0.68/0.73 WORST_CASE(?,O(n^1)) 0.68/0.73 0.68/0.73 Preprocessing Cost Relations 0.68/0.73 ===================================== 0.68/0.73 0.68/0.73 #### Computed strongly connected components 0.68/0.73 0. recursive : [eval_foo_bb2_in/5,eval_foo_bb3_in/5] 0.68/0.73 1. recursive : [eval_foo_bb1_in/3,eval_foo_bb2_in_loop_cont/6,eval_foo_bb4_in/5] 0.68/0.73 2. non_recursive : [eval_foo_stop/1] 0.68/0.73 3. non_recursive : [eval_foo_bb5_in/1] 0.68/0.73 4. non_recursive : [eval_foo_bb1_in_loop_cont/2] 0.68/0.73 5. non_recursive : [eval_foo_bb0_in/3] 0.68/0.73 6. non_recursive : [eval_foo_start/3] 0.68/0.73 0.68/0.73 #### Obtained direct recursion through partial evaluation 0.68/0.73 0. SCC is partially evaluated into eval_foo_bb2_in/5 0.68/0.73 1. SCC is partially evaluated into eval_foo_bb1_in/3 0.68/0.73 2. SCC is completely evaluated into other SCCs 0.68/0.73 3. SCC is completely evaluated into other SCCs 0.68/0.73 4. SCC is completely evaluated into other SCCs 0.68/0.73 5. SCC is partially evaluated into eval_foo_bb0_in/3 0.68/0.73 6. SCC is partially evaluated into eval_foo_start/3 0.68/0.73 0.68/0.73 Control-Flow Refinement of Cost Relations 0.68/0.73 ===================================== 0.68/0.73 0.68/0.73 ### Specialization of cost equations eval_foo_bb2_in/5 0.68/0.73 * CE 7 is refined into CE [8] 0.68/0.73 * CE 5 is refined into CE [9] 0.68/0.73 * CE 6 is refined into CE [10] 0.68/0.73 0.68/0.73 0.68/0.73 ### Cost equations --> "Loop" of eval_foo_bb2_in/5 0.68/0.73 * CEs [9] --> Loop 8 0.68/0.73 * CEs [10] --> Loop 9 0.68/0.73 * CEs [8] --> Loop 10 0.68/0.73 0.68/0.73 ### Ranking functions of CR eval_foo_bb2_in(V__12,V__1,B,C,D) 0.68/0.73 * RF of phase [8]: [-V__12+V__1,-V__12/2+3] 0.68/0.73 * RF of phase [9]: [-V__12/6+V__1/6] 0.68/0.73 0.68/0.73 #### Partial ranking functions of CR eval_foo_bb2_in(V__12,V__1,B,C,D) 0.68/0.73 * Partial RF of phase [8]: 0.68/0.73 - RF of loop [8:1]: 0.68/0.73 -V__12+V__1 0.68/0.73 -V__12/2+3 0.68/0.73 * Partial RF of phase [9]: 0.68/0.73 - RF of loop [9:1]: 0.68/0.73 -V__12/6+V__1/6 0.68/0.73 0.68/0.73 0.68/0.73 ### Specialization of cost equations eval_foo_bb1_in/3 0.68/0.73 * CE 4 is refined into CE [11] 0.68/0.73 * CE 3 is refined into CE [12,13,14,15] 0.68/0.73 0.68/0.73 0.68/0.73 ### Cost equations --> "Loop" of eval_foo_bb1_in/3 0.68/0.73 * CEs [15] --> Loop 11 0.68/0.73 * CEs [14] --> Loop 12 0.68/0.73 * CEs [13] --> Loop 13 0.68/0.73 * CEs [12] --> Loop 14 0.68/0.73 * CEs [11] --> Loop 15 0.68/0.73 0.68/0.73 ### Ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 0.68/0.73 * RF of phase [11,12]: [-V__0/3+10] 0.68/0.73 * RF of phase [13]: [V__01/14-V__0/7+4/7] 0.68/0.73 * RF of phase [14]: [-V__0/2+15,V__01/12-V__0/12+1/12] 0.68/0.73 0.68/0.73 #### Partial ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 0.68/0.73 * Partial RF of phase [11,12]: 0.68/0.73 - RF of loop [11:1]: 0.68/0.73 -V__0/4+15/2 0.68/0.73 - RF of loop [12:1]: 0.68/0.73 -V__0/3+10 0.68/0.73 V__01/24-7/24*V__0+33/4 0.68/0.73 * Partial RF of phase [13]: 0.68/0.73 - RF of loop [13:1]: 0.68/0.73 V__01/14-V__0/7+4/7 0.68/0.73 * Partial RF of phase [14]: 0.68/0.73 - RF of loop [14:1]: 0.68/0.73 -V__0/2+15 0.68/0.73 V__01/12-V__0/12+1/12 0.68/0.73 0.68/0.73 0.68/0.73 ### Specialization of cost equations eval_foo_bb0_in/3 0.68/0.73 * CE 2 is refined into CE [16,17,18,19,20,21] 0.68/0.73 0.68/0.73 0.68/0.73 ### Cost equations --> "Loop" of eval_foo_bb0_in/3 0.68/0.73 * CEs [21] --> Loop 16 0.68/0.73 * CEs [20] --> Loop 17 0.68/0.73 * CEs [19] --> Loop 18 0.68/0.73 * CEs [18] --> Loop 19 0.68/0.73 * CEs [16] --> Loop 20 0.68/0.73 * CEs [17] --> Loop 21 0.68/0.73 0.68/0.73 ### Ranking functions of CR eval_foo_bb0_in(V_a,V_b,B) 0.68/0.73 0.68/0.73 #### Partial ranking functions of CR eval_foo_bb0_in(V_a,V_b,B) 0.68/0.73 0.68/0.73 0.68/0.73 ### Specialization of cost equations eval_foo_start/3 0.68/0.73 * CE 1 is refined into CE [22,23,24,25,26,27] 0.68/0.73 0.68/0.73 0.68/0.73 ### Cost equations --> "Loop" of eval_foo_start/3 0.68/0.73 * CEs [27] --> Loop 22 0.68/0.73 * CEs [26] --> Loop 23 0.68/0.73 * CEs [25] --> Loop 24 0.68/0.73 * CEs [24] --> Loop 25 0.68/0.73 * CEs [23] --> Loop 26 0.68/0.73 * CEs [22] --> Loop 27 0.68/0.73 0.68/0.73 ### Ranking functions of CR eval_foo_start(V_a,V_b,B) 0.68/0.73 0.68/0.73 #### Partial ranking functions of CR eval_foo_start(V_a,V_b,B) 0.68/0.73 0.68/0.73 0.68/0.73 Computing Bounds 0.68/0.73 ===================================== 0.68/0.73 0.68/0.73 #### Cost of chains of eval_foo_bb2_in(V__12,V__1,B,C,D): 0.68/0.73 * Chain [[9],10]: 1*it(9)+0 0.68/0.73 Such that:it(9) =< -V__12/6+V__1/6 0.68/0.73 0.68/0.73 with precondition: [B=2,V__12+7*D=7*V__1+C,V__12>=6,C>=V__12+7,V__12+6*C>=7*V__1,7*V__1+35>=6*C+V__12] 0.68/0.73 0.68/0.73 * Chain [[8],[9],10]: 1*it(8)+1*it(9)+0 0.68/0.74 Such that:it(8) =< -V__12/2+3 0.68/0.74 it(9) =< -V__12/5+2/5*V__1+C/30-7/30*D 0.68/0.74 0.68/0.74 with precondition: [B=2,D+5>=C,C>=D,7*V__12+14*D>=14*V__1+2*C+30,2*C+14*V__1+35>=14*D+7*V__12,V__12+7*D>=7*V__1+C+5,C+2*V__1>=2*D+V__12+5] 0.68/0.74 0.68/0.74 * Chain [[8],10]: 1*it(8)+0 0.68/0.74 Such that:it(8) =< -V__12/2+3 0.68/0.74 it(8) =< -V__12/2+D/2 0.68/0.74 0.68/0.74 with precondition: [B=2,V__12+C=2*V__1,V__12+D=2*V__1,V__12+7>=2*V__1,V__1>=V__12+1] 0.68/0.74 0.68/0.74 * Chain [10]: 0 0.68/0.74 with precondition: [B=2,V__12=C,V__1=D,V__12>=V__1] 0.68/0.74 0.68/0.74 0.68/0.74 #### Cost of chains of eval_foo_bb1_in(V__01,V__0,B): 0.68/0.74 * Chain [[14],[13],[11,12],15]: 1*it(11)+1*it(12)+1*it(13)+1*it(14)+1*s(7)+1*s(8)+1*s(9)+1*s(12)+0 0.68/0.74 Such that:s(9) =< 35 0.68/0.74 aux(4) =< 34/3 0.68/0.74 it(12) =< 35/4 0.68/0.74 s(7) =< 55/2 0.68/0.74 aux(1) =< 187/8 0.68/0.74 s(8) =< 440/29 0.68/0.74 aux(5) =< 641/36 0.68/0.74 aux(2) =< 4727/96 0.68/0.74 aux(7) =< -132*V__01-660*V__0+26158 0.68/0.74 aux(5) =< -48*V__01-240*V__0+38113/4 0.68/0.74 aux(7) =< -44*V__01-220*V__0+5786 0.68/0.74 aux(1) =< -42*V__01-210*V__0+10601/2 0.68/0.74 aux(2) =< -42*V__01-210*V__0+282391/32 0.68/0.74 aux(5) =< -16*V__01-80*V__0+8429/4 0.68/0.74 aux(2) =< -14*V__01-70*V__0+62123/32 0.68/0.74 aux(4) =< -12*V__01-60*V__0+1988 0.68/0.74 aux(8) =< -12*V__01-60*V__0+2053 0.68/0.74 s(7) =< -12*V__01-60*V__0+3131/2 0.68/0.74 it(12) =< -6*V__01-30*V__0+2053/2 0.68/0.74 aux(4) =< -4*V__01-20*V__0+448 0.68/0.74 aux(8) =< -4*V__01-20*V__0+461 0.68/0.74 s(7) =< -4*V__01-20*V__0+727/2 0.68/0.74 it(12) =< -2*V__01-10*V__0+461/2 0.68/0.74 it(11) =< -V__01-5*V__0+49 0.68/0.74 it(11) =< -V__01-5*V__0+119 0.68/0.74 aux(3) =< -V__01-5*V__0+1213/12 0.68/0.74 it(13) =< -V__01/7-5/7*V__0+39/7 0.68/0.74 it(13) =< -V__01/7-5/7*V__0+69/7 0.68/0.74 it(14) =< V__01/12-V__0/12+1/12 0.68/0.74 aux(9) =< -14*V__01-70*V__0+2473/2 0.68/0.74 aux(10) =< -V__01-5*V__0+545/12 0.68/0.74 aux(1) =< aux(9) 0.68/0.74 aux(6) =< aux(9) 0.68/0.74 aux(3) =< aux(10) 0.68/0.74 aux(6) =< aux(10) 0.68/0.74 s(8) =< aux(7) 0.68/0.74 s(12) =< aux(7) 0.68/0.74 s(9) =< aux(8) 0.68/0.74 s(12) =< aux(8) 0.68/0.74 it(11) =< aux(4) 0.68/0.74 it(12) =< aux(4) 0.68/0.74 it(11) =< aux(5) 0.68/0.74 it(12) =< aux(5) 0.68/0.74 s(7) =< it(12)*(3/8)+aux(2) 0.68/0.74 s(7) =< it(12)*(3/8)+aux(1) 0.68/0.74 s(7) =< it(11)*aux(3) 0.68/0.74 s(12) =< it(13)*aux(6) 0.68/0.74 0.68/0.74 with precondition: [B=3,35>=5*V__0+V__01,V__01>=2*V__0+7,V__01>=V__0] 0.68/0.74 0.68/0.74 * Chain [[14],[11,12],15]: 1*it(11)+1*it(12)+1*it(14)+1*s(7)+1*s(8)+1*s(9)+0 0.68/0.74 Such that:aux(3) =< 25/2 0.68/0.74 aux(2) =< -97/96*V__01-485/96*V__0+16745/96 0.68/0.74 s(7) =< -47/24*V__01-235/24*V__0+737/2 0.68/0.74 aux(5) =< -29/24*V__01-145/24*V__0+461/2 0.68/0.74 s(7) =< -13/4*V__01-65/4*V__0+2311/4 0.68/0.74 aux(4) =< -13/6*V__01-65/6*V__0+2311/6 0.68/0.74 aux(5) =< -7/4*V__01-35/4*V__0+1273/4 0.68/0.74 aux(4) =< -7/6*V__01-35/6*V__0+1273/6 0.68/0.74 aux(2) =< -7/36*V__01-35/36*V__0+4055/96 0.68/0.74 aux(1) =< -7/48*V__01-35/48*V__0+145/8 0.68/0.74 it(12) =< -V__01/2-5/2*V__0+199/2 0.68/0.74 aux(3) =< -V__01/2-5/2*V__0+935/12 0.68/0.74 s(9) =< -V__01/6-5/6*V__0+29 0.68/0.74 s(7) =< -V__01/6-5/6*V__0+43/2 0.68/0.74 aux(3) =< -V__01/12-5/12*V__0+125/12 0.68/0.74 it(14) =< V__01/12-V__0/12+1/12 0.68/0.74 aux(11) =< -3*V__01-15*V__0+570 0.68/0.74 aux(12) =< -V__01-5*V__0+361/2 0.68/0.74 aux(13) =< -29/12*V__01-145/12*V__0+951/2 0.68/0.74 aux(14) =< -V__01/2-5/2*V__0+151/2 0.68/0.74 it(11) =< aux(11) 0.68/0.74 s(8) =< aux(11) 0.68/0.74 aux(3) =< aux(12) 0.68/0.74 it(11) =< aux(12) 0.68/0.74 it(12) =< aux(13) 0.68/0.74 s(8) =< aux(13) 0.68/0.74 aux(1) =< aux(14) 0.68/0.74 s(7) =< aux(14) 0.68/0.74 it(11) =< aux(4) 0.68/0.74 it(12) =< aux(4) 0.68/0.74 it(11) =< aux(5) 0.68/0.74 it(12) =< aux(5) 0.68/0.74 s(7) =< it(12)*(3/8)+aux(2) 0.68/0.74 s(7) =< it(12)*(3/8)+aux(1) 0.68/0.74 s(7) =< it(11)*aux(3) 0.68/0.74 0.68/0.74 with precondition: [B=3,27>=V__0,173>=5*V__0+V__01,V__01>=V__0,V__01+5*V__0+36>=0] 0.68/0.74 0.68/0.74 * Chain [[14],15]: 1*it(14)+0 0.68/0.74 Such that:it(14) =< V__01/12-V__0/12+1/12 0.68/0.74 it(14) =< -V__0/2+15 0.68/0.74 0.68/0.74 with precondition: [B=3,29>=V__0,V__01>=V__0,V__01+5*V__0>=168] 0.68/0.74 0.68/0.74 * Chain [[13],[11,12],15]: 1*it(11)+1*it(12)+1*it(13)+1*s(7)+1*s(8)+1*s(9)+1*s(12)+0 0.68/0.74 Such that:s(9) =< 35 0.68/0.74 aux(4) =< 34/3 0.68/0.74 it(12) =< 35/4 0.68/0.74 s(7) =< 55/2 0.68/0.74 aux(1) =< 187/8 0.68/0.74 s(8) =< 440/29 0.68/0.74 aux(5) =< 641/36 0.68/0.74 aux(2) =< 4727/96 0.68/0.74 aux(5) =< -4*V__01-48*V__0+7309/4 0.68/0.74 aux(4) =< -V__01-12*V__0+378 0.68/0.74 s(7) =< -V__01-12*V__0+587/2 0.68/0.74 aux(1) =< -7/2*V__01-42*V__0+1983/2 0.68/0.74 aux(2) =< -7/2*V__01-42*V__0+54283/32 0.68/0.74 aux(6) =< -3/14*V__01-4/7*V__0+5 0.68/0.74 aux(6) =< -V__01/2+7 0.68/0.74 it(11) =< -V__01/2-6*V__0+189 0.68/0.74 it(12) =< -V__01/2-6*V__0+391/2 0.68/0.74 aux(3) =< -V__01/2-6*V__0+1709/12 0.68/0.74 aux(3) =< V__01/2-V__0+125/12 0.68/0.74 it(11) =< V__01/4-V__0/2+7 0.68/0.74 it(13) =< V__01/14-V__0/7+4/7 0.68/0.74 aux(7) =< -11*V__01-132*V__0+5016 0.68/0.74 aux(8) =< -V__01-12*V__0+391 0.68/0.74 s(8) =< aux(7) 0.68/0.74 s(12) =< aux(7) 0.68/0.74 s(9) =< aux(8) 0.68/0.74 s(12) =< aux(8) 0.68/0.74 it(11) =< aux(4) 0.68/0.74 it(12) =< aux(4) 0.68/0.74 it(11) =< aux(5) 0.68/0.74 it(12) =< aux(5) 0.68/0.74 s(7) =< it(12)*(3/8)+aux(2) 0.68/0.74 s(7) =< it(12)*(3/8)+aux(1) 0.68/0.74 s(7) =< it(11)*aux(3) 0.68/0.74 s(12) =< it(13)*aux(6) 0.68/0.74 0.68/0.74 with precondition: [B=3,V__01+7>=2*V__0,V__0>=V__01+1] 0.68/0.74 0.68/0.74 * Chain [[11,12],15]: 1*it(11)+1*it(12)+1*s(7)+1*s(8)+1*s(9)+0 0.68/0.74 Such that:aux(3) =< -V__01+V__0+1/2 0.68/0.74 s(8) =< -113/348*V__01-21/116*V__0+5171/348 0.68/0.74 aux(2) =< -97/96*V__01-5/32*V__0+3115/96 0.68/0.74 s(7) =< -13/12*V__01-V__0/4+451/12 0.68/0.74 aux(5) =< -7/36*V__01-V__0/4+493/36 0.68/0.74 it(12) =< -5/48*V__01-11/48*V__0+169/16 0.68/0.74 s(8) =< -3/29*V__01-8/29*V__0+360/29 0.68/0.74 aux(3) =< -V__01/2+65/12 0.68/0.74 aux(1) =< -V__01/2-3/8*V__0+111/8 0.68/0.74 s(7) =< -V__01/2-V__0/2+35/2 0.68/0.74 s(9) =< -V__01/6-5/6*V__0+29 0.68/0.74 it(12) =< V__01/24-7/24*V__0+33/4 0.68/0.74 s(9) =< 23/144*V__01-161/144*V__0+5083/144 0.68/0.74 aux(4) =< -V__0/3+10 0.68/0.74 it(11) =< -V__0/4+15/2 0.68/0.74 it(11) =< aux(4) 0.68/0.74 it(12) =< aux(4) 0.68/0.74 it(11) =< aux(5) 0.68/0.74 it(12) =< aux(5) 0.68/0.74 s(7) =< it(12)*(3/8)+aux(2) 0.68/0.74 s(7) =< it(12)*(3/8)+aux(1) 0.68/0.74 s(7) =< it(11)*aux(3) 0.68/0.74 0.68/0.74 with precondition: [B=3,29>=V__0,V__0>=V__01+1,2*V__0>=V__01+8] 0.68/0.74 0.68/0.74 * Chain [15]: 0 0.68/0.74 with precondition: [B=3,V__0>=30] 0.68/0.74 0.68/0.74 0.68/0.74 #### Cost of chains of eval_foo_bb0_in(V_a,V_b,B): 0.68/0.74 * Chain [21]: 1*s(13)+0 0.68/0.74 Such that:s(13) =< -V_a/2+15 0.68/0.74 s(13) =< -V_a/12+V_b/12+1/12 0.68/0.74 0.68/0.74 with precondition: [29>=V_a,V_b>=V_a,V_b+5*V_a>=168] 0.68/0.74 0.68/0.74 * Chain [20]: 1*s(15)+1*s(17)+1*s(19)+1*s(21)+1*s(23)+0 0.68/0.74 Such that:s(14) =< V_a-V_b+1/2 0.68/0.74 s(21) =< -161/144*V_a+23/144*V_b+5083/144 0.68/0.74 s(15) =< -21/116*V_a-113/348*V_b+5171/348 0.68/0.74 s(19) =< -11/48*V_a-5/48*V_b+169/16 0.68/0.74 s(15) =< -8/29*V_a-3/29*V_b+360/29 0.68/0.74 s(19) =< -7/24*V_a+V_b/24+33/4 0.68/0.74 s(21) =< -5/6*V_a-V_b/6+29 0.68/0.74 s(16) =< -5/32*V_a-97/96*V_b+3115/96 0.68/0.74 s(20) =< -3/8*V_a-V_b/2+111/8 0.68/0.74 s(17) =< -V_a/2-V_b/2+35/2 0.68/0.74 s(22) =< -V_a/3+10 0.68/0.74 s(23) =< -V_a/4+15/2 0.68/0.74 s(17) =< -V_a/4-13/12*V_b+451/12 0.68/0.74 s(18) =< -V_a/4-7/36*V_b+493/36 0.68/0.74 s(17) =< -V_b+17 0.68/0.74 s(16) =< -209/192*V_b+3055/96 0.68/0.74 s(21) =< -115/288*V_b+4439/144 0.68/0.74 s(20) =< -11/16*V_b+99/8 0.68/0.74 s(19) =< -5/48*V_b+85/12 0.68/0.74 s(14) =< -V_b/2+65/12 0.68/0.74 s(23) =< s(22) 0.68/0.74 s(19) =< s(22) 0.68/0.74 s(23) =< s(18) 0.68/0.74 s(19) =< s(18) 0.68/0.74 s(17) =< s(19)*(3/8)+s(16) 0.68/0.74 s(17) =< s(19)*(3/8)+s(20) 0.68/0.74 s(17) =< s(23)*s(14) 0.68/0.74 0.68/0.74 with precondition: [29>=V_a,V_a>=V_b+1,2*V_a>=V_b+8] 0.68/0.74 0.68/0.74 * Chain [19]: 1*s(26)+1*s(30)+1*s(31)+1*s(32)+1*s(37)+1*s(38)+0 0.68/0.74 Such that:s(24) =< 25/2 0.68/0.74 s(26) =< 55/2 0.68/0.74 s(24) =< 161/12 0.68/0.74 s(36) =< 187/2 0.68/0.74 s(29) =< 187/8 0.68/0.74 s(24) =< 1151/12 0.68/0.74 s(25) =< 20237/96 0.68/0.74 s(33) =< -15*V_a-3*V_b+570 0.68/0.74 s(34) =< -5*V_a-V_b+361/2 0.68/0.74 s(25) =< -485/96*V_a-97/96*V_b+16745/96 0.68/0.74 s(26) =< -235/24*V_a-47/24*V_b+737/2 0.68/0.74 s(35) =< -145/12*V_a-29/12*V_b+951/2 0.68/0.74 s(27) =< -145/24*V_a-29/24*V_b+461/2 0.68/0.74 s(26) =< -65/4*V_a-13/4*V_b+2311/4 0.68/0.74 s(27) =< -35/4*V_a-7/4*V_b+1273/4 0.68/0.74 s(28) =< -35/6*V_a-7/6*V_b+1273/6 0.68/0.74 s(25) =< -35/36*V_a-7/36*V_b+4055/96 0.68/0.74 s(29) =< -35/48*V_a-7/48*V_b+145/8 0.68/0.74 s(36) =< -5/2*V_a-V_b/2+151/2 0.68/0.74 s(30) =< -5/2*V_a-V_b/2+199/2 0.68/0.74 s(24) =< -5/2*V_a-V_b/2+935/12 0.68/0.74 s(31) =< -5/6*V_a-V_b/6+29 0.68/0.74 s(26) =< -5/6*V_a-V_b/6+43/2 0.68/0.74 s(24) =< -5/12*V_a-V_b/12+125/12 0.68/0.74 s(32) =< -V_a/12+V_b/12+1/12 0.68/0.74 s(37) =< s(33) 0.68/0.74 s(38) =< s(33) 0.68/0.74 s(24) =< s(34) 0.68/0.74 s(37) =< s(34) 0.68/0.74 s(30) =< s(35) 0.68/0.74 s(38) =< s(35) 0.68/0.74 s(29) =< s(36) 0.68/0.74 s(26) =< s(36) 0.68/0.74 s(37) =< s(28) 0.68/0.74 s(30) =< s(28) 0.68/0.74 s(37) =< s(27) 0.68/0.74 s(30) =< s(27) 0.68/0.74 s(26) =< s(30)*(3/8)+s(25) 0.68/0.74 s(26) =< s(30)*(3/8)+s(29) 0.68/0.74 s(26) =< s(37)*s(24) 0.68/0.74 0.68/0.74 with precondition: [27>=V_a,173>=5*V_a+V_b,V_b>=V_a,V_b+5*V_a+36>=0] 0.68/0.74 0.68/0.74 * Chain [18]: 0 0.68/0.74 with precondition: [V_a>=30] 0.68/0.74 0.68/0.74 * Chain [17]: 1*s(39)+1*s(41)+1*s(42)+1*s(44)+1*s(49)+1*s(51)+1*s(52)+1*s(56)+0 0.68/0.74 Such that:s(39) =< 35 0.68/0.74 s(40) =< 34/3 0.68/0.74 s(41) =< 35/4 0.68/0.74 s(42) =< 55/2 0.68/0.74 s(43) =< 187/8 0.68/0.74 s(44) =< 440/29 0.68/0.74 s(45) =< 641/36 0.68/0.74 s(46) =< 4727/96 0.68/0.74 s(47) =< -220*V_a-44*V_b+5786 0.68/0.74 s(43) =< -210*V_a-42*V_b+10601/2 0.68/0.74 s(45) =< -80*V_a-16*V_b+8429/4 0.68/0.74 s(53) =< -70*V_a-14*V_b+2473/2 0.68/0.74 s(46) =< -70*V_a-14*V_b+62123/32 0.68/0.74 s(40) =< -20*V_a-4*V_b+448 0.68/0.74 s(48) =< -20*V_a-4*V_b+461 0.68/0.74 s(42) =< -20*V_a-4*V_b+727/2 0.68/0.74 s(41) =< -10*V_a-2*V_b+461/2 0.68/0.74 s(49) =< -5*V_a-V_b+49 0.68/0.74 s(54) =< -5*V_a-V_b+545/12 0.68/0.74 s(50) =< -5*V_a-V_b+1213/12 0.68/0.74 s(51) =< -5/7*V_a-V_b/7+39/7 0.68/0.74 s(52) =< -V_a/12+V_b/12+1/12 0.68/0.74 s(43) =< s(53) 0.68/0.74 s(55) =< s(53) 0.68/0.74 s(50) =< s(54) 0.68/0.74 s(55) =< s(54) 0.68/0.74 s(44) =< s(47) 0.68/0.74 s(56) =< s(47) 0.68/0.74 s(39) =< s(48) 0.68/0.74 s(56) =< s(48) 0.68/0.74 s(49) =< s(40) 0.68/0.74 s(41) =< s(40) 0.68/0.74 s(49) =< s(45) 0.68/0.74 s(41) =< s(45) 0.68/0.74 s(42) =< s(41)*(3/8)+s(46) 0.68/0.74 s(42) =< s(41)*(3/8)+s(43) 0.68/0.74 s(42) =< s(49)*s(50) 0.68/0.74 s(56) =< s(51)*s(55) 0.68/0.74 0.68/0.74 with precondition: [35>=5*V_a+V_b,V_b>=2*V_a+7,V_b>=V_a] 0.68/0.74 0.68/0.74 * Chain [16]: 1*s(57)+1*s(59)+1*s(60)+1*s(62)+1*s(66)+1*s(68)+1*s(71)+0 0.68/0.74 Such that:s(57) =< 35 0.68/0.74 s(58) =< 34/3 0.68/0.74 s(59) =< 35/4 0.68/0.74 s(60) =< 55/2 0.68/0.74 s(61) =< 187/8 0.68/0.74 s(62) =< 440/29 0.68/0.74 s(63) =< 641/36 0.68/0.74 s(64) =< 4727/96 0.68/0.74 s(69) =< -132*V_a-11*V_b+5016 0.68/0.74 s(63) =< -48*V_a-4*V_b+7309/4 0.68/0.74 s(61) =< -42*V_a-7/2*V_b+1983/2 0.68/0.74 s(64) =< -42*V_a-7/2*V_b+54283/32 0.68/0.74 s(58) =< -12*V_a-V_b+378 0.68/0.74 s(70) =< -12*V_a-V_b+391 0.68/0.74 s(60) =< -12*V_a-V_b+587/2 0.68/0.74 s(59) =< -6*V_a-V_b/2+391/2 0.68/0.74 s(67) =< -V_a+V_b/2+125/12 0.68/0.74 s(65) =< -4/7*V_a-3/14*V_b+5 0.68/0.74 s(66) =< -V_a/2+V_b/4+7 0.68/0.74 s(68) =< -V_a/7+V_b/14+4/7 0.68/0.74 s(65) =< -V_b/2+7 0.68/0.74 s(62) =< s(69) 0.68/0.74 s(71) =< s(69) 0.68/0.74 s(57) =< s(70) 0.68/0.74 s(71) =< s(70) 0.68/0.74 s(66) =< s(58) 0.68/0.74 s(59) =< s(58) 0.68/0.74 s(66) =< s(63) 0.68/0.74 s(59) =< s(63) 0.68/0.74 s(60) =< s(59)*(3/8)+s(64) 0.68/0.74 s(60) =< s(59)*(3/8)+s(61) 0.68/0.74 s(60) =< s(66)*s(67) 0.68/0.74 s(71) =< s(68)*s(65) 0.68/0.74 0.68/0.74 with precondition: [V_b+7>=2*V_a,V_a>=V_b+1] 0.68/0.74 0.68/0.74 0.68/0.74 #### Cost of chains of eval_foo_start(V_a,V_b,B): 0.68/0.74 * Chain [27]: 1*s(72)+0 0.68/0.74 Such that:s(72) =< -V_a/2+15 0.68/0.74 s(72) =< -V_a/12+V_b/12+1/12 0.68/0.74 0.68/0.74 with precondition: [29>=V_a,V_b>=V_a,V_b+5*V_a>=168] 0.68/0.74 0.68/0.74 * Chain [26]: 1*s(74)+1*s(75)+1*s(76)+1*s(79)+1*s(81)+0 0.68/0.74 Such that:s(73) =< V_a-V_b+1/2 0.68/0.74 s(74) =< -161/144*V_a+23/144*V_b+5083/144 0.68/0.74 s(75) =< -21/116*V_a-113/348*V_b+5171/348 0.68/0.74 s(76) =< -11/48*V_a-5/48*V_b+169/16 0.68/0.74 s(75) =< -8/29*V_a-3/29*V_b+360/29 0.68/0.74 s(76) =< -7/24*V_a+V_b/24+33/4 0.68/0.74 s(74) =< -5/6*V_a-V_b/6+29 0.68/0.74 s(77) =< -5/32*V_a-97/96*V_b+3115/96 0.68/0.74 s(78) =< -3/8*V_a-V_b/2+111/8 0.68/0.74 s(79) =< -V_a/2-V_b/2+35/2 0.68/0.74 s(80) =< -V_a/3+10 0.68/0.74 s(81) =< -V_a/4+15/2 0.68/0.74 s(79) =< -V_a/4-13/12*V_b+451/12 0.68/0.74 s(82) =< -V_a/4-7/36*V_b+493/36 0.68/0.74 s(79) =< -V_b+17 0.68/0.74 s(77) =< -209/192*V_b+3055/96 0.68/0.74 s(74) =< -115/288*V_b+4439/144 0.68/0.74 s(78) =< -11/16*V_b+99/8 0.68/0.74 s(76) =< -5/48*V_b+85/12 0.68/0.74 s(73) =< -V_b/2+65/12 0.68/0.74 s(81) =< s(80) 0.68/0.74 s(76) =< s(80) 0.68/0.74 s(81) =< s(82) 0.68/0.74 s(76) =< s(82) 0.68/0.74 s(79) =< s(76)*(3/8)+s(77) 0.68/0.74 s(79) =< s(76)*(3/8)+s(78) 0.68/0.74 s(79) =< s(81)*s(73) 0.68/0.74 0.68/0.74 with precondition: [29>=V_a,V_a>=V_b+1,2*V_a>=V_b+8] 0.68/0.74 0.68/0.74 * Chain [25]: 1*s(84)+1*s(93)+1*s(94)+1*s(95)+1*s(96)+1*s(97)+0 0.68/0.74 Such that:s(83) =< 25/2 0.68/0.74 s(84) =< 55/2 0.68/0.74 s(83) =< 161/12 0.68/0.74 s(85) =< 187/2 0.68/0.74 s(86) =< 187/8 0.68/0.74 s(83) =< 1151/12 0.68/0.74 s(87) =< 20237/96 0.68/0.74 s(88) =< -15*V_a-3*V_b+570 0.68/0.74 s(89) =< -5*V_a-V_b+361/2 0.68/0.74 s(87) =< -485/96*V_a-97/96*V_b+16745/96 0.68/0.74 s(84) =< -235/24*V_a-47/24*V_b+737/2 0.68/0.74 s(90) =< -145/12*V_a-29/12*V_b+951/2 0.68/0.74 s(91) =< -145/24*V_a-29/24*V_b+461/2 0.68/0.74 s(84) =< -65/4*V_a-13/4*V_b+2311/4 0.68/0.74 s(91) =< -35/4*V_a-7/4*V_b+1273/4 0.68/0.74 s(92) =< -35/6*V_a-7/6*V_b+1273/6 0.68/0.74 s(87) =< -35/36*V_a-7/36*V_b+4055/96 0.68/0.74 s(86) =< -35/48*V_a-7/48*V_b+145/8 0.68/0.74 s(85) =< -5/2*V_a-V_b/2+151/2 0.68/0.74 s(93) =< -5/2*V_a-V_b/2+199/2 0.68/0.74 s(83) =< -5/2*V_a-V_b/2+935/12 0.68/0.74 s(94) =< -5/6*V_a-V_b/6+29 0.68/0.74 s(84) =< -5/6*V_a-V_b/6+43/2 0.68/0.74 s(83) =< -5/12*V_a-V_b/12+125/12 0.68/0.74 s(95) =< -V_a/12+V_b/12+1/12 0.68/0.74 s(96) =< s(88) 0.68/0.74 s(97) =< s(88) 0.68/0.74 s(83) =< s(89) 0.68/0.74 s(96) =< s(89) 0.68/0.74 s(93) =< s(90) 0.68/0.74 s(97) =< s(90) 0.68/0.74 s(86) =< s(85) 0.68/0.74 s(84) =< s(85) 0.68/0.74 s(96) =< s(92) 0.68/0.74 s(93) =< s(92) 0.68/0.74 s(96) =< s(91) 0.68/0.74 s(93) =< s(91) 0.68/0.74 s(84) =< s(93)*(3/8)+s(87) 0.68/0.74 s(84) =< s(93)*(3/8)+s(86) 0.68/0.74 s(84) =< s(96)*s(83) 0.68/0.74 0.68/0.74 with precondition: [27>=V_a,173>=5*V_a+V_b,V_b>=V_a,V_b+5*V_a+36>=0] 0.68/0.74 0.68/0.74 * Chain [24]: 0 0.68/0.74 with precondition: [V_a>=30] 0.68/0.74 0.68/0.74 * Chain [23]: 1*s(98)+1*s(100)+1*s(101)+1*s(103)+1*s(109)+1*s(112)+1*s(113)+1*s(115)+0 0.68/0.74 Such that:s(98) =< 35 0.68/0.74 s(99) =< 34/3 0.68/0.74 s(100) =< 35/4 0.68/0.74 s(101) =< 55/2 0.68/0.74 s(102) =< 187/8 0.68/0.74 s(103) =< 440/29 0.68/0.74 s(104) =< 641/36 0.68/0.74 s(105) =< 4727/96 0.68/0.74 s(106) =< -220*V_a-44*V_b+5786 0.68/0.74 s(102) =< -210*V_a-42*V_b+10601/2 0.68/0.74 s(104) =< -80*V_a-16*V_b+8429/4 0.68/0.74 s(107) =< -70*V_a-14*V_b+2473/2 0.68/0.74 s(105) =< -70*V_a-14*V_b+62123/32 0.68/0.74 s(99) =< -20*V_a-4*V_b+448 0.68/0.74 s(108) =< -20*V_a-4*V_b+461 0.68/0.74 s(101) =< -20*V_a-4*V_b+727/2 0.68/0.74 s(100) =< -10*V_a-2*V_b+461/2 0.68/0.74 s(109) =< -5*V_a-V_b+49 0.68/0.74 s(110) =< -5*V_a-V_b+545/12 0.68/0.74 s(111) =< -5*V_a-V_b+1213/12 0.68/0.74 s(112) =< -5/7*V_a-V_b/7+39/7 0.68/0.74 s(113) =< -V_a/12+V_b/12+1/12 0.68/0.74 s(102) =< s(107) 0.68/0.74 s(114) =< s(107) 0.68/0.74 s(111) =< s(110) 0.68/0.74 s(114) =< s(110) 0.68/0.74 s(103) =< s(106) 0.68/0.74 s(115) =< s(106) 0.68/0.74 s(98) =< s(108) 0.68/0.74 s(115) =< s(108) 0.68/0.74 s(109) =< s(99) 0.68/0.74 s(100) =< s(99) 0.68/0.74 s(109) =< s(104) 0.68/0.74 s(100) =< s(104) 0.68/0.74 s(101) =< s(100)*(3/8)+s(105) 0.68/0.74 s(101) =< s(100)*(3/8)+s(102) 0.68/0.74 s(101) =< s(109)*s(111) 0.68/0.74 s(115) =< s(112)*s(114) 0.68/0.74 0.68/0.74 with precondition: [35>=5*V_a+V_b,V_b>=2*V_a+7,V_b>=V_a] 0.68/0.74 0.68/0.74 * Chain [22]: 1*s(116)+1*s(118)+1*s(119)+1*s(121)+1*s(128)+1*s(129)+1*s(130)+0 0.68/0.74 Such that:s(116) =< 35 0.68/0.74 s(117) =< 34/3 0.68/0.74 s(118) =< 35/4 0.68/0.74 s(119) =< 55/2 0.68/0.74 s(120) =< 187/8 0.68/0.74 s(121) =< 440/29 0.68/0.74 s(122) =< 641/36 0.68/0.74 s(123) =< 4727/96 0.68/0.74 s(124) =< -132*V_a-11*V_b+5016 0.68/0.74 s(122) =< -48*V_a-4*V_b+7309/4 0.68/0.74 s(120) =< -42*V_a-7/2*V_b+1983/2 0.68/0.74 s(123) =< -42*V_a-7/2*V_b+54283/32 0.68/0.74 s(117) =< -12*V_a-V_b+378 0.68/0.74 s(125) =< -12*V_a-V_b+391 0.68/0.74 s(119) =< -12*V_a-V_b+587/2 0.68/0.74 s(118) =< -6*V_a-V_b/2+391/2 0.68/0.74 s(126) =< -V_a+V_b/2+125/12 0.68/0.74 s(127) =< -4/7*V_a-3/14*V_b+5 0.68/0.74 s(128) =< -V_a/2+V_b/4+7 0.68/0.74 s(129) =< -V_a/7+V_b/14+4/7 0.68/0.74 s(127) =< -V_b/2+7 0.68/0.74 s(121) =< s(124) 0.68/0.74 s(130) =< s(124) 0.68/0.74 s(116) =< s(125) 0.74/0.74 s(130) =< s(125) 0.74/0.74 s(128) =< s(117) 0.74/0.74 s(118) =< s(117) 0.74/0.74 s(128) =< s(122) 0.74/0.74 s(118) =< s(122) 0.74/0.74 s(119) =< s(118)*(3/8)+s(123) 0.74/0.74 s(119) =< s(118)*(3/8)+s(120) 0.74/0.74 s(119) =< s(128)*s(126) 0.74/0.74 s(130) =< s(129)*s(127) 0.74/0.74 0.74/0.74 with precondition: [V_b+7>=2*V_a,V_a>=V_b+1] 0.74/0.74 0.74/0.74 0.74/0.74 Closed-form bounds of eval_foo_start(V_a,V_b,B): 0.74/0.74 ------------------------------------- 0.74/0.74 * Chain [27] with precondition: [29>=V_a,V_b>=V_a,V_b+5*V_a>=168] 0.74/0.74 - Upper bound: -V_a/2+15 0.74/0.74 - Complexity: n 0.74/0.74 * Chain [26] with precondition: [29>=V_a,V_a>=V_b+1,2*V_a>=V_b+8] 0.74/0.74 - Upper bound: -V_a/4+15/2+(-11/48*V_a-5/48*V_b+169/16+(-21/116*V_a-113/348*V_b+5171/348+nat(-161/144*V_a+23/144*V_b+5083/144))+nat(-V_a/2-V_b/2+35/2)) 0.74/0.74 - Complexity: n 0.74/0.74 * Chain [25] with precondition: [27>=V_a,173>=5*V_a+V_b,V_b>=V_a,V_b+5*V_a+36>=0] 0.74/0.74 - Upper bound: -401/12*V_a-79/12*V_b+15553/12 0.74/0.74 - Complexity: n 0.74/0.74 * Chain [24] with precondition: [V_a>=30] 0.74/0.74 - Upper bound: 0 0.74/0.74 - Complexity: constant 0.74/0.74 * Chain [23] with precondition: [35>=5*V_a+V_b,V_b>=2*V_a+7,V_b>=V_a] 0.74/0.74 - Upper bound: -18547/84*V_a-3701/84*V_b+3586651/609 0.74/0.74 - Complexity: n 0.74/0.74 * Chain [22] with precondition: [V_b+7>=2*V_a,V_a>=V_b+1] 0.74/0.74 - Upper bound: -925/7*V_a-153/14*V_b+12458501/2436 0.74/0.74 - Complexity: n 0.74/0.74 0.74/0.74 ### Maximum cost of eval_foo_start(V_a,V_b,B): max([max([nat(-V_a/2+15),nat(-21/116*V_a-113/348*V_b+5171/348)+nat(-161/144*V_a+23/144*V_b+5083/144)+nat(-11/48*V_a-5/48*V_b+169/16)+nat(-V_a/2-V_b/2+35/2)+nat(-V_a/4+15/2),34019/348+nat(-V_a/7+V_b/14+4/7)+nat(-132*V_a-11*V_b+5016)]),55/2+nat(-V_a/12+V_b/12+1/12)+max([nat(-15*V_a-3*V_b+570)*2+nat(-5/2*V_a-V_b/2+199/2)+nat(-5/6*V_a-V_b/6+29),24449/348+nat(-220*V_a-44*V_b+5786)+nat(-5/7*V_a-V_b/7+39/7)])]) 0.74/0.74 Asymptotic class: n 0.74/0.74 * Total analysis performed in 626 ms. 0.74/0.74 0.74/0.84 EOF