0.05/0.19	WORST_CASE(?,O(n^1))  
0.05/0.19	
0.05/0.19	Preprocessing Cost Relations
0.05/0.19	=====================================
0.05/0.19	
0.05/0.19	#### Computed strongly connected components 
0.05/0.19	0. recursive  : [eval_peed_pldi09_fig4_2_bb1_in/4,eval_peed_pldi09_fig4_2_bb2_in/4,eval_peed_pldi09_fig4_2_bb3_in/4]
0.05/0.19	1. non_recursive  : [eval_peed_pldi09_fig4_2_stop/1]
0.05/0.19	2. non_recursive  : [eval_peed_pldi09_fig4_2_bb4_in/1]
0.05/0.19	3. non_recursive  : [eval_peed_pldi09_fig4_2_bb1_in_loop_cont/2]
0.05/0.19	4. non_recursive  : [eval_peed_pldi09_fig4_2_bb0_in/3]
0.05/0.19	5. non_recursive  : [eval_peed_pldi09_fig4_2_start/3]
0.05/0.19	
0.05/0.19	#### Obtained direct recursion through partial evaluation 
0.05/0.19	0. SCC is partially evaluated into eval_peed_pldi09_fig4_2_bb1_in/4
0.05/0.19	1. SCC is completely evaluated into other SCCs
0.05/0.19	2. SCC is completely evaluated into other SCCs
0.05/0.19	3. SCC is completely evaluated into other SCCs
0.05/0.19	4. SCC is partially evaluated into eval_peed_pldi09_fig4_2_bb0_in/3
0.05/0.19	5. SCC is partially evaluated into eval_peed_pldi09_fig4_2_start/3
0.05/0.19	
0.05/0.19	Control-Flow Refinement of Cost Relations
0.05/0.19	=====================================
0.05/0.19	
0.05/0.19	### Specialization of cost equations eval_peed_pldi09_fig4_2_bb1_in/4 
0.05/0.19	* CE 6 is refined into CE [7] 
0.05/0.19	* CE 5 is refined into CE [8] 
0.05/0.19	* CE 4 is refined into CE [9] 
0.05/0.19	
0.05/0.19	
0.05/0.19	### Cost equations --> "Loop" of eval_peed_pldi09_fig4_2_bb1_in/4 
0.05/0.19	* CEs [8] --> Loop 7 
0.05/0.19	* CEs [9] --> Loop 8 
0.05/0.19	* CEs [7] --> Loop 9 
0.05/0.19	
0.05/0.19	### Ranking functions of CR eval_peed_pldi09_fig4_2_bb1_in(V_m,V_va_0,V_vb_0,B) 
0.05/0.19	* RF of phase [7,8]: [2*V_va_0+V_vb_0-1]
0.05/0.19	
0.05/0.19	#### Partial ranking functions of CR eval_peed_pldi09_fig4_2_bb1_in(V_m,V_va_0,V_vb_0,B) 
0.05/0.19	* Partial RF of phase [7,8]:
0.05/0.19	  - RF of loop [7:1]:
0.05/0.19	    V_m-V_vb_0 depends on loops [8:1] 
0.05/0.19	    V_va_0
0.05/0.19	  - RF of loop [8:1]:
0.05/0.19	    -V_m+V_vb_0+1 depends on loops [7:1] 
0.05/0.19	    V_vb_0 depends on loops [7:1] 
0.05/0.19	
0.05/0.19	
0.05/0.19	### Specialization of cost equations eval_peed_pldi09_fig4_2_bb0_in/3 
0.05/0.19	* CE 3 is refined into CE [10,11] 
0.05/0.19	* CE 2 is refined into CE [12] 
0.05/0.19	
0.05/0.19	
0.05/0.19	### Cost equations --> "Loop" of eval_peed_pldi09_fig4_2_bb0_in/3 
0.05/0.19	* CEs [11] --> Loop 10 
0.05/0.19	* CEs [12] --> Loop 11 
0.05/0.19	* CEs [10] --> Loop 12 
0.05/0.19	
0.05/0.19	### Ranking functions of CR eval_peed_pldi09_fig4_2_bb0_in(V_n,V_m,B) 
0.05/0.19	
0.05/0.19	#### Partial ranking functions of CR eval_peed_pldi09_fig4_2_bb0_in(V_n,V_m,B) 
0.05/0.19	
0.05/0.19	
0.05/0.19	### Specialization of cost equations eval_peed_pldi09_fig4_2_start/3 
0.05/0.19	* CE 1 is refined into CE [13,14,15] 
0.05/0.19	
0.05/0.19	
0.05/0.19	### Cost equations --> "Loop" of eval_peed_pldi09_fig4_2_start/3 
0.05/0.19	* CEs [15] --> Loop 13 
0.05/0.19	* CEs [14] --> Loop 14 
0.05/0.19	* CEs [13] --> Loop 15 
0.05/0.19	
0.05/0.19	### Ranking functions of CR eval_peed_pldi09_fig4_2_start(V_n,V_m,B) 
0.05/0.19	
0.05/0.19	#### Partial ranking functions of CR eval_peed_pldi09_fig4_2_start(V_n,V_m,B) 
0.05/0.19	
0.05/0.19	
0.05/0.19	Computing Bounds
0.05/0.19	=====================================
0.05/0.19	
0.05/0.19	#### Cost of chains of eval_peed_pldi09_fig4_2_bb1_in(V_m,V_va_0,V_vb_0,B):
0.05/0.19	* Chain [[7,8],9]: 1*it(7)+1*it(8)+0
0.05/0.19	  Such that:it(7) =< V_va_0
0.05/0.19	aux(20) =< 2*V_va_0+V_vb_0
0.05/0.19	it(7) =< aux(20)
0.05/0.19	it(8) =< aux(20)
0.05/0.19	
0.05/0.19	  with precondition: [B=2,V_m>=1,V_va_0>=1,V_vb_0>=0] 
0.05/0.19	
0.05/0.19	* Chain [9]: 0
0.05/0.19	  with precondition: [B=2,0>=V_va_0,V_m>=1,V_vb_0>=0] 
0.05/0.19	
0.05/0.19	
0.05/0.19	#### Cost of chains of eval_peed_pldi09_fig4_2_bb0_in(V_n,V_m,B):
0.05/0.19	* Chain [12]: 0
0.05/0.19	  with precondition: [0>=V_n,V_m>=1] 
0.05/0.19	
0.05/0.19	* Chain [11]: 0
0.05/0.19	  with precondition: [0>=V_m] 
0.05/0.19	
0.05/0.19	* Chain [10]: 1*s(1)+1*s(3)+0
0.05/0.19	  Such that:s(1) =< V_n
0.05/0.19	s(2) =< 2*V_n
0.05/0.19	s(1) =< s(2)
0.05/0.19	s(3) =< s(2)
0.05/0.19	
0.05/0.19	  with precondition: [V_n>=1,V_m>=1] 
0.05/0.19	
0.05/0.19	
0.05/0.19	#### Cost of chains of eval_peed_pldi09_fig4_2_start(V_n,V_m,B):
0.05/0.19	* Chain [15]: 0
0.05/0.19	  with precondition: [0>=V_n,V_m>=1] 
0.05/0.19	
0.05/0.19	* Chain [14]: 0
0.05/0.19	  with precondition: [0>=V_m] 
0.05/0.19	
0.05/0.19	* Chain [13]: 1*s(4)+1*s(6)+0
0.05/0.19	  Such that:s(4) =< V_n
0.05/0.19	s(5) =< 2*V_n
0.05/0.19	s(4) =< s(5)
0.05/0.19	s(6) =< s(5)
0.05/0.19	
0.05/0.19	  with precondition: [V_n>=1,V_m>=1] 
0.05/0.19	
0.05/0.19	
0.05/0.19	Closed-form bounds of eval_peed_pldi09_fig4_2_start(V_n,V_m,B): 
0.05/0.19	-------------------------------------
0.05/0.19	* Chain [15] with precondition: [0>=V_n,V_m>=1] 
0.05/0.19	    - Upper bound: 0 
0.05/0.19	    - Complexity: constant 
0.05/0.19	* Chain [14] with precondition: [0>=V_m] 
0.05/0.19	    - Upper bound: 0 
0.05/0.19	    - Complexity: constant 
0.05/0.19	* Chain [13] with precondition: [V_n>=1,V_m>=1] 
0.05/0.19	    - Upper bound: 3*V_n 
0.05/0.19	    - Complexity: n 
0.05/0.19	
0.05/0.19	### Maximum cost of eval_peed_pldi09_fig4_2_start(V_n,V_m,B): nat(2*V_n)+nat(V_n) 
0.05/0.19	Asymptotic class: n 
0.05/0.19	* Total analysis performed in 114 ms.
0.05/0.19	
0.05/0.29	EOF