0.05/0.48 WORST_CASE(?,O(n^1)) 0.05/0.48 0.05/0.48 Preprocessing Cost Relations 0.05/0.48 ===================================== 0.05/0.48 0.05/0.48 #### Computed strongly connected components 0.05/0.48 0. recursive : [eval_foo_bb1_in/5,eval_foo_bb2_in/5] 0.05/0.48 1. recursive : [eval_foo_bb5_in/7,eval_foo_bb6_in/7] 0.05/0.48 2. recursive : [eval_foo_bb3_in/3,eval_foo_bb4_in/3,eval_foo_bb5_in_loop_cont/4] 0.05/0.48 3. non_recursive : [eval_foo_stop/1] 0.05/0.48 4. non_recursive : [eval_foo_bb7_in/1] 0.05/0.48 5. non_recursive : [eval_foo_bb3_in_loop_cont/2] 0.05/0.48 6. non_recursive : [eval_foo_bb1_in_loop_cont/4] 0.05/0.48 7. non_recursive : [eval_foo_bb0_in/3] 0.05/0.48 8. non_recursive : [eval_foo_start/4] 0.05/0.48 0.05/0.48 #### Obtained direct recursion through partial evaluation 0.05/0.48 0. SCC is partially evaluated into eval_foo_bb1_in/5 0.05/0.48 1. SCC is partially evaluated into eval_foo_bb5_in/7 0.05/0.48 2. SCC is partially evaluated into eval_foo_bb3_in/3 0.05/0.48 3. SCC is completely evaluated into other SCCs 0.05/0.48 4. SCC is completely evaluated into other SCCs 0.05/0.48 5. SCC is completely evaluated into other SCCs 0.05/0.48 6. SCC is partially evaluated into eval_foo_bb1_in_loop_cont/4 0.05/0.48 7. SCC is partially evaluated into eval_foo_bb0_in/3 0.05/0.48 8. SCC is partially evaluated into eval_foo_start/4 0.05/0.48 0.05/0.48 Control-Flow Refinement of Cost Relations 0.05/0.48 ===================================== 0.05/0.48 0.05/0.48 ### Specialization of cost equations eval_foo_bb1_in/5 0.05/0.48 * CE 4 is refined into CE [12] 0.05/0.48 * CE 5 is refined into CE [13] 0.05/0.48 * CE 3 is refined into CE [14] 0.05/0.48 0.05/0.48 0.05/0.48 ### Cost equations --> "Loop" of eval_foo_bb1_in/5 0.05/0.48 * CEs [14] --> Loop 12 0.05/0.48 * CEs [12] --> Loop 13 0.05/0.48 * CEs [13] --> Loop 14 0.05/0.48 0.05/0.48 ### Ranking functions of CR eval_foo_bb1_in(V__01,V__0,B,C,D) 0.05/0.48 * RF of phase [12]: [V__0,V__01] 0.05/0.48 0.05/0.48 #### Partial ranking functions of CR eval_foo_bb1_in(V__01,V__0,B,C,D) 0.05/0.48 * Partial RF of phase [12]: 0.05/0.48 - RF of loop [12:1]: 0.05/0.48 V__0 0.05/0.48 V__01 0.05/0.48 0.05/0.48 0.05/0.48 ### Specialization of cost equations eval_foo_bb5_in/7 0.05/0.48 * CE 10 is refined into CE [15] 0.05/0.48 * CE 11 is refined into CE [16] 0.05/0.48 * CE 9 is refined into CE [17] 0.05/0.48 0.05/0.48 0.05/0.48 ### Cost equations --> "Loop" of eval_foo_bb5_in/7 0.05/0.48 * CEs [17] --> Loop 15 0.05/0.48 * CEs [15] --> Loop 16 0.05/0.48 * CEs [16] --> Loop 17 0.05/0.48 0.05/0.48 ### Ranking functions of CR eval_foo_bb5_in(V__12,V__1,V__23,V__2,B,C,D) 0.05/0.48 * RF of phase [15]: [-V__12+V__1+V__23-1,V__12-V__1+V__2+1,V__2,V__23] 0.05/0.48 0.05/0.48 #### Partial ranking functions of CR eval_foo_bb5_in(V__12,V__1,V__23,V__2,B,C,D) 0.05/0.48 * Partial RF of phase [15]: 0.05/0.48 - RF of loop [15:1]: 0.05/0.48 -V__12+V__1+V__23-1 0.05/0.48 V__12-V__1+V__2+1 0.05/0.48 V__2 0.05/0.48 V__23 0.05/0.48 0.05/0.48 0.05/0.48 ### Specialization of cost equations eval_foo_bb3_in/3 0.05/0.48 * CE 8 is refined into CE [18] 0.05/0.48 * CE 7 is refined into CE [19,20,21] 0.05/0.48 0.05/0.48 0.05/0.48 ### Cost equations --> "Loop" of eval_foo_bb3_in/3 0.05/0.48 * CEs [21] --> Loop 18 0.05/0.48 * CEs [20] --> Loop 19 0.05/0.48 * CEs [19] --> Loop 20 0.05/0.48 * CEs [18] --> Loop 21 0.05/0.48 0.05/0.48 ### Ranking functions of CR eval_foo_bb3_in(V__12,V__1,B) 0.05/0.48 * RF of phase [18]: [-V__12] 0.05/0.48 * RF of phase [20]: [V__1,-V__12+V__1] 0.05/0.48 0.05/0.48 #### Partial ranking functions of CR eval_foo_bb3_in(V__12,V__1,B) 0.05/0.48 * Partial RF of phase [18]: 0.05/0.48 - RF of loop [18:1]: 0.05/0.48 -V__12 0.05/0.48 * Partial RF of phase [20]: 0.05/0.48 - RF of loop [20:1]: 0.05/0.48 V__1 0.05/0.48 -V__12+V__1 0.05/0.48 0.05/0.48 0.05/0.48 ### Specialization of cost equations eval_foo_bb1_in_loop_cont/4 0.05/0.48 * CE 6 is refined into CE [22,23,24,25,26,27,28] 0.05/0.48 0.05/0.48 0.05/0.48 ### Cost equations --> "Loop" of eval_foo_bb1_in_loop_cont/4 0.05/0.48 * CEs [28] --> Loop 22 0.05/0.48 * CEs [27] --> Loop 23 0.05/0.48 * CEs [26] --> Loop 24 0.05/0.48 * CEs [25] --> Loop 25 0.05/0.48 * CEs [24] --> Loop 26 0.05/0.48 * CEs [23] --> Loop 27 0.05/0.48 * CEs [22] --> Loop 28 0.05/0.48 0.05/0.48 ### Ranking functions of CR eval_foo_bb1_in_loop_cont(A,B,C,D) 0.05/0.48 0.05/0.48 #### Partial ranking functions of CR eval_foo_bb1_in_loop_cont(A,B,C,D) 0.05/0.48 0.05/0.48 0.05/0.48 ### Specialization of cost equations eval_foo_bb0_in/3 0.05/0.48 * CE 2 is refined into CE [29,30,31,32,33,34,35,36,37,38,39,40,41] 0.05/0.48 0.05/0.48 0.05/0.48 ### Cost equations --> "Loop" of eval_foo_bb0_in/3 0.05/0.48 * CEs [31] --> Loop 29 0.05/0.48 * CEs [30] --> Loop 30 0.05/0.48 * CEs [33] --> Loop 31 0.05/0.48 * CEs [37] --> Loop 32 0.05/0.48 * CEs [36] --> Loop 33 0.05/0.48 * CEs [38] --> Loop 34 0.05/0.48 * CEs [34] --> Loop 35 0.05/0.48 * CEs [32] --> Loop 36 0.05/0.48 * CEs [29] --> Loop 37 0.05/0.48 * CEs [40] --> Loop 38 0.05/0.48 * CEs [39] --> Loop 39 0.05/0.48 * CEs [35] --> Loop 40 0.05/0.48 * CEs [41] --> Loop 41 0.05/0.48 0.05/0.48 ### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 0.05/0.48 0.05/0.48 #### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 0.05/0.48 0.05/0.48 0.05/0.48 ### Specialization of cost equations eval_foo_start/4 0.05/0.48 * CE 1 is refined into CE [42,43,44,45,46,47,48,49,50,51,52,53,54] 0.05/0.48 0.05/0.48 0.05/0.48 ### Cost equations --> "Loop" of eval_foo_start/4 0.05/0.48 * CEs [54] --> Loop 42 0.05/0.48 * CEs [53] --> Loop 43 0.05/0.48 * CEs [52] --> Loop 44 0.05/0.48 * CEs [51] --> Loop 45 0.05/0.48 * CEs [50] --> Loop 46 0.05/0.48 * CEs [49] --> Loop 47 0.05/0.48 * CEs [48] --> Loop 48 0.05/0.48 * CEs [47] --> Loop 49 0.05/0.48 * CEs [46] --> Loop 50 0.05/0.48 * CEs [45] --> Loop 51 0.05/0.48 * CEs [44] --> Loop 52 0.05/0.48 * CEs [43] --> Loop 53 0.05/0.48 * CEs [42] --> Loop 54 0.05/0.48 0.05/0.48 ### Ranking functions of CR eval_foo_start(V_x,V_y,V_res,B) 0.05/0.48 0.05/0.48 #### Partial ranking functions of CR eval_foo_start(V_x,V_y,V_res,B) 0.05/0.48 0.05/0.48 0.05/0.48 Computing Bounds 0.05/0.48 ===================================== 0.05/0.48 0.05/0.48 #### Cost of chains of eval_foo_bb1_in(V__01,V__0,B,C,D): 0.05/0.48 * Chain [[12],14]: 1*it(12)+0 0.05/0.48 Such that:it(12) =< V__01 0.05/0.48 0.05/0.48 with precondition: [B=2,C=0,V__01+D=V__0,V__01>=1,V__0>=V__01] 0.05/0.48 0.05/0.48 * Chain [[12],13]: 1*it(12)+0 0.05/0.48 Such that:it(12) =< V__01-C 0.05/0.48 0.05/0.48 with precondition: [B=2,D=0,V__01=V__0+C,V__0>=1,V__01>=V__0] 0.05/0.48 0.05/0.48 * Chain [14]: 0 0.05/0.48 with precondition: [B=2,D=V__0,V__01=C,0>=V__01] 0.05/0.48 0.05/0.48 * Chain [13]: 0 0.05/0.48 with precondition: [B=2,C=V__01,V__0=D,0>=V__0] 0.05/0.48 0.05/0.48 0.05/0.48 #### Cost of chains of eval_foo_bb5_in(V__12,V__1,V__23,V__2,B,C,D): 0.05/0.48 * Chain [[15],17]: 1*it(15)+0 0.05/0.48 Such that:it(15) =< V__2-D 0.05/0.48 0.05/0.48 with precondition: [B=2,C=0,V__1=V__12+D+1,V__1+V__23=V__12+V__2+1,V__1>=V__12+1,V__1>=V__2,V__12+V__2>=V__1] 0.05/0.48 0.05/0.48 * Chain [[15],16]: 1*it(15)+0 0.05/0.48 Such that:it(15) =< V__2 0.05/0.48 0.05/0.48 with precondition: [B=2,D=0,V__1+C=V__12+1,V__1+V__23=V__12+V__2+1,V__2>=1,V__12+1>=V__1,V__1>=V__2] 0.05/0.48 0.05/0.48 * Chain [17]: 0 0.05/0.48 with precondition: [B=2,V__23=C,V__2=D,V__1+V__23=V__12+V__2+1,0>=V__23,V__1>=1,V__1>=V__2] 0.05/0.48 0.05/0.48 0.05/0.48 #### Cost of chains of eval_foo_bb3_in(V__12,V__1,B): 0.05/0.48 * Chain [[20],21]: 1*it(20)+1*s(3)+0 0.05/0.48 Such that:it(20) =< -V__12+V__1 0.05/0.48 aux(3) =< V__1 0.05/0.48 it(20) =< aux(3) 0.05/0.48 s(3) =< aux(3) 0.05/0.48 0.05/0.48 with precondition: [B=3,V__12>=0,V__1>=V__12+1] 0.05/0.48 0.05/0.48 * Chain [[20],19,21]: 1*it(20)+1*s(3)+1*s(4)+1 0.05/0.48 Such that:s(4) =< 1 0.05/0.48 it(20) =< -V__12+V__1 0.05/0.48 aux(4) =< V__1 0.05/0.48 it(20) =< aux(4) 0.05/0.48 s(3) =< aux(4) 0.05/0.48 0.05/0.48 with precondition: [B=3,V__12>=0,V__1>=V__12+2] 0.05/0.48 0.05/0.48 * Chain [[18],[20],21]: 1*it(18)+2*it(20)+0 0.05/0.48 Such that:it(18) =< -V__12 0.05/0.48 aux(5) =< V__1 0.05/0.48 it(20) =< aux(5) 0.05/0.48 0.05/0.48 with precondition: [B=3,0>=V__12+1,V__1>=1] 0.05/0.48 0.05/0.48 * Chain [[18],[20],19,21]: 1*it(18)+2*it(20)+1*s(4)+1 0.05/0.48 Such that:s(4) =< 1 0.05/0.48 it(18) =< -V__12 0.05/0.48 aux(6) =< V__1 0.05/0.48 it(20) =< aux(6) 0.05/0.48 0.05/0.48 with precondition: [B=3,0>=V__12+1,V__1>=2] 0.05/0.48 0.05/0.48 * Chain [[18],19,21]: 1*it(18)+1*s(4)+1 0.05/0.48 Such that:s(4) =< 1 0.05/0.48 it(18) =< -V__12 0.05/0.48 0.05/0.48 with precondition: [V__1=1,B=3,0>=V__12+1] 0.05/0.48 0.05/0.48 * Chain [21]: 0 0.05/0.48 with precondition: [B=3,0>=V__1] 0.05/0.48 0.05/0.48 * Chain [19,21]: 1*s(4)+1 0.05/0.48 Such that:s(4) =< V__1 0.05/0.48 0.05/0.48 with precondition: [B=3,V__1>=1,V__12+1>=V__1] 0.05/0.48 0.05/0.48 0.05/0.48 #### Cost of chains of eval_foo_bb1_in_loop_cont(A,B,C,D): 0.05/0.48 * Chain [28]: 1*s(5)+1*s(6)+1 0.05/0.48 Such that:s(5) =< 1 0.05/0.48 s(6) =< -B 0.05/0.48 0.05/0.48 with precondition: [A=2,C=1,0>=B+1] 0.05/0.48 0.05/0.48 * Chain [27]: 1*s(7)+2*s(9)+0 0.05/0.48 Such that:s(7) =< -B 0.05/0.48 s(8) =< C 0.05/0.48 s(9) =< s(8) 0.05/0.48 0.05/0.48 with precondition: [A=2,0>=B+1,C>=1] 0.05/0.48 0.05/0.48 * Chain [26]: 1*s(10)+1*s(11)+2*s(13)+1 0.05/0.48 Such that:s(10) =< 1 0.05/0.48 s(11) =< -B 0.05/0.48 s(12) =< C 0.05/0.48 s(13) =< s(12) 0.05/0.48 0.05/0.48 with precondition: [A=2,0>=B+1,C>=2] 0.05/0.48 0.05/0.48 * Chain [25]: 0 0.05/0.48 with precondition: [A=2,0>=C] 0.05/0.48 0.05/0.48 * Chain [24]: 1*s(14)+1*s(16)+0 0.05/0.48 Such that:s(14) =< -B+C 0.05/0.48 s(15) =< C 0.05/0.48 s(14) =< s(15) 0.05/0.48 s(16) =< s(15) 0.05/0.48 0.05/0.48 with precondition: [A=2,B>=0,C>=B+1] 0.05/0.48 0.05/0.48 * Chain [23]: 1*s(17)+1*s(18)+1*s(20)+1 0.05/0.48 Such that:s(17) =< 1 0.05/0.48 s(18) =< -B+C 0.05/0.48 s(19) =< C 0.05/0.48 s(18) =< s(19) 0.05/0.48 s(20) =< s(19) 0.05/0.48 0.05/0.48 with precondition: [A=2,B>=0,C>=B+2] 0.05/0.48 0.05/0.48 * Chain [22]: 1*s(21)+1 0.05/0.48 Such that:s(21) =< C 0.05/0.48 0.05/0.48 with precondition: [A=2,C>=1,B+1>=C] 0.05/0.48 0.05/0.48 0.05/0.48 #### Cost of chains of eval_foo_bb0_in(V_x,V_y,B): 0.05/0.48 * Chain [41]: 1*s(22)+1 0.05/0.48 Such that:s(22) =< 1 0.05/0.48 0.05/0.48 with precondition: [V_x=1,V_y=0] 0.05/0.48 0.05/0.48 * Chain [40]: 1*s(23)+1*s(24)+1 0.05/0.48 Such that:s(23) =< 1 0.05/0.48 s(24) =< -V_y 0.05/0.48 0.05/0.48 with precondition: [V_x=1,0>=V_y+1] 0.05/0.48 0.05/0.48 * Chain [39]: 2*s(25)+0 0.05/0.48 Such that:aux(7) =< V_x 0.05/0.48 s(25) =< aux(7) 0.05/0.48 0.05/0.48 with precondition: [V_y=0,V_x>=1] 0.05/0.48 0.05/0.48 * Chain [38]: 1*s(28)+2*s(29)+1 0.05/0.48 Such that:s(28) =< 1 0.05/0.48 aux(8) =< V_x 0.05/0.48 s(29) =< aux(8) 0.05/0.48 0.05/0.48 with precondition: [V_y=0,V_x>=2] 0.05/0.48 0.05/0.48 * Chain [37]: 1*s(32)+0 0.05/0.48 Such that:s(32) =< V_y 0.05/0.48 0.05/0.48 with precondition: [V_x=V_y,V_x>=1] 0.05/0.48 0.05/0.48 * Chain [36]: 1*s(33)+1*s(34)+1 0.05/0.48 Such that:s(34) =< 1 0.05/0.48 s(33) =< V_y 0.05/0.48 0.05/0.48 with precondition: [V_x=V_y+1,V_x>=2] 0.05/0.48 0.05/0.48 * Chain [35]: 0 0.05/0.48 with precondition: [0>=V_x] 0.05/0.48 0.05/0.48 * Chain [34]: 0 0.05/0.48 with precondition: [0>=V_x,0>=V_y] 0.05/0.48 0.05/0.48 * Chain [33]: 1*s(35)+2*s(37)+0 0.05/0.48 Such that:s(36) =< V_x 0.05/0.48 s(35) =< -V_y 0.05/0.48 s(37) =< s(36) 0.05/0.48 0.05/0.48 with precondition: [0>=V_y+1,V_x>=1] 0.05/0.48 0.05/0.48 * Chain [32]: 1*s(38)+1*s(39)+2*s(41)+1 0.05/0.48 Such that:s(38) =< 1 0.05/0.48 s(40) =< V_x 0.05/0.48 s(39) =< -V_y 0.05/0.48 s(41) =< s(40) 0.05/0.48 0.05/0.48 with precondition: [0>=V_y+1,V_x>=2] 0.05/0.48 0.05/0.48 * Chain [31]: 1*s(42)+0 0.05/0.48 Such that:s(42) =< V_x 0.05/0.48 0.05/0.48 with precondition: [V_x>=1,V_y>=V_x] 0.05/0.48 0.05/0.48 * Chain [30]: 1*s(43)+2*s(44)+0 0.05/0.48 Such that:s(43) =< V_y 0.05/0.48 aux(9) =< V_x-V_y 0.05/0.48 s(44) =< aux(9) 0.05/0.48 0.05/0.48 with precondition: [V_y>=1,V_x>=V_y+1] 0.05/0.48 0.05/0.48 * Chain [29]: 1*s(47)+1*s(48)+2*s(49)+1 0.05/0.48 Such that:s(48) =< 1 0.05/0.48 s(47) =< V_y 0.05/0.48 aux(10) =< V_x-V_y 0.05/0.48 s(49) =< aux(10) 0.05/0.48 0.05/0.48 with precondition: [V_y>=1,V_x>=V_y+2] 0.05/0.48 0.05/0.48 0.05/0.48 #### Cost of chains of eval_foo_start(V_x,V_y,V_res,B): 0.05/0.48 * Chain [54]: 1*s(52)+1 0.05/0.48 Such that:s(52) =< 1 0.05/0.48 0.05/0.48 with precondition: [V_x=1,V_y=0] 0.05/0.48 0.05/0.48 * Chain [53]: 1*s(53)+1*s(54)+1 0.05/0.48 Such that:s(53) =< 1 0.05/0.48 s(54) =< -V_y 0.05/0.48 0.05/0.48 with precondition: [V_x=1,0>=V_y+1] 0.05/0.48 0.05/0.48 * Chain [52]: 2*s(56)+0 0.05/0.48 Such that:s(55) =< V_x 0.05/0.48 s(56) =< s(55) 0.05/0.48 0.05/0.48 with precondition: [V_y=0,V_x>=1] 0.05/0.48 0.05/0.48 * Chain [51]: 1*s(57)+2*s(59)+1 0.05/0.48 Such that:s(57) =< 1 0.05/0.48 s(58) =< V_x 0.05/0.48 s(59) =< s(58) 0.05/0.48 0.05/0.48 with precondition: [V_y=0,V_x>=2] 0.05/0.48 0.05/0.48 * Chain [50]: 1*s(60)+0 0.05/0.48 Such that:s(60) =< V_y 0.05/0.48 0.05/0.48 with precondition: [V_x=V_y,V_x>=1] 0.05/0.48 0.05/0.48 * Chain [49]: 1*s(61)+1*s(62)+1 0.05/0.48 Such that:s(61) =< 1 0.05/0.48 s(62) =< V_y 0.05/0.48 0.05/0.48 with precondition: [V_x=V_y+1,V_x>=2] 0.05/0.48 0.05/0.48 * Chain [48]: 0 0.05/0.48 with precondition: [0>=V_x] 0.05/0.48 0.05/0.48 * Chain [47]: 0 0.05/0.48 with precondition: [0>=V_x,0>=V_y] 0.05/0.48 0.05/0.48 * Chain [46]: 1*s(64)+2*s(65)+0 0.05/0.48 Such that:s(63) =< V_x 0.05/0.48 s(64) =< -V_y 0.05/0.48 s(65) =< s(63) 0.05/0.48 0.05/0.48 with precondition: [0>=V_y+1,V_x>=1] 0.05/0.48 0.05/0.48 * Chain [45]: 1*s(66)+1*s(68)+2*s(69)+1 0.05/0.48 Such that:s(66) =< 1 0.05/0.48 s(67) =< V_x 0.05/0.48 s(68) =< -V_y 0.05/0.48 s(69) =< s(67) 0.05/0.48 0.05/0.48 with precondition: [0>=V_y+1,V_x>=2] 0.05/0.48 0.05/0.48 * Chain [44]: 1*s(70)+0 0.05/0.48 Such that:s(70) =< V_x 0.05/0.48 0.05/0.48 with precondition: [V_x>=1,V_y>=V_x] 0.05/0.48 0.05/0.48 * Chain [43]: 1*s(71)+2*s(73)+0 0.05/0.48 Such that:s(72) =< V_x-V_y 0.05/0.48 s(71) =< V_y 0.05/0.48 s(73) =< s(72) 0.05/0.48 0.05/0.48 with precondition: [V_y>=1,V_x>=V_y+1] 0.05/0.48 0.05/0.48 * Chain [42]: 1*s(74)+1*s(75)+2*s(77)+1 0.05/0.48 Such that:s(74) =< 1 0.05/0.48 s(76) =< V_x-V_y 0.05/0.48 s(75) =< V_y 0.05/0.48 s(77) =< s(76) 0.05/0.48 0.05/0.48 with precondition: [V_y>=1,V_x>=V_y+2] 0.05/0.48 0.05/0.48 0.05/0.48 Closed-form bounds of eval_foo_start(V_x,V_y,V_res,B): 0.05/0.48 ------------------------------------- 0.05/0.48 * Chain [54] with precondition: [V_x=1,V_y=0] 0.05/0.48 - Upper bound: 2 0.05/0.48 - Complexity: constant 0.05/0.48 * Chain [53] with precondition: [V_x=1,0>=V_y+1] 0.05/0.48 - Upper bound: -V_y+2 0.05/0.48 - Complexity: n 0.05/0.48 * Chain [52] with precondition: [V_y=0,V_x>=1] 0.05/0.48 - Upper bound: 2*V_x 0.05/0.48 - Complexity: n 0.05/0.48 * Chain [51] with precondition: [V_y=0,V_x>=2] 0.05/0.48 - Upper bound: 2*V_x+2 0.05/0.48 - Complexity: n 0.05/0.48 * Chain [50] with precondition: [V_x=V_y,V_x>=1] 0.05/0.48 - Upper bound: V_y 0.05/0.48 - Complexity: n 0.05/0.48 * Chain [49] with precondition: [V_x=V_y+1,V_x>=2] 0.05/0.48 - Upper bound: V_y+2 0.05/0.48 - Complexity: n 0.05/0.48 * Chain [48] with precondition: [0>=V_x] 0.05/0.48 - Upper bound: 0 0.05/0.48 - Complexity: constant 0.05/0.48 * Chain [47] with precondition: [0>=V_x,0>=V_y] 0.05/0.48 - Upper bound: 0 0.05/0.48 - Complexity: constant 0.05/0.48 * Chain [46] with precondition: [0>=V_y+1,V_x>=1] 0.05/0.48 - Upper bound: 2*V_x-V_y 0.05/0.48 - Complexity: n 0.05/0.48 * Chain [45] with precondition: [0>=V_y+1,V_x>=2] 0.05/0.48 - Upper bound: 2*V_x-V_y+2 0.05/0.48 - Complexity: n 0.05/0.48 * Chain [44] with precondition: [V_x>=1,V_y>=V_x] 0.05/0.48 - Upper bound: V_x 0.05/0.48 - Complexity: n 0.05/0.48 * Chain [43] with precondition: [V_y>=1,V_x>=V_y+1] 0.05/0.48 - Upper bound: 2*V_x-V_y 0.05/0.48 - Complexity: n 0.05/0.48 * Chain [42] with precondition: [V_y>=1,V_x>=V_y+2] 0.05/0.48 - Upper bound: 2*V_x-V_y+2 0.05/0.48 - Complexity: n 0.05/0.48 0.05/0.48 ### Maximum cost of eval_foo_start(V_x,V_y,V_res,B): max([max([max([2,nat(-V_y)+2]),nat(V_y)+2+nat(V_x-V_y)*2]),nat(V_x)+2+nat(-V_y)+nat(V_x)]) 0.05/0.48 Asymptotic class: n 0.05/0.48 * Total analysis performed in 393 ms. 0.05/0.48 0.05/0.58 EOF