0.06/0.56 WORST_CASE(?,O(n^1)) 0.06/0.56 0.06/0.56 Preprocessing Cost Relations 0.06/0.56 ===================================== 0.06/0.56 0.06/0.56 #### Computed strongly connected components 0.06/0.56 0. recursive : [eval_inflate_stored_bb1_in/3,eval_inflate_stored_bb2_in/3] 0.06/0.56 1. recursive : [eval_inflate_stored_bb4_in/3,eval_inflate_stored_bb5_in/3] 0.06/0.56 2. non_recursive : [eval_inflate_stored_stop/1] 0.06/0.56 3. non_recursive : [eval_inflate_stored_bb12_in/1] 0.06/0.56 4. recursive : [eval_inflate_stored_bb10_in/4,eval_inflate_stored_bb9_in/4] 0.06/0.56 5. recursive : [eval_inflate_stored_bb11_in/6,eval_inflate_stored_bb8_in/4,eval_inflate_stored_bb9_in_loop_cont/7] 0.06/0.56 6. non_recursive : [eval_inflate_stored_bb8_in_loop_cont/2] 0.06/0.56 7. non_recursive : [eval_inflate_stored_bb7_in/4] 0.06/0.56 8. non_recursive : [eval_inflate_stored_9/5] 0.06/0.56 9. non_recursive : [eval_inflate_stored_8/4] 0.06/0.56 10. non_recursive : [eval_inflate_stored_bb6_in/4] 0.06/0.56 11. non_recursive : [eval_inflate_stored_bb4_in_loop_cont/5] 0.06/0.56 12. non_recursive : [eval_inflate_stored_bb3_in/4] 0.06/0.56 13. non_recursive : [eval_inflate_stored_bb1_in_loop_cont/5] 0.06/0.56 14. non_recursive : [eval_inflate_stored_bb0_in/4] 0.06/0.56 15. non_recursive : [eval_inflate_stored_start/4] 0.06/0.56 0.06/0.56 #### Obtained direct recursion through partial evaluation 0.06/0.56 0. SCC is partially evaluated into eval_inflate_stored_bb1_in/3 0.06/0.56 1. SCC is partially evaluated into eval_inflate_stored_bb4_in/3 0.06/0.56 2. SCC is completely evaluated into other SCCs 0.06/0.56 3. SCC is completely evaluated into other SCCs 0.06/0.56 4. SCC is partially evaluated into eval_inflate_stored_bb9_in/4 0.06/0.56 5. SCC is partially evaluated into eval_inflate_stored_bb8_in/4 0.06/0.56 6. SCC is completely evaluated into other SCCs 0.06/0.56 7. SCC is partially evaluated into eval_inflate_stored_bb7_in/4 0.06/0.56 8. SCC is partially evaluated into eval_inflate_stored_9/5 0.06/0.56 9. SCC is completely evaluated into other SCCs 0.06/0.56 10. SCC is completely evaluated into other SCCs 0.06/0.56 11. SCC is completely evaluated into other SCCs 0.06/0.56 12. SCC is partially evaluated into eval_inflate_stored_bb3_in/4 0.06/0.56 13. SCC is completely evaluated into other SCCs 0.06/0.56 14. SCC is partially evaluated into eval_inflate_stored_bb0_in/4 0.06/0.56 15. SCC is partially evaluated into eval_inflate_stored_start/4 0.06/0.56 0.06/0.56 Control-Flow Refinement of Cost Relations 0.06/0.56 ===================================== 0.06/0.56 0.06/0.56 ### Specialization of cost equations eval_inflate_stored_bb1_in/3 0.06/0.56 * CE 4 is refined into CE [16] 0.06/0.56 * CE 3 is refined into CE [17] 0.06/0.56 0.06/0.56 0.06/0.56 ### Cost equations --> "Loop" of eval_inflate_stored_bb1_in/3 0.06/0.56 * CEs [17] --> Loop 16 0.06/0.56 * CEs [16] --> Loop 17 0.06/0.56 0.06/0.56 ### Ranking functions of CR eval_inflate_stored_bb1_in(V__01,B,C) 0.06/0.56 * RF of phase [16]: [-V__01/8+2] 0.06/0.56 0.06/0.56 #### Partial ranking functions of CR eval_inflate_stored_bb1_in(V__01,B,C) 0.06/0.56 * Partial RF of phase [16]: 0.06/0.56 - RF of loop [16:1]: 0.06/0.56 -V__01/8+2 0.06/0.56 0.06/0.56 0.06/0.56 ### Specialization of cost equations eval_inflate_stored_bb4_in/3 0.06/0.56 * CE 7 is refined into CE [18] 0.06/0.56 * CE 6 is refined into CE [19] 0.06/0.56 0.06/0.56 0.06/0.56 ### Cost equations --> "Loop" of eval_inflate_stored_bb4_in/3 0.06/0.56 * CEs [19] --> Loop 18 0.06/0.56 * CEs [18] --> Loop 19 0.06/0.56 0.06/0.56 ### Ranking functions of CR eval_inflate_stored_bb4_in(V__1,B,C) 0.06/0.56 * RF of phase [18]: [-V__1/8+2] 0.06/0.56 0.06/0.56 #### Partial ranking functions of CR eval_inflate_stored_bb4_in(V__1,B,C) 0.06/0.56 * Partial RF of phase [18]: 0.06/0.56 - RF of loop [18:1]: 0.06/0.56 -V__1/8+2 0.06/0.56 0.06/0.56 0.06/0.56 ### Specialization of cost equations eval_inflate_stored_bb9_in/4 0.06/0.56 * CE 15 is refined into CE [20] 0.06/0.56 * CE 14 is refined into CE [21] 0.06/0.56 0.06/0.56 0.06/0.56 ### Cost equations --> "Loop" of eval_inflate_stored_bb9_in/4 0.06/0.56 * CEs [21] --> Loop 20 0.06/0.56 * CEs [20] --> Loop 21 0.06/0.56 0.06/0.56 ### Ranking functions of CR eval_inflate_stored_bb9_in(V_limit,V__3,B,C) 0.06/0.56 * RF of phase [20]: [V_limit/8-V__3/8] 0.06/0.56 0.06/0.56 #### Partial ranking functions of CR eval_inflate_stored_bb9_in(V_limit,V__3,B,C) 0.06/0.56 * Partial RF of phase [20]: 0.06/0.56 - RF of loop [20:1]: 0.06/0.56 V_limit/8-V__3/8 0.06/0.56 0.06/0.56 0.06/0.56 ### Specialization of cost equations eval_inflate_stored_bb8_in/4 0.06/0.56 * CE 13 is refined into CE [22] 0.06/0.56 * CE 12 is refined into CE [23,24] 0.06/0.56 0.06/0.56 0.06/0.56 ### Cost equations --> "Loop" of eval_inflate_stored_bb8_in/4 0.06/0.56 * CEs [24] --> Loop 22 0.06/0.56 * CEs [23] --> Loop 23 0.06/0.56 * CEs [22] --> Loop 24 0.06/0.56 0.06/0.56 ### Ranking functions of CR eval_inflate_stored_bb8_in(V_limit,V__2,V__0,B) 0.06/0.56 * RF of phase [22]: [V__0] 0.06/0.56 * RF of phase [23]: [V__0,-V_limit/8+V__2/8+1/8] 0.06/0.56 0.06/0.56 #### Partial ranking functions of CR eval_inflate_stored_bb8_in(V_limit,V__2,V__0,B) 0.06/0.56 * Partial RF of phase [22]: 0.06/0.56 - RF of loop [22:1]: 0.06/0.56 V__0 0.06/0.56 * Partial RF of phase [23]: 0.06/0.56 - RF of loop [23:1]: 0.06/0.56 V__0 0.06/0.56 -V_limit/8+V__2/8+1/8 0.06/0.56 0.06/0.56 0.06/0.56 ### Specialization of cost equations eval_inflate_stored_bb7_in/4 0.06/0.56 * CE 11 is refined into CE [25,26,27,28] 0.06/0.56 0.06/0.56 0.06/0.56 ### Cost equations --> "Loop" of eval_inflate_stored_bb7_in/4 0.06/0.56 * CEs [28] --> Loop 25 0.06/0.56 * CEs [27] --> Loop 26 0.06/0.56 * CEs [26] --> Loop 27 0.06/0.56 * CEs [25] --> Loop 28 0.06/0.56 0.06/0.56 ### Ranking functions of CR eval_inflate_stored_bb7_in(V_n,V_limit,V__1,B) 0.06/0.56 0.06/0.56 #### Partial ranking functions of CR eval_inflate_stored_bb7_in(V_n,V_limit,V__1,B) 0.06/0.56 0.06/0.56 0.06/0.56 ### Specialization of cost equations eval_inflate_stored_9/5 0.06/0.56 * CE 9 is refined into CE [29] 0.06/0.56 * CE 8 is refined into CE [30] 0.06/0.56 * CE 10 is refined into CE [31,32,33,34] 0.06/0.56 0.06/0.56 0.06/0.56 ### Cost equations --> "Loop" of eval_inflate_stored_9/5 0.06/0.56 * CEs [29] --> Loop 29 0.06/0.56 * CEs [30] --> Loop 30 0.06/0.56 * CEs [34] --> Loop 31 0.06/0.56 * CEs [33] --> Loop 32 0.06/0.56 * CEs [32] --> Loop 33 0.06/0.56 * CEs [31] --> Loop 34 0.06/0.56 0.06/0.56 ### Ranking functions of CR eval_inflate_stored_9(V_n,V_limit,V__1,V_6,B) 0.06/0.56 0.06/0.56 #### Partial ranking functions of CR eval_inflate_stored_9(V_n,V_limit,V__1,V_6,B) 0.06/0.56 0.06/0.56 0.06/0.56 ### Specialization of cost equations eval_inflate_stored_bb3_in/4 0.06/0.56 * CE 5 is refined into CE [35,36,37,38,39,40,41,42,43,44,45,46] 0.06/0.56 0.06/0.56 0.06/0.56 ### Cost equations --> "Loop" of eval_inflate_stored_bb3_in/4 0.06/0.56 * CEs [39,40] --> Loop 35 0.06/0.56 * CEs [38] --> Loop 36 0.06/0.56 * CEs [37] --> Loop 37 0.06/0.56 * CEs [36] --> Loop 38 0.06/0.56 * CEs [43] --> Loop 39 0.06/0.56 * CEs [42] --> Loop 40 0.06/0.56 * CEs [45,46] --> Loop 41 0.06/0.56 * CEs [44] --> Loop 42 0.06/0.56 * CEs [35] --> Loop 43 0.06/0.56 * CEs [41] --> Loop 44 0.06/0.56 0.06/0.56 ### Ranking functions of CR eval_inflate_stored_bb3_in(V_n,V_limit,V__01,B) 0.06/0.56 0.06/0.56 #### Partial ranking functions of CR eval_inflate_stored_bb3_in(V_n,V_limit,V__01,B) 0.06/0.56 0.06/0.56 0.06/0.56 ### Specialization of cost equations eval_inflate_stored_bb0_in/4 0.06/0.56 * CE 2 is refined into CE [47,48,49,50,51,52,53,54,55,56,57,58,59,60,61] 0.06/0.56 0.06/0.56 0.06/0.56 ### Cost equations --> "Loop" of eval_inflate_stored_bb0_in/4 0.06/0.56 * CEs [59] --> Loop 45 0.06/0.56 * CEs [56] --> Loop 46 0.06/0.56 * CEs [50] --> Loop 47 0.06/0.56 * CEs [55] --> Loop 48 0.06/0.56 * CEs [53] --> Loop 49 0.06/0.56 * CEs [54] --> Loop 50 0.06/0.56 * CEs [61] --> Loop 51 0.06/0.56 * CEs [52] --> Loop 52 0.06/0.56 * CEs [60] --> Loop 53 0.06/0.56 * CEs [51] --> Loop 54 0.06/0.56 * CEs [58] --> Loop 55 0.06/0.56 * CEs [49] --> Loop 56 0.06/0.56 * CEs [57] --> Loop 57 0.06/0.56 * CEs [48] --> Loop 58 0.06/0.56 * CEs [47] --> Loop 59 0.06/0.56 0.06/0.56 ### Ranking functions of CR eval_inflate_stored_bb0_in(V_n,V_k,V_limit,B) 0.06/0.56 0.06/0.56 #### Partial ranking functions of CR eval_inflate_stored_bb0_in(V_n,V_k,V_limit,B) 0.06/0.56 0.06/0.56 0.06/0.56 ### Specialization of cost equations eval_inflate_stored_start/4 0.06/0.56 * CE 1 is refined into CE [62,63,64,65,66,67,68,69,70,71,72,73,74,75,76] 0.06/0.56 0.06/0.56 0.06/0.56 ### Cost equations --> "Loop" of eval_inflate_stored_start/4 0.06/0.56 * CEs [76] --> Loop 60 0.06/0.56 * CEs [75] --> Loop 61 0.06/0.56 * CEs [74] --> Loop 62 0.06/0.56 * CEs [73] --> Loop 63 0.06/0.56 * CEs [72] --> Loop 64 0.06/0.56 * CEs [71] --> Loop 65 0.06/0.56 * CEs [70] --> Loop 66 0.06/0.56 * CEs [69] --> Loop 67 0.06/0.56 * CEs [68] --> Loop 68 0.06/0.56 * CEs [67] --> Loop 69 0.06/0.56 * CEs [66] --> Loop 70 0.06/0.56 * CEs [65] --> Loop 71 0.06/0.56 * CEs [64] --> Loop 72 0.06/0.56 * CEs [63] --> Loop 73 0.06/0.56 * CEs [62] --> Loop 74 0.06/0.56 0.06/0.56 ### Ranking functions of CR eval_inflate_stored_start(V_n,V_k,V_limit,B) 0.06/0.56 0.06/0.56 #### Partial ranking functions of CR eval_inflate_stored_start(V_n,V_k,V_limit,B) 0.06/0.56 0.06/0.56 0.06/0.56 Computing Bounds 0.06/0.56 ===================================== 0.06/0.56 0.06/0.56 #### Cost of chains of eval_inflate_stored_bb1_in(V__01,B,C): 0.06/0.56 * Chain [[16],17]: 1*it(16)+0 0.06/0.56 Such that:it(16) =< -V__01/8+2 0.06/0.56 0.06/0.56 with precondition: [B=3,23>=C,C>=16,C>=V__01+8] 0.06/0.56 0.06/0.56 * Chain [17]: 0 0.06/0.56 with precondition: [B=3,V__01=C,V__01>=16] 0.06/0.56 0.06/0.56 0.06/0.56 #### Cost of chains of eval_inflate_stored_bb4_in(V__1,B,C): 0.06/0.56 * Chain [[18],19]: 1*it(18)+0 0.06/0.56 Such that:it(18) =< -V__1/8+2 0.06/0.56 0.06/0.56 with precondition: [B=4,23>=C,C>=16,C>=V__1+8] 0.06/0.56 0.06/0.56 * Chain [19]: 0 0.06/0.56 with precondition: [B=4,V__1=C,V__1>=16] 0.06/0.56 0.06/0.56 0.06/0.56 #### Cost of chains of eval_inflate_stored_bb9_in(V_limit,V__3,B,C): 0.06/0.56 * Chain [[20],21]: 1*it(20)+0 0.06/0.56 Such that:it(20) =< V_limit/8-V__3/8 0.06/0.56 0.06/0.56 with precondition: [B=2,C>=V_limit,C>=V__3+8,V_limit+7>=C] 0.06/0.56 0.06/0.56 * Chain [21]: 0 0.06/0.56 with precondition: [B=2,V__3=C,V__3>=V_limit] 0.06/0.56 0.06/0.56 0.06/0.56 #### Cost of chains of eval_inflate_stored_bb8_in(V_limit,V__2,V__0,B): 0.06/0.56 * Chain [[23],[22],24]: 1*it(22)+1*it(23)+1*s(3)+0 0.06/0.56 Such that:it(23) =< -V_limit/8+V__2/8+1/8 0.06/0.56 it(22) =< V__0 0.06/0.56 aux(1) =< V_limit/8-V__2/8+V__0 0.06/0.56 it(22) =< aux(1) 0.06/0.56 s(3) =< aux(1) 0.06/0.56 0.06/0.56 with precondition: [B=5,V__0>=2,V__2>=V_limit,V_limit+8*V__0>=V__2+9] 0.06/0.56 0.06/0.56 * Chain [[23],24]: 1*it(23)+0 0.06/0.56 Such that:it(23) =< -V_limit/8+V__2/8+1/8 0.06/0.56 it(23) =< V__0 0.06/0.56 0.06/0.56 with precondition: [B=5,V__0>=1,V__2+8>=8*V__0+V_limit] 0.06/0.56 0.06/0.56 * Chain [[22],24]: 1*it(22)+1*s(3)+0 0.06/0.56 Such that:s(3) =< V_limit/8-V__2/8+V__0 0.06/0.56 it(22) =< V__0 0.06/0.56 0.06/0.56 with precondition: [B=5,V__0>=1,V_limit>=V__2+1] 0.06/0.56 0.06/0.56 * Chain [24]: 0 0.06/0.56 with precondition: [B=5,0>=V__0] 0.06/0.56 0.06/0.56 0.06/0.56 #### Cost of chains of eval_inflate_stored_bb7_in(V_n,V_limit,V__1,B): 0.06/0.56 * Chain [28]: 0 0.06/0.56 with precondition: [0>=V_n] 0.06/0.56 0.06/0.56 * Chain [27]: 1*s(4)+1*s(5)+0 0.06/0.56 Such that:s(5) =< V_n 0.06/0.56 s(4) =< V_n+V_limit/8-V__1/8+2 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,V_limit+15>=V__1] 0.06/0.56 0.06/0.56 * Chain [26]: 1*s(6)+0 0.06/0.56 Such that:s(6) =< V_n 0.06/0.56 s(6) =< -V_limit/8+V__1/8 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,V__1>=8*V_n+V_limit+8] 0.06/0.56 0.06/0.56 * Chain [25]: 1*s(7)+1*s(8)+1*s(10)+0 0.06/0.56 Such that:s(8) =< V_n 0.06/0.56 s(9) =< V_n+V_limit/8-V__1/8+2 0.06/0.56 s(7) =< -V_limit/8+V__1/8 0.06/0.56 s(8) =< s(9) 0.06/0.56 s(10) =< s(9) 0.06/0.56 0.06/0.56 with precondition: [V_n>=2,V__1>=V_limit+16,V_limit+8*V_n+7>=V__1] 0.06/0.56 0.06/0.56 0.06/0.56 #### Cost of chains of eval_inflate_stored_9(V_n,V_limit,V__1,V_6,B): 0.06/0.56 * Chain [34]: 0 0.06/0.56 with precondition: [V_6=0,0>=V_n] 0.06/0.56 0.06/0.56 * Chain [33]: 1*s(11)+1*s(12)+0 0.06/0.56 Such that:s(11) =< V_n 0.06/0.56 s(12) =< V_n+V_limit/8-V__1/8+2 0.06/0.56 0.06/0.56 with precondition: [V_6=0,V_n>=1,V_limit+15>=V__1] 0.06/0.56 0.06/0.56 * Chain [32]: 1*s(13)+0 0.06/0.56 Such that:s(13) =< V_n 0.06/0.56 0.06/0.56 with precondition: [V_6=0,V_n>=1,V__1>=8*V_n+V_limit+8] 0.06/0.56 0.06/0.56 * Chain [31]: 1*s(14)+1*s(16)+1*s(17)+0 0.06/0.56 Such that:s(14) =< V_n 0.06/0.56 s(15) =< V_n+V_limit/8-V__1/8+2 0.06/0.56 s(16) =< -V_limit/8+V__1/8 0.06/0.56 s(14) =< s(15) 0.06/0.56 s(17) =< s(15) 0.06/0.56 0.06/0.56 with precondition: [V_6=0,V_n>=2,V__1>=V_limit+16,V_limit+8*V_n+7>=V__1] 0.06/0.56 0.06/0.56 * Chain [30]: 0 0.06/0.56 with precondition: [0>=V_6+1] 0.06/0.56 0.06/0.56 * Chain [29]: 0 0.06/0.56 with precondition: [V_6>=1] 0.06/0.56 0.06/0.56 0.06/0.56 #### Cost of chains of eval_inflate_stored_bb3_in(V_n,V_limit,V__01,B): 0.06/0.56 * Chain [44]: 1*s(18)+0 0.06/0.56 Such that:s(18) =< -V__01/8+4 0.06/0.56 0.06/0.56 with precondition: [0>=V_n,31>=V__01] 0.06/0.56 0.06/0.56 * Chain [43]: 0 0.06/0.56 with precondition: [0>=V_n,V__01>=32] 0.06/0.56 0.06/0.56 * Chain [42]: 1*s(19)+1*s(20)+1*s(22)+1*s(23)+0 0.06/0.56 Such that:s(20) =< V_n 0.06/0.56 s(21) =< V_n+V_limit/8-V__01/8+3 0.06/0.56 s(22) =< -V_limit/8+23/8 0.06/0.56 s(19) =< -V__01/8+4 0.06/0.56 aux(2) =< V_n+2 0.06/0.56 s(21) =< aux(2) 0.06/0.56 s(22) =< aux(2) 0.06/0.56 s(20) =< s(21) 0.06/0.56 s(23) =< s(21) 0.06/0.56 0.06/0.56 with precondition: [7>=V_limit,31>=V__01,V_n>=2,V_limit+8*V_n>=9,V_limit+8*V_n+15>=V__01] 0.06/0.56 0.06/0.56 * Chain [41]: 2*s(24)+0 0.06/0.56 Such that:aux(3) =< -V__01/8+4 0.06/0.56 s(24) =< aux(3) 0.06/0.56 0.06/0.56 with precondition: [31>=V__01] 0.06/0.56 0.06/0.56 * Chain [40]: 1*s(26)+1*s(27)+1*s(28)+0 0.06/0.56 Such that:s(27) =< V_n 0.06/0.56 s(28) =< V_n+V_limit/8 0.06/0.56 s(28) =< V_n+V_limit/8-V__01/8+3 0.06/0.56 s(26) =< -V__01/8+4 0.06/0.56 0.06/0.56 with precondition: [31>=V__01,V_n>=1,V_limit>=1,V_limit+23>=V__01] 0.06/0.56 0.06/0.56 * Chain [39]: 1*s(29)+1*s(30)+0 0.06/0.56 Such that:s(30) =< V_n 0.06/0.56 s(29) =< -V__01/8+4 0.06/0.56 0.06/0.56 with precondition: [31>=V__01,V_n>=1,15>=8*V_n+V_limit] 0.06/0.56 0.06/0.56 * Chain [38]: 1*s(31)+1*s(32)+0 0.06/0.56 Such that:s(31) =< V_n 0.06/0.56 s(32) =< V_n+V_limit/8-V__01/8+4 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,V__01>=32,V_limit+31>=V__01] 0.06/0.56 0.06/0.56 * Chain [37]: 1*s(33)+0 0.06/0.56 Such that:s(33) =< V_n 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,V__01>=32,V__01>=8*V_n+V_limit+24] 0.06/0.56 0.06/0.56 * Chain [36]: 1*s(34)+1*s(36)+1*s(37)+0 0.06/0.56 Such that:s(34) =< V_n 0.06/0.56 s(35) =< V_n+V_limit/8-V__01/8+4 0.06/0.56 s(36) =< -V_limit/8+V__01/8 0.06/0.56 s(34) =< s(35) 0.06/0.56 s(37) =< s(35) 0.06/0.56 0.06/0.56 with precondition: [V_n>=2,V__01>=32,V__01>=V_limit+32,V_limit+8*V_n+23>=V__01] 0.06/0.56 0.06/0.56 * Chain [35]: 0 0.06/0.56 with precondition: [V__01>=32] 0.06/0.56 0.06/0.56 0.06/0.56 #### Cost of chains of eval_inflate_stored_bb0_in(V_n,V_k,V_limit,B): 0.06/0.56 * Chain [59]: 1*s(38)+0 0.06/0.56 Such that:s(38) =< V_n/8-V_k/8+4 0.06/0.56 0.06/0.56 with precondition: [0>=V_n,V_k>=V_n+16,V_n+31>=V_k] 0.06/0.56 0.06/0.56 * Chain [58]: 0 0.06/0.56 with precondition: [0>=V_n,V_k>=V_n+32] 0.06/0.56 0.06/0.56 * Chain [57]: 1*s(39)+1*s(40)+0 0.06/0.56 Such that:s(40) =< 2 0.06/0.56 s(39) =< V_n/8-V_k/8+2 0.06/0.56 s(40) =< V_n/8-V_k/8+3 0.06/0.56 0.06/0.56 with precondition: [0>=V_n,V_n+15>=V_k] 0.06/0.56 0.06/0.56 * Chain [56]: 1*s(41)+1*s(43)+1*s(44)+1*s(46)+0 0.06/0.56 Such that:s(41) =< V_n 0.06/0.56 s(45) =< V_n+2 0.06/0.56 s(44) =< V_n/8-V_k/8+4 0.06/0.56 s(42) =< 9/8*V_n-V_k/8+V_limit/8+3 0.06/0.56 s(43) =< -V_limit/8+23/8 0.06/0.56 s(42) =< s(45) 0.06/0.56 s(43) =< s(45) 0.06/0.56 s(41) =< s(42) 0.06/0.56 s(46) =< s(42) 0.06/0.56 0.06/0.56 with precondition: [7>=V_limit,V_n>=2,V_k>=V_n+16,V_n+31>=V_k,V_limit+8*V_n>=9,V_limit+9*V_n+15>=V_k] 0.06/0.56 0.06/0.56 * Chain [55]: 1*s(47)+1*s(48)+1*s(50)+1*s(51)+1*s(53)+0 0.06/0.56 Such that:s(51) =< 2 0.06/0.56 s(48) =< V_n 0.06/0.56 s(52) =< V_n+2 0.06/0.56 s(49) =< V_n+V_limit/8+1 0.06/0.56 s(47) =< V_n/8-V_k/8+2 0.06/0.56 s(51) =< V_n/8-V_k/8+3 0.06/0.56 s(49) =< 9/8*V_n-V_k/8+V_limit/8+2 0.06/0.56 s(50) =< -V_limit/8+23/8 0.06/0.56 s(49) =< s(52) 0.06/0.56 s(50) =< s(52) 0.06/0.56 s(48) =< s(49) 0.06/0.56 s(53) =< s(49) 0.06/0.56 0.06/0.56 with precondition: [7>=V_limit,V_n>=2,V_n+15>=V_k,V_limit+8*V_n>=9] 0.06/0.56 0.06/0.56 * Chain [54]: 1*s(54)+1*s(55)+1*s(56)+0 0.06/0.56 Such that:s(54) =< V_n 0.06/0.56 s(55) =< V_n+V_limit/8 0.06/0.56 s(56) =< V_n/8-V_k/8+4 0.06/0.56 s(55) =< 9/8*V_n-V_k/8+V_limit/8+3 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,V_limit>=1,V_k>=V_n+16,V_n+31>=V_k,V_limit+V_n+23>=V_k] 0.06/0.56 0.06/0.56 * Chain [53]: 1*s(57)+1*s(58)+1*s(59)+1*s(60)+0 0.06/0.56 Such that:s(60) =< 2 0.06/0.56 s(58) =< V_n 0.06/0.56 s(59) =< V_n+V_limit/8 0.06/0.56 s(57) =< V_n/8-V_k/8+2 0.06/0.56 s(60) =< V_n/8-V_k/8+3 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,V_limit>=1,V_n+15>=V_k] 0.06/0.56 0.06/0.56 * Chain [52]: 1*s(61)+1*s(62)+0 0.06/0.56 Such that:s(61) =< V_n 0.06/0.56 s(62) =< V_n/8-V_k/8+4 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,15>=8*V_n+V_limit,V_k>=V_n+16,V_n+31>=V_k] 0.06/0.56 0.06/0.56 * Chain [51]: 1*s(63)+1*s(64)+1*s(65)+0 0.06/0.56 Such that:s(65) =< 2 0.06/0.56 s(64) =< V_n 0.06/0.56 s(63) =< V_n/8-V_k/8+2 0.06/0.56 s(65) =< V_n/8-V_k/8+3 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,15>=8*V_n+V_limit,V_n+15>=V_k] 0.06/0.56 0.06/0.56 * Chain [50]: 1*s(66)+0 0.06/0.56 Such that:s(66) =< V_n 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,V_k>=V_n+32,V_k>=9*V_n+V_limit+24] 0.06/0.56 0.06/0.56 * Chain [49]: 1*s(67)+1*s(68)+0 0.06/0.56 Such that:s(67) =< V_n 0.06/0.56 s(68) =< 9/8*V_n-V_k/8+V_limit/8+4 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,V_k>=V_n+32,V_limit+V_n+31>=V_k] 0.06/0.56 0.06/0.56 * Chain [48]: 1*s(69)+1*s(71)+1*s(72)+0 0.06/0.56 Such that:s(69) =< V_n 0.06/0.56 s(71) =< -V_n/8+V_k/8-V_limit/8 0.06/0.56 s(70) =< 9/8*V_n-V_k/8+V_limit/8+4 0.06/0.56 s(69) =< s(70) 0.06/0.56 s(72) =< s(70) 0.06/0.56 0.06/0.56 with precondition: [V_n>=2,V_k>=V_n+32,V_k>=V_limit+V_n+32,V_limit+9*V_n+23>=V_k] 0.06/0.56 0.06/0.56 * Chain [47]: 2*s(74)+0 0.06/0.56 Such that:s(73) =< V_n/8-V_k/8+4 0.06/0.56 s(74) =< s(73) 0.06/0.56 0.06/0.56 with precondition: [V_k>=V_n+16,V_n+31>=V_k] 0.06/0.56 0.06/0.56 * Chain [46]: 0 0.06/0.56 with precondition: [V_k>=V_n+32] 0.06/0.56 0.06/0.56 * Chain [45]: 1*s(75)+2*s(77)+0 0.06/0.56 Such that:s(76) =< 2 0.06/0.56 s(75) =< V_n/8-V_k/8+2 0.06/0.56 s(76) =< V_n/8-V_k/8+3 0.06/0.56 s(77) =< s(76) 0.06/0.56 0.06/0.56 with precondition: [V_n+15>=V_k] 0.06/0.56 0.06/0.56 0.06/0.56 #### Cost of chains of eval_inflate_stored_start(V_n,V_k,V_limit,B): 0.06/0.56 * Chain [74]: 1*s(78)+0 0.06/0.56 Such that:s(78) =< V_n/8-V_k/8+4 0.06/0.56 0.06/0.56 with precondition: [0>=V_n,V_k>=V_n+16,V_n+31>=V_k] 0.06/0.56 0.06/0.56 * Chain [73]: 0 0.06/0.56 with precondition: [0>=V_n,V_k>=V_n+32] 0.06/0.56 0.06/0.56 * Chain [72]: 1*s(79)+1*s(80)+0 0.06/0.56 Such that:s(79) =< 2 0.06/0.56 s(80) =< V_n/8-V_k/8+2 0.06/0.56 s(79) =< V_n/8-V_k/8+3 0.06/0.56 0.06/0.56 with precondition: [0>=V_n,V_n+15>=V_k] 0.06/0.56 0.06/0.56 * Chain [71]: 1*s(81)+1*s(83)+1*s(85)+1*s(86)+0 0.06/0.56 Such that:s(81) =< V_n 0.06/0.56 s(82) =< V_n+2 0.06/0.56 s(83) =< V_n/8-V_k/8+4 0.06/0.56 s(84) =< 9/8*V_n-V_k/8+V_limit/8+3 0.06/0.56 s(85) =< -V_limit/8+23/8 0.06/0.56 s(84) =< s(82) 0.06/0.56 s(85) =< s(82) 0.06/0.56 s(81) =< s(84) 0.06/0.56 s(86) =< s(84) 0.06/0.56 0.06/0.56 with precondition: [7>=V_limit,V_n>=2,V_k>=V_n+16,V_n+31>=V_k,V_limit+8*V_n>=9,V_limit+9*V_n+15>=V_k] 0.06/0.56 0.06/0.56 * Chain [70]: 1*s(87)+1*s(88)+1*s(91)+1*s(92)+1*s(93)+0 0.06/0.56 Such that:s(87) =< 2 0.06/0.56 s(88) =< V_n 0.06/0.56 s(89) =< V_n+2 0.06/0.56 s(90) =< V_n+V_limit/8+1 0.06/0.56 s(91) =< V_n/8-V_k/8+2 0.06/0.56 s(87) =< V_n/8-V_k/8+3 0.06/0.56 s(90) =< 9/8*V_n-V_k/8+V_limit/8+2 0.06/0.56 s(92) =< -V_limit/8+23/8 0.06/0.56 s(90) =< s(89) 0.06/0.56 s(92) =< s(89) 0.06/0.56 s(88) =< s(90) 0.06/0.56 s(93) =< s(90) 0.06/0.56 0.06/0.56 with precondition: [7>=V_limit,V_n>=2,V_n+15>=V_k,V_limit+8*V_n>=9] 0.06/0.56 0.06/0.56 * Chain [69]: 1*s(94)+1*s(95)+1*s(96)+0 0.06/0.56 Such that:s(94) =< V_n 0.06/0.56 s(95) =< V_n+V_limit/8 0.06/0.56 s(96) =< V_n/8-V_k/8+4 0.06/0.56 s(95) =< 9/8*V_n-V_k/8+V_limit/8+3 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,V_limit>=1,V_k>=V_n+16,V_n+31>=V_k,V_limit+V_n+23>=V_k] 0.06/0.56 0.06/0.56 * Chain [68]: 1*s(97)+1*s(98)+1*s(99)+1*s(100)+0 0.06/0.56 Such that:s(97) =< 2 0.06/0.56 s(98) =< V_n 0.06/0.56 s(99) =< V_n+V_limit/8 0.06/0.56 s(100) =< V_n/8-V_k/8+2 0.06/0.56 s(97) =< V_n/8-V_k/8+3 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,V_limit>=1,V_n+15>=V_k] 0.06/0.56 0.06/0.56 * Chain [67]: 1*s(101)+1*s(102)+0 0.06/0.56 Such that:s(101) =< V_n 0.06/0.56 s(102) =< V_n/8-V_k/8+4 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,15>=8*V_n+V_limit,V_k>=V_n+16,V_n+31>=V_k] 0.06/0.56 0.06/0.56 * Chain [66]: 1*s(103)+1*s(104)+1*s(105)+0 0.06/0.56 Such that:s(103) =< 2 0.06/0.56 s(104) =< V_n 0.06/0.56 s(105) =< V_n/8-V_k/8+2 0.06/0.56 s(103) =< V_n/8-V_k/8+3 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,15>=8*V_n+V_limit,V_n+15>=V_k] 0.06/0.56 0.06/0.56 * Chain [65]: 1*s(106)+0 0.06/0.56 Such that:s(106) =< V_n 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,V_k>=V_n+32,V_k>=9*V_n+V_limit+24] 0.06/0.56 0.06/0.56 * Chain [64]: 1*s(107)+1*s(108)+0 0.06/0.56 Such that:s(107) =< V_n 0.06/0.56 s(108) =< 9/8*V_n-V_k/8+V_limit/8+4 0.06/0.56 0.06/0.56 with precondition: [V_n>=1,V_k>=V_n+32,V_limit+V_n+31>=V_k] 0.06/0.56 0.06/0.56 * Chain [63]: 1*s(109)+1*s(110)+1*s(112)+0 0.06/0.56 Such that:s(109) =< V_n 0.06/0.56 s(110) =< -V_n/8+V_k/8-V_limit/8 0.06/0.56 s(111) =< 9/8*V_n-V_k/8+V_limit/8+4 0.06/0.56 s(109) =< s(111) 0.06/0.56 s(112) =< s(111) 0.06/0.56 0.06/0.56 with precondition: [V_n>=2,V_k>=V_n+32,V_k>=V_limit+V_n+32,V_limit+9*V_n+23>=V_k] 0.06/0.56 0.06/0.56 * Chain [62]: 2*s(114)+0 0.06/0.56 Such that:s(113) =< V_n/8-V_k/8+4 0.06/0.56 s(114) =< s(113) 0.06/0.56 0.06/0.56 with precondition: [V_k>=V_n+16,V_n+31>=V_k] 0.06/0.56 0.06/0.56 * Chain [61]: 0 0.06/0.56 with precondition: [V_k>=V_n+32] 0.06/0.56 0.06/0.56 * Chain [60]: 1*s(116)+2*s(117)+0 0.06/0.56 Such that:s(115) =< 2 0.06/0.56 s(116) =< V_n/8-V_k/8+2 0.06/0.56 s(115) =< V_n/8-V_k/8+3 0.06/0.56 s(117) =< s(115) 0.06/0.56 0.06/0.56 with precondition: [V_n+15>=V_k] 0.06/0.56 0.06/0.56 0.06/0.56 Closed-form bounds of eval_inflate_stored_start(V_n,V_k,V_limit,B): 0.06/0.56 ------------------------------------- 0.06/0.56 * Chain [74] with precondition: [0>=V_n,V_k>=V_n+16,V_n+31>=V_k] 0.06/0.56 - Upper bound: V_n/8-V_k/8+4 0.06/0.56 - Complexity: n 0.06/0.56 * Chain [73] with precondition: [0>=V_n,V_k>=V_n+32] 0.06/0.56 - Upper bound: 0 0.06/0.56 - Complexity: constant 0.06/0.56 * Chain [72] with precondition: [0>=V_n,V_n+15>=V_k] 0.06/0.56 - Upper bound: V_n/8-V_k/8+4 0.06/0.56 - Complexity: n 0.06/0.56 * Chain [71] with precondition: [7>=V_limit,V_n>=2,V_k>=V_n+16,V_n+31>=V_k,V_limit+8*V_n>=9,V_limit+9*V_n+15>=V_k] 0.06/0.56 - Upper bound: 9/4*V_n-V_k/4+79/8 0.06/0.56 - Complexity: n 0.06/0.56 * Chain [70] with precondition: [7>=V_limit,V_n>=2,V_n+15>=V_k,V_limit+8*V_n>=9] 0.06/0.56 - Upper bound: 17/8*V_n-V_k/8+63/8 0.06/0.56 - Complexity: n 0.06/0.56 * Chain [69] with precondition: [V_n>=1,V_limit>=1,V_k>=V_n+16,V_n+31>=V_k,V_n+V_limit+23>=V_k] 0.06/0.56 - Upper bound: 17/8*V_n-V_k/8+V_limit/8+4 0.06/0.56 - Complexity: n 0.06/0.56 * Chain [68] with precondition: [V_n>=1,V_limit>=1,V_n+15>=V_k] 0.06/0.56 - Upper bound: 17/8*V_n-V_k/8+V_limit/8+4 0.06/0.56 - Complexity: n 0.06/0.56 * Chain [67] with precondition: [V_n>=1,15>=8*V_n+V_limit,V_k>=V_n+16,V_n+31>=V_k] 0.06/0.56 - Upper bound: 9/8*V_n-V_k/8+4 0.06/0.56 - Complexity: n 0.06/0.56 * Chain [66] with precondition: [V_n>=1,15>=8*V_n+V_limit,V_n+15>=V_k] 0.06/0.56 - Upper bound: 9/8*V_n-V_k/8+4 0.06/0.56 - Complexity: n 0.06/0.56 * Chain [65] with precondition: [V_n>=1,V_k>=V_n+32,V_k>=9*V_n+V_limit+24] 0.06/0.56 - Upper bound: V_n 0.06/0.56 - Complexity: n 0.06/0.56 * Chain [64] with precondition: [V_n>=1,V_k>=V_n+32,V_n+V_limit+31>=V_k] 0.06/0.56 - Upper bound: 17/8*V_n-V_k/8+V_limit/8+4 0.06/0.56 - Complexity: n 0.06/0.56 * Chain [63] with precondition: [V_n>=2,V_k>=V_n+32,V_k>=V_n+V_limit+32,V_limit+9*V_n+23>=V_k] 0.06/0.56 - Upper bound: 2*V_n+4 0.06/0.56 - Complexity: n 0.06/0.56 * Chain [62] with precondition: [V_k>=V_n+16,V_n+31>=V_k] 0.06/0.56 - Upper bound: V_n/4-V_k/4+8 0.06/0.56 - Complexity: n 0.06/0.56 * Chain [61] with precondition: [V_k>=V_n+32] 0.06/0.56 - Upper bound: 0 0.06/0.56 - Complexity: constant 0.06/0.56 * Chain [60] with precondition: [V_n+15>=V_k] 0.06/0.56 - Upper bound: V_n/8-V_k/8+6 0.06/0.56 - Complexity: n 0.06/0.56 0.06/0.56 ### Maximum cost of eval_inflate_stored_start(V_n,V_k,V_limit,B): max([max([nat(V_n/8-V_k/8+4)*2,nat(V_n/8-V_k/8+2)+4]),nat(V_n)+max([max([nat(V_n/8-V_k/8+4)+max([nat(V_n+V_limit/8),nat(-V_limit/8+23/8)+nat(9/8*V_n-V_k/8+V_limit/8+3)]),nat(-V_n/8+V_k/8-V_limit/8)+nat(9/8*V_n-V_k/8+V_limit/8+4)]),nat(V_n/8-V_k/8+2)+2+max([nat(V_n+V_limit/8),nat(-V_limit/8+23/8)+nat(V_n+V_limit/8+1)])])]) 0.06/0.56 Asymptotic class: n 0.06/0.56 * Total analysis performed in 471 ms. 0.06/0.56 0.57/0.67 EOF