0.05/0.16	WORST_CASE(?,O(n^1))  
0.05/0.16	
0.05/0.16	Preprocessing Cost Relations
0.05/0.16	=====================================
0.05/0.16	
0.05/0.16	#### Computed strongly connected components 
0.05/0.16	0. recursive  : [eval_speed_pldi09_fig1_bb1_in/4,eval_speed_pldi09_fig1_bb2_in/4,eval_speed_pldi09_fig1_bb3_in/4,eval_speed_pldi09_fig1_bb4_in/4]
0.05/0.16	1. non_recursive  : [eval_speed_pldi09_fig1_stop/1]
0.05/0.16	2. non_recursive  : [eval_speed_pldi09_fig1_bb5_in/1]
0.05/0.16	3. non_recursive  : [eval_speed_pldi09_fig1_bb1_in_loop_cont/2]
0.05/0.16	4. non_recursive  : [eval_speed_pldi09_fig1_bb0_in/2]
0.05/0.16	5. non_recursive  : [eval_speed_pldi09_fig1_start/2]
0.05/0.16	
0.05/0.16	#### Obtained direct recursion through partial evaluation 
0.05/0.16	0. SCC is partially evaluated into eval_speed_pldi09_fig1_bb1_in/4
0.05/0.16	1. SCC is completely evaluated into other SCCs
0.05/0.16	2. SCC is completely evaluated into other SCCs
0.05/0.16	3. SCC is completely evaluated into other SCCs
0.05/0.16	4. SCC is partially evaluated into eval_speed_pldi09_fig1_bb0_in/2
0.05/0.16	5. SCC is partially evaluated into eval_speed_pldi09_fig1_start/2
0.05/0.16	
0.05/0.16	Control-Flow Refinement of Cost Relations
0.05/0.16	=====================================
0.05/0.16	
0.05/0.16	### Specialization of cost equations eval_speed_pldi09_fig1_bb1_in/4 
0.05/0.16	* CE 4 is refined into CE [6] 
0.05/0.16	* CE 5 is refined into CE [7] 
0.05/0.16	* CE 3 is refined into CE [8] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_speed_pldi09_fig1_bb1_in/4 
0.05/0.16	* CEs [8] --> Loop 6 
0.05/0.16	* CEs [6] --> Loop 7 
0.05/0.16	* CEs [7] --> Loop 8 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_speed_pldi09_fig1_bb1_in(V_n,V_y_0,V_x_0,B) 
0.05/0.16	* RF of phase [7]: [V_y_0]
0.05/0.16	* RF of phase [8]: [V_n-V_x_0,V_n-V_y_0]
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_speed_pldi09_fig1_bb1_in(V_n,V_y_0,V_x_0,B) 
0.05/0.16	* Partial RF of phase [7]:
0.05/0.16	  - RF of loop [7:1]:
0.05/0.16	    V_y_0
0.05/0.16	* Partial RF of phase [8]:
0.05/0.16	  - RF of loop [8:1]:
0.05/0.16	    V_n-V_x_0
0.05/0.16	    V_n-V_y_0
0.05/0.16	
0.05/0.16	
0.05/0.16	### Specialization of cost equations eval_speed_pldi09_fig1_bb0_in/2 
0.05/0.16	* CE 2 is refined into CE [9,10] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_speed_pldi09_fig1_bb0_in/2 
0.05/0.16	* CEs [10] --> Loop 9 
0.05/0.16	* CEs [9] --> Loop 10 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_speed_pldi09_fig1_bb0_in(V_n,B) 
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_speed_pldi09_fig1_bb0_in(V_n,B) 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Specialization of cost equations eval_speed_pldi09_fig1_start/2 
0.05/0.16	* CE 1 is refined into CE [11,12] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_speed_pldi09_fig1_start/2 
0.05/0.16	* CEs [12] --> Loop 11 
0.05/0.16	* CEs [11] --> Loop 12 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_speed_pldi09_fig1_start(V_n,B) 
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_speed_pldi09_fig1_start(V_n,B) 
0.05/0.16	
0.05/0.16	
0.05/0.16	Computing Bounds
0.05/0.16	=====================================
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_speed_pldi09_fig1_bb1_in(V_n,V_y_0,V_x_0,B):
0.05/0.16	* Chain [[8],[7],6]: 1*it(7)+1*it(8)+0
0.05/0.16	  Such that:it(7) =< V_n
0.05/0.16	it(8) =< V_n-V_x_0
0.05/0.16	
0.05/0.16	  with precondition: [B=2,V_y_0=V_x_0,V_y_0>=0,V_n>=V_y_0+1] 
0.05/0.16	
0.05/0.16	* Chain [6]: 0
0.05/0.16	  with precondition: [V_y_0=0,B=2,V_x_0>=0,V_x_0>=V_n] 
0.05/0.16	
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_speed_pldi09_fig1_bb0_in(V_n,B):
0.05/0.16	* Chain [10]: 0
0.05/0.16	  with precondition: [0>=V_n] 
0.05/0.16	
0.05/0.16	* Chain [9]: 2*s(1)+0
0.05/0.16	  Such that:aux(1) =< V_n
0.05/0.16	s(1) =< aux(1)
0.05/0.16	
0.05/0.16	  with precondition: [V_n>=1] 
0.05/0.16	
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_speed_pldi09_fig1_start(V_n,B):
0.05/0.16	* Chain [12]: 0
0.05/0.16	  with precondition: [0>=V_n] 
0.05/0.16	
0.05/0.16	* Chain [11]: 2*s(4)+0
0.05/0.16	  Such that:s(3) =< V_n
0.05/0.16	s(4) =< s(3)
0.05/0.16	
0.05/0.16	  with precondition: [V_n>=1] 
0.05/0.16	
0.05/0.16	
0.05/0.16	Closed-form bounds of eval_speed_pldi09_fig1_start(V_n,B): 
0.05/0.16	-------------------------------------
0.05/0.16	* Chain [12] with precondition: [0>=V_n] 
0.05/0.16	    - Upper bound: 0 
0.05/0.16	    - Complexity: constant 
0.05/0.16	* Chain [11] with precondition: [V_n>=1] 
0.05/0.16	    - Upper bound: 2*V_n 
0.05/0.16	    - Complexity: n 
0.05/0.16	
0.05/0.16	### Maximum cost of eval_speed_pldi09_fig1_start(V_n,B): nat(V_n)*2 
0.05/0.16	Asymptotic class: n 
0.05/0.16	* Total analysis performed in 91 ms.
0.05/0.16	
0.05/0.26	EOF