_i_0,v_j_0) [0 >= v_j_0] (?,1) 11. eval_while2_bb3_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb2_in(v_3,v_N,v_i_0,-1 + v_j_0) True (?,1) 12. eval_while2_bb4_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_8(-1 + v_i_0,v_N,v_i_0,v_j_0) True (?,1) 13. eval_while2_8(v_3,v_N,v_i_0,v_j_0) -> eval_while2_9(v_3,v_N,v_i_0,v_j_0) True (?,1) 14. eval_while2_9(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb1_in(v_3,v_N,v_3,v_j_0) True (?,1) 15. eval_while2_bb5_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_stop(v_3,v_N,v_i_0,v_j_0) True (?,1) Signature: {(eval_while2_0,4) ;(eval_while2_1,4) ;(eval_while2_2,4) ;(eval_while2_3,4) ;(eval_while2_4,4) ;(eval_while2_8,4) ;(eval_while2_9,4) ;(eval_while2_bb0_in,4) ;(eval_while2_bb1_in,4) ;(eval_while2_bb2_in,4) ;(eval_while2_bb3_in,4) ;(eval_while2_bb4_in,4) ;(eval_while2_bb5_in,4) ;(eval_while2_start,4) ;(eval_while2_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: FromIts + Details: () * Step 2: AddSinks WORST_CASE(?,POLY) + Considered Problem: Rules: eval_while2_start(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb0_in(v_3,v_N,v_i_0,v_j_0) True eval_while2_bb0_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_0(v_3,v_N,v_i_0,v_j_0) True eval_while2_0(v_3,v_N,v_i_0,v_j_0) -> eval_while2_1(v_3,v_N,v_i_0,v_j_0) True eval_while2_1(v_3,v_N,v_i_0,v_j_0) -> eval_while2_2(v_3,v_N,v_i_0,v_j_0) True eval_while2_2(v_3,v_N,v_i_0,v_j_0) -> eval_while2_3(v_3,v_N,v_i_0,v_j_0) True eval_while2_3(v_3,v_N,v_i_0,v_j_0) -> eval_while2_4(v_3,v_N,v_i_0,v_j_0) True eval_while2_4(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb1_in(v_3,v_N,v_N,v_j_0) True eval_while2_bb1_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb2_in(v_3,v_N,v_i_0,v_N) [-1 + v_i_0 >= 0] eval_while2_bb1_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb5_in(v_3,v_N,v_i_0,v_j_0) [0 >= v_i_0] eval_while2_bb2_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb3_in(v_3,v_N,v_i_0,v_j_0) [-1 + v_j_0 >= 0] eval_while2_bb2_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb4_in(v_3,v_N,v_i_0,v_j_0) [0 >= v_j_0] eval_while2_bb3_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb2_in(v_3,v_N,v_i_0,-1 + v_j_0) True eval_while2_bb4_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_8(-1 + v_i_0,v_N,v_i_0,v_j_0) True eval_while2_8(v_3,v_N,v_i_0,v_j_0) -> eval_while2_9(v_3,v_N,v_i_0,v_j_0) True eval_while2_9(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb1_in(v_3,v_N,v_3,v_j_0) True eval_while2_bb5_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_stop(v_3,v_N,v_i_0,v_j_0) True Signature: {(eval_while2_0,4) ;(eval_while2_1,4) ;(eval_while2_2,4) ;(eval_while2_3,4) ;(eval_while2_4,4) ;(eval_while2_8,4) ;(eval_while2_9,4) ;(eval_while2_bb0_in,4) ;(eval_while2_bb1_in,4) ;(eval_while2_bb2_in,4) ;(eval_while2_bb3_in,4) ;(eval_while2_bb4_in,4) ;(eval_while2_bb5_in,4) ;(eval_while2_start,4) ;(eval_while2_stop,4)} Rule 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: AddSinks + Details: () * Step 3: Decompose WORST_CASE(?,POLY) + Considered Problem: Rules: eval_while2_start(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb0_in(v_3,v_N,v_i_0,v_j_0) True eval_while2_bb0_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_0(v_3,v_N,v_i_0,v_j_0) True eval_while2_0(v_3,v_N,v_i_0,v_j_0) -> eval_while2_1(v_3,v_N,v_i_0,v_j_0) True eval_while2_1(v_3,v_N,v_i_0,v_j_0) -> eval_while2_2(v_3,v_N,v_i_0,v_j_0) True eval_while2_2(v_3,v_N,v_i_0,v_j_0) -> eval_while2_3(v_3,v_N,v_i_0,v_j_0) True eval_while2_3(v_3,v_N,v_i_0,v_j_0) -> eval_while2_4(v_3,v_N,v_i_0,v_j_0) True eval_while2_4(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb1_in(v_3,v_N,v_N,v_j_0) True eval_while2_bb1_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb2_in(v_3,v_N,v_i_0,v_N) [-1 + v_i_0 >= 0] eval_while2_bb1_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb5_in(v_3,v_N,v_i_0,v_j_0) [0 >= v_i_0] eval_while2_bb2_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb3_in(v_3,v_N,v_i_0,v_j_0) [-1 + v_j_0 >= 0] eval_while2_bb2_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb4_in(v_3,v_N,v_i_0,v_j_0) [0 >= v_j_0] eval_while2_bb3_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb2_in(v_3,v_N,v_i_0,-1 + v_j_0) True eval_while2_bb4_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_8(-1 + v_i_0,v_N,v_i_0,v_j_0) True eval_while2_8(v_3,v_N,v_i_0,v_j_0) -> eval_while2_9(v_3,v_N,v_i_0,v_j_0) True eval_while2_9(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb1_in(v_3,v_N,v_3,v_j_0) True eval_while2_bb5_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_stop(v_3,v_N,v_i_0,v_j_0) True eval_while2_stop(v_3,v_N,v_i_0,v_j_0) -> exitus616(v_3,v_N,v_i_0,v_j_0) True Signature: {(eval_while2_0,4) ;(eval_while2_1,4) ;(eval_while2_2,4) ;(eval_while2_3,4) ;(eval_while2_4,4) ;(eval_while2_8,4) ;(eval_while2_9,4) ;(eval_while2_bb0_in,4) ;(eval_while2_bb1_in,4) ;(eval_while2_bb2_in,4) ;(eval_while2_bb3_in,4) ;(eval_while2_bb4_in,4) ;(eval_while2_bb5_in,4) ;(eval_while2_start,4) ;(eval_while2_stop,4) ;(exitus616,4)} Rule 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->{16}] + 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] | `- p:[7,14,13,12,10,11,9] c: [7,10,12,13,14] | `- p:[9,11] c: [9,11] * Step 4: AbstractSize WORST_CASE(?,POLY) + Considered Problem: (Rules: eval_while2_start(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb0_in(v_3,v_N,v_i_0,v_j_0) True eval_while2_bb0_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_0(v_3,v_N,v_i_0,v_j_0) True eval_while2_0(v_3,v_N,v_i_0,v_j_0) -> eval_while2_1(v_3,v_N,v_i_0,v_j_0) True eval_while2_1(v_3,v_N,v_i_0,v_j_0) -> eval_while2_2(v_3,v_N,v_i_0,v_j_0) True eval_while2_2(v_3,v_N,v_i_0,v_j_0) -> eval_while2_3(v_3,v_N,v_i_0,v_j_0) True eval_while2_3(v_3,v_N,v_i_0,v_j_0) -> eval_while2_4(v_3,v_N,v_i_0,v_j_0) True eval_while2_4(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb1_in(v_3,v_N,v_N,v_j_0) True eval_while2_bb1_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb2_in(v_3,v_N,v_i_0,v_N) [-1 + v_i_0 >= 0] eval_while2_bb1_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb5_in(v_3,v_N,v_i_0,v_j_0) [0 >= v_i_0] eval_while2_bb2_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb3_in(v_3,v_N,v_i_0,v_j_0) [-1 + v_j_0 >= 0] eval_while2_bb2_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb4_in(v_3,v_N,v_i_0,v_j_0) [0 >= v_j_0] eval_while2_bb3_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb2_in(v_3,v_N,v_i_0,-1 + v_j_0) True eval_while2_bb4_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_8(-1 + v_i_0,v_N,v_i_0,v_j_0) True eval_while2_8(v_3,v_N,v_i_0,v_j_0) -> eval_while2_9(v_3,v_N,v_i_0,v_j_0) True eval_while2_9(v_3,v_N,v_i_0,v_j_0) -> eval_while2_bb1_in(v_3,v_N,v_3,v_j_0) True eval_while2_bb5_in(v_3,v_N,v_i_0,v_j_0) -> eval_while2_stop(v_3,v_N,v_i_0,v_j_0) True eval_while2_stop(v_3,v_N,v_i_0,v_j_0) -> exitus616(v_3,v_N,v_i_0,v_j_0) True Signature: {(eval_while2_0,4) ;(eval_while2_1,4) ;(eval_while2_2,4) ;(eval_while2_3,4) ;(eval_while2_4,4) ;(eval_while2_8,4) ;(eval_while2_9,4) ;(eval_while2_bb0_in,4) ;(eval_while2_bb1_in,4) ;(eval_while2_bb2_in,4) ;(eval_while2_bb3_in,4) ;(eval_while2_bb4_in,4) ;(eval_while2_bb5_in,4) ;(eval_while2_start,4) ;(eval_while2_stop,4) ;(exitus616,4)} Rule 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->{16}] ,We construct a looptree: P: [0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16] | `- p:[7,14,13,12,10,11,9] c: [7,10,12,13,14] | `- p:[9,11] c: [9,11]) + Applied Processor: AbstractSize Minimize + Details: () * Step 5: AbstractFlow WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [v_3,v_N,v_i_0,v_j_0,0.0,0.0.0] eval_while2_start ~> eval_while2_bb0_in [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_bb0_in ~> eval_while2_0 [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_0 ~> eval_while2_1 [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_1 ~> eval_while2_2 [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_2 ~> eval_while2_3 [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_3 ~> eval_while2_4 [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_4 ~> eval_while2_bb1_in [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_N, v_j_0 <= v_j_0] eval_while2_bb1_in ~> eval_while2_bb2_in [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_N] eval_while2_bb1_in ~> eval_while2_bb5_in [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_bb2_in ~> eval_while2_bb3_in [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_bb2_in ~> eval_while2_bb4_in [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_bb3_in ~> eval_while2_bb2_in [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= K + v_j_0] eval_while2_bb4_in ~> eval_while2_8 [v_3 <= K + v_i_0, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_8 ~> eval_while2_9 [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_9 ~> eval_while2_bb1_in [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_3, v_j_0 <= v_j_0] eval_while2_bb5_in ~> eval_while2_stop [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_stop ~> exitus616 [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] + Loop: [0.0 <= K + v_i_0] eval_while2_bb1_in ~> eval_while2_bb2_in [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_N] eval_while2_9 ~> eval_while2_bb1_in [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_3, v_j_0 <= v_j_0] eval_while2_8 ~> eval_while2_9 [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_bb4_in ~> eval_while2_8 [v_3 <= K + v_i_0, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_bb2_in ~> eval_while2_bb4_in [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_bb3_in ~> eval_while2_bb2_in [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= K + v_j_0] eval_while2_bb2_in ~> eval_while2_bb3_in [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] + Loop: [0.0.0 <= K + v_j_0] eval_while2_bb2_in ~> eval_while2_bb3_in [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= v_j_0] eval_while2_bb3_in ~> eval_while2_bb2_in [v_3 <= v_3, v_N <= v_N, v_i_0 <= v_i_0, v_j_0 <= K + v_j_0] + Applied Processor: AbstractFlow + Details: () * Step 6: Lare WORST_CASE(?,POLY) + Considered Problem: Program: Domain: [tick,huge,K,v_3,v_N,v_i_0,v_j_0,0.0,0.0.0] eval_while2_start ~> eval_while2_bb0_in [] eval_while2_bb0_in ~> eval_while2_0 [] eval_while2_0 ~> eval_while2_1 [] eval_while2_1 ~> eval_while2_2 [] eval_while2_2 ~> eval_while2_3 [] eval_while2_3 ~> eval_while2_4 [] eval_while2_4 ~> eval_while2_bb1_in [v_N ~=> v_i_0] eval_while2_bb1_in ~> eval_while2_bb2_in [v_N ~=> v_j_0] eval_while2_bb1_in ~> eval_while2_bb5_in [] eval_while2_bb2_in ~> eval_while2_bb3_in [] eval_while2_bb2_in ~> eval_while2_bb4_in [] eval_while2_bb3_in ~> eval_while2_bb2_in [v_j_0 ~+> v_j_0,K ~+> v_j_0] eval_while2_bb4_in ~> eval_while2_8 [v_i_0 ~+> v_3,K ~+> v_3] eval_while2_8 ~> eval_while2_9 [] eval_while2_9 ~> eval_while2_bb1_in [v_3 ~=> v_i_0] eval_while2_bb5_in ~> eval_while2_stop [] eval_while2_stop ~> exitus616 [] + Loop: [v_i_0 ~+> 0.0,K ~+> 0.0] eval_while2_bb1_in ~> eval_while2_bb2_in [v_N ~=> v_j_0] eval_while2_9 ~> eval_while2_bb1_in [v_3 ~=> v_i_0] eval_while2_8 ~> eval_while2_9 [] eval_while2_bb4_in ~> eval_while2_8 [v_i_0 ~+> v_3,K ~+> v_3] eval_while2_bb2_in ~> eval_while2_bb4_in [] eval_while2_bb3_in ~> eval_while2_bb2_in [v_j_0 ~+> v_j_0,K ~+> v_j_0] eval_while2_bb2_in ~> eval_while2_bb3_in [] + Loop: [v_j_0 ~+> 0.0.0,K ~+> 0.0.0] eval_while2_bb2_in ~> eval_while2_bb3_in [] eval_while2_bb3_in ~> eval_while2_bb2_in [v_j_0 ~+> v_j_0,K ~+> v_j_0] + Applied Processor: Lare + Details: eval_while2_start ~> exitus616 [v_N ~=> v_i_0 ,v_N ~=> v_j_0 ,v_N ~+> v_3 ,v_N ~+> v_i_0 ,v_N ~+> v_j_0 ,v_N ~+> 0.0 ,v_N ~+> 0.0.0 ,v_N ~+> tick ,tick ~+> tick ,K ~+> v_3 ,K ~+> v_i_0 ,K ~+> v_j_0 ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,v_N ~*> v_i_0 ,v_N ~*> v_j_0 ,v_N ~*> 0.0.0 ,v_N ~*> tick ,K ~*> v_3 ,K ~*> v_i_0 ,K ~*> v_j_0 ,K ~*> 0.0.0 ,K ~*> tick ,v_N ~^> v_j_0 ,K ~^> v_j_0] + eval_while2_bb1_in> [v_N ~=> v_j_0 ,v_N ~+> v_j_0 ,v_N ~+> 0.0.0 ,v_N ~+> tick ,v_i_0 ~+> v_3 ,v_i_0 ~+> v_i_0 ,v_i_0 ~+> 0.0 ,v_i_0 ~+> tick ,tick ~+> tick ,K ~+> v_3 ,K ~+> v_i_0 ,K ~+> v_j_0 ,K ~+> 0.0 ,K ~+> 0.0.0 ,K ~+> tick ,v_N ~*> v_j_0 ,v_N ~*> 0.0.0 ,v_N ~*> tick ,v_i_0 ~*> v_i_0 ,v_i_0 ~*> v_j_0 ,v_i_0 ~*> tick ,K ~*> v_3 ,K ~*> v_i_0 ,K ~*> v_j_0 ,K ~*> 0.0.0 ,K ~*> tick ,v_i_0 ~^> v_j_0 ,K ~^> v_j_0] + eval_while2_bb2_in> [v_j_0 ~+> v_j_0 ,v_j_0 ~+> 0.0.0 ,v_j_0 ~+> tick ,tick ~+> tick ,K ~+> v_j_0 ,K ~+> 0.0.0 ,K ~+> tick ,v_j_0 ~*> v_j_0 ,K ~*> v_j_0] YES(?,POLY)