0.05/0.17	WORST_CASE(?,O(n^1))  
0.05/0.17	
0.05/0.17	Preprocessing Cost Relations
0.05/0.17	=====================================
0.05/0.17	
0.05/0.17	#### Computed strongly connected components 
0.05/0.17	0. recursive  : [eval_speed_popl10_fig2_1_bb1_in/5,eval_speed_popl10_fig2_1_bb2_in/5]
0.05/0.17	1. non_recursive  : [eval_speed_popl10_fig2_1_stop/1]
0.05/0.17	2. non_recursive  : [eval_speed_popl10_fig2_1_bb3_in/1]
0.05/0.17	3. non_recursive  : [eval_speed_popl10_fig2_1_bb1_in_loop_cont/2]
0.05/0.17	4. non_recursive  : [eval_speed_popl10_fig2_1_bb0_in/5]
0.05/0.17	5. non_recursive  : [eval_speed_popl10_fig2_1_start/5]
0.05/0.17	
0.05/0.17	#### Obtained direct recursion through partial evaluation 
0.05/0.17	0. SCC is partially evaluated into eval_speed_popl10_fig2_1_bb1_in/5
0.05/0.17	1. SCC is completely evaluated into other SCCs
0.05/0.17	2. SCC is completely evaluated into other SCCs
0.05/0.17	3. SCC is completely evaluated into other SCCs
0.05/0.17	4. SCC is partially evaluated into eval_speed_popl10_fig2_1_bb0_in/5
0.05/0.17	5. SCC is partially evaluated into eval_speed_popl10_fig2_1_start/5
0.05/0.17	
0.05/0.17	Control-Flow Refinement of Cost Relations
0.05/0.17	=====================================
0.05/0.17	
0.05/0.17	### Specialization of cost equations eval_speed_popl10_fig2_1_bb1_in/5 
0.05/0.17	* CE 5 is refined into CE [6] 
0.05/0.17	* CE 3 is refined into CE [7] 
0.05/0.17	* CE 4 is refined into CE [8] 
0.05/0.17	
0.05/0.17	
0.05/0.17	### Cost equations --> "Loop" of eval_speed_popl10_fig2_1_bb1_in/5 
0.05/0.17	* CEs [7] --> Loop 6 
0.05/0.17	* CEs [8] --> Loop 7 
0.05/0.17	* CEs [6] --> Loop 8 
0.05/0.17	
0.05/0.17	### Ranking functions of CR eval_speed_popl10_fig2_1_bb1_in(V_n,V_m,V__01,V__0,B) 
0.05/0.17	* RF of phase [6]: [V_n-V__0]
0.05/0.17	* RF of phase [7]: [V_m-V__01]
0.05/0.17	
0.05/0.17	#### Partial ranking functions of CR eval_speed_popl10_fig2_1_bb1_in(V_n,V_m,V__01,V__0,B) 
0.05/0.17	* Partial RF of phase [6]:
0.05/0.17	  - RF of loop [6:1]:
0.05/0.17	    V_n-V__0
0.05/0.17	* Partial RF of phase [7]:
0.05/0.17	  - RF of loop [7:1]:
0.05/0.17	    V_m-V__01
0.05/0.17	
0.05/0.17	
0.05/0.17	### Specialization of cost equations eval_speed_popl10_fig2_1_bb0_in/5 
0.05/0.17	* CE 2 is refined into CE [9,10,11] 
0.05/0.17	
0.05/0.17	
0.05/0.17	### Cost equations --> "Loop" of eval_speed_popl10_fig2_1_bb0_in/5 
0.05/0.17	* CEs [9] --> Loop 9 
0.05/0.17	* CEs [10] --> Loop 10 
0.05/0.17	* CEs [11] --> Loop 11 
0.05/0.17	
0.05/0.17	### Ranking functions of CR eval_speed_popl10_fig2_1_bb0_in(V_x,V_y,V_n,V_m,B) 
0.05/0.17	
0.05/0.17	#### Partial ranking functions of CR eval_speed_popl10_fig2_1_bb0_in(V_x,V_y,V_n,V_m,B) 
0.05/0.17	
0.05/0.17	
0.05/0.17	### Specialization of cost equations eval_speed_popl10_fig2_1_start/5 
0.05/0.17	* CE 1 is refined into CE [12,13,14] 
0.05/0.17	
0.05/0.17	
0.05/0.17	### Cost equations --> "Loop" of eval_speed_popl10_fig2_1_start/5 
0.05/0.17	* CEs [14] --> Loop 12 
0.05/0.17	* CEs [13] --> Loop 13 
0.05/0.17	* CEs [12] --> Loop 14 
0.05/0.17	
0.05/0.17	### Ranking functions of CR eval_speed_popl10_fig2_1_start(V_x,V_y,V_n,V_m,B) 
0.05/0.17	
0.05/0.17	#### Partial ranking functions of CR eval_speed_popl10_fig2_1_start(V_x,V_y,V_n,V_m,B) 
0.05/0.17	
0.05/0.17	
0.05/0.17	Computing Bounds
0.05/0.17	=====================================
0.05/0.17	
0.05/0.17	#### Cost of chains of eval_speed_popl10_fig2_1_bb1_in(V_n,V_m,V__01,V__0,B):
0.05/0.17	* Chain [[7],[6],8]: 1*it(6)+1*it(7)+0
0.05/0.17	  Such that:it(6) =< V_n-V__0
0.05/0.17	it(7) =< V_m-V__01
0.05/0.17	
0.05/0.17	  with precondition: [B=2,V_m>=V__01+1,V_n>=V__0+1] 
0.05/0.17	
0.05/0.17	* Chain [[6],8]: 1*it(6)+0
0.05/0.17	  Such that:it(6) =< V_n-V__0
0.05/0.17	
0.05/0.17	  with precondition: [B=2,V__01>=V_m,V_n>=V__0+1] 
0.05/0.17	
0.05/0.17	* Chain [8]: 0
0.05/0.17	  with precondition: [B=2,V__0>=V_n] 
0.05/0.17	
0.05/0.17	
0.05/0.17	#### Cost of chains of eval_speed_popl10_fig2_1_bb0_in(V_x,V_y,V_n,V_m,B):
0.05/0.17	* Chain [11]: 1*s(1)+1*s(2)+0
0.05/0.17	  Such that:s(1) =< -V_x+V_n
0.05/0.17	s(2) =< -V_y+V_m
0.05/0.17	
0.05/0.17	  with precondition: [V_n>=V_x+1,V_m>=V_y+1] 
0.05/0.17	
0.05/0.17	* Chain [10]: 1*s(3)+0
0.05/0.17	  Such that:s(3) =< -V_x+V_n
0.05/0.17	
0.05/0.17	  with precondition: [V_n>=V_x+1,V_y>=V_m] 
0.05/0.17	
0.05/0.17	* Chain [9]: 0
0.05/0.17	  with precondition: [V_x>=V_n] 
0.05/0.17	
0.05/0.17	
0.05/0.17	#### Cost of chains of eval_speed_popl10_fig2_1_start(V_x,V_y,V_n,V_m,B):
0.05/0.17	* Chain [14]: 1*s(4)+1*s(5)+0
0.05/0.17	  Such that:s(4) =< -V_x+V_n
0.05/0.17	s(5) =< -V_y+V_m
0.05/0.17	
0.05/0.17	  with precondition: [V_n>=V_x+1,V_m>=V_y+1] 
0.05/0.17	
0.05/0.17	* Chain [13]: 1*s(6)+0
0.05/0.17	  Such that:s(6) =< -V_x+V_n
0.05/0.17	
0.05/0.17	  with precondition: [V_n>=V_x+1,V_y>=V_m] 
0.05/0.17	
0.05/0.17	* Chain [12]: 0
0.05/0.17	  with precondition: [V_x>=V_n] 
0.05/0.17	
0.05/0.17	
0.05/0.17	Closed-form bounds of eval_speed_popl10_fig2_1_start(V_x,V_y,V_n,V_m,B): 
0.05/0.17	-------------------------------------
0.05/0.17	* Chain [14] with precondition: [V_n>=V_x+1,V_m>=V_y+1] 
0.05/0.17	    - Upper bound: -V_x-V_y+V_n+V_m 
0.05/0.17	    - Complexity: n 
0.05/0.17	* Chain [13] with precondition: [V_n>=V_x+1,V_y>=V_m] 
0.05/0.17	    - Upper bound: -V_x+V_n 
0.05/0.17	    - Complexity: n 
0.05/0.17	* Chain [12] with precondition: [V_x>=V_n] 
0.05/0.17	    - Upper bound: 0 
0.05/0.17	    - Complexity: constant 
0.05/0.17	
0.05/0.17	### Maximum cost of eval_speed_popl10_fig2_1_start(V_x,V_y,V_n,V_m,B): nat(-V_y+V_m)+nat(-V_x+V_n) 
0.05/0.17	Asymptotic class: n 
0.05/0.17	* Total analysis performed in 102 ms.
0.05/0.17	
0.05/0.27	EOF