0.05/0.11	WORST_CASE(?,O(n^1))  
0.05/0.11	
0.05/0.11	Preprocessing Cost Relations
0.05/0.11	=====================================
0.05/0.11	
0.05/0.11	#### Computed strongly connected components 
0.05/0.11	0. recursive  : [eval_textbook_ex1_bb1_in/3,eval_textbook_ex1_bb2_in/3]
0.05/0.11	1. non_recursive  : [eval_textbook_ex1_stop/1]
0.05/0.11	2. non_recursive  : [eval_textbook_ex1_bb3_in/1]
0.05/0.11	3. non_recursive  : [eval_textbook_ex1_bb1_in_loop_cont/2]
0.05/0.11	4. non_recursive  : [eval_textbook_ex1_bb0_in/3]
0.05/0.11	5. non_recursive  : [eval_textbook_ex1_start/3]
0.05/0.11	
0.05/0.11	#### Obtained direct recursion through partial evaluation 
0.05/0.11	0. SCC is partially evaluated into eval_textbook_ex1_bb1_in/3
0.05/0.11	1. SCC is completely evaluated into other SCCs
0.05/0.11	2. SCC is completely evaluated into other SCCs
0.05/0.11	3. SCC is completely evaluated into other SCCs
0.05/0.11	4. SCC is partially evaluated into eval_textbook_ex1_bb0_in/3
0.05/0.11	5. SCC is partially evaluated into eval_textbook_ex1_start/3
0.05/0.11	
0.05/0.11	Control-Flow Refinement of Cost Relations
0.05/0.11	=====================================
0.05/0.11	
0.05/0.11	### Specialization of cost equations eval_textbook_ex1_bb1_in/3 
0.05/0.11	* CE 4 is refined into CE [5] 
0.05/0.11	* CE 3 is refined into CE [6] 
0.05/0.11	
0.05/0.11	
0.05/0.11	### Cost equations --> "Loop" of eval_textbook_ex1_bb1_in/3 
0.05/0.11	* CEs [6] --> Loop 5 
0.05/0.11	* CEs [5] --> Loop 6 
0.05/0.11	
0.05/0.11	### Ranking functions of CR eval_textbook_ex1_bb1_in(V_b,V_i_0,B) 
0.05/0.11	* RF of phase [5]: [V_b-V_i_0+1]
0.05/0.11	
0.05/0.11	#### Partial ranking functions of CR eval_textbook_ex1_bb1_in(V_b,V_i_0,B) 
0.05/0.11	* Partial RF of phase [5]:
0.05/0.11	  - RF of loop [5:1]:
0.05/0.11	    V_b-V_i_0+1
0.05/0.11	
0.05/0.11	
0.05/0.11	### Specialization of cost equations eval_textbook_ex1_bb0_in/3 
0.05/0.11	* CE 2 is refined into CE [7,8] 
0.05/0.11	
0.05/0.11	
0.05/0.11	### Cost equations --> "Loop" of eval_textbook_ex1_bb0_in/3 
0.05/0.11	* CEs [7] --> Loop 7 
0.05/0.11	* CEs [8] --> Loop 8 
0.05/0.11	
0.05/0.11	### Ranking functions of CR eval_textbook_ex1_bb0_in(V_a,V_b,B) 
0.05/0.11	
0.05/0.11	#### Partial ranking functions of CR eval_textbook_ex1_bb0_in(V_a,V_b,B) 
0.05/0.11	
0.05/0.11	
0.05/0.11	### Specialization of cost equations eval_textbook_ex1_start/3 
0.05/0.11	* CE 1 is refined into CE [9,10] 
0.05/0.11	
0.05/0.11	
0.05/0.11	### Cost equations --> "Loop" of eval_textbook_ex1_start/3 
0.05/0.11	* CEs [10] --> Loop 9 
0.05/0.11	* CEs [9] --> Loop 10 
0.05/0.11	
0.05/0.11	### Ranking functions of CR eval_textbook_ex1_start(V_a,V_b,B) 
0.05/0.11	
0.05/0.11	#### Partial ranking functions of CR eval_textbook_ex1_start(V_a,V_b,B) 
0.05/0.11	
0.05/0.11	
0.05/0.11	Computing Bounds
0.05/0.11	=====================================
0.05/0.11	
0.05/0.11	#### Cost of chains of eval_textbook_ex1_bb1_in(V_b,V_i_0,B):
0.05/0.11	* Chain [[5],6]: 1*it(5)+0
0.05/0.11	  Such that:it(5) =< V_b-V_i_0+1
0.05/0.11	
0.05/0.11	  with precondition: [B=2,V_b>=V_i_0] 
0.05/0.11	
0.05/0.11	* Chain [6]: 0
0.05/0.11	  with precondition: [B=2,V_i_0>=V_b+1] 
0.05/0.11	
0.05/0.11	
0.05/0.11	#### Cost of chains of eval_textbook_ex1_bb0_in(V_a,V_b,B):
0.05/0.11	* Chain [8]: 1*s(1)+0
0.05/0.11	  Such that:s(1) =< -V_a+V_b+1
0.05/0.11	
0.05/0.11	  with precondition: [V_b>=V_a] 
0.05/0.11	
0.05/0.11	* Chain [7]: 0
0.05/0.11	  with precondition: [V_a>=V_b+1] 
0.05/0.11	
0.05/0.11	
0.05/0.11	#### Cost of chains of eval_textbook_ex1_start(V_a,V_b,B):
0.05/0.11	* Chain [10]: 1*s(2)+0
0.05/0.11	  Such that:s(2) =< -V_a+V_b+1
0.05/0.11	
0.05/0.11	  with precondition: [V_b>=V_a] 
0.05/0.11	
0.05/0.11	* Chain [9]: 0
0.05/0.11	  with precondition: [V_a>=V_b+1] 
0.05/0.11	
0.05/0.11	
0.05/0.11	Closed-form bounds of eval_textbook_ex1_start(V_a,V_b,B): 
0.05/0.11	-------------------------------------
0.05/0.11	* Chain [10] with precondition: [V_b>=V_a] 
0.05/0.11	    - Upper bound: -V_a+V_b+1 
0.05/0.11	    - Complexity: n 
0.05/0.11	* Chain [9] with precondition: [V_a>=V_b+1] 
0.05/0.11	    - Upper bound: 0 
0.05/0.11	    - Complexity: constant 
0.05/0.11	
0.05/0.11	### Maximum cost of eval_textbook_ex1_start(V_a,V_b,B): nat(-V_a+V_b+1) 
0.05/0.11	Asymptotic class: n 
0.05/0.11	* Total analysis performed in 41 ms.
0.05/0.11	
0.05/0.21	EOF