0.04/0.11	WORST_CASE(?,O(n^1))  
0.04/0.11	
0.04/0.11	Preprocessing Cost Relations
0.04/0.11	=====================================
0.04/0.11	
0.04/0.11	#### Computed strongly connected components 
0.04/0.11	0. recursive  : [eval_foo_bb1_in/3,eval_foo_bb2_in/3]
0.04/0.11	1. non_recursive  : [eval_foo_stop/1]
0.04/0.11	2. non_recursive  : [eval_foo_bb3_in/1]
0.04/0.11	3. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
0.04/0.11	4. non_recursive  : [eval_foo_bb0_in/3]
0.04/0.11	5. non_recursive  : [eval_foo_start/4]
0.04/0.11	
0.04/0.11	#### Obtained direct recursion through partial evaluation 
0.04/0.11	0. SCC is partially evaluated into eval_foo_bb1_in/3
0.04/0.11	1. SCC is completely evaluated into other SCCs
0.04/0.11	2. SCC is completely evaluated into other SCCs
0.04/0.11	3. SCC is completely evaluated into other SCCs
0.04/0.11	4. SCC is partially evaluated into eval_foo_bb0_in/3
0.04/0.11	5. SCC is partially evaluated into eval_foo_start/4
0.04/0.11	
0.04/0.11	Control-Flow Refinement of Cost Relations
0.04/0.11	=====================================
0.04/0.11	
0.04/0.11	### Specialization of cost equations eval_foo_bb1_in/3 
0.04/0.11	* CE 4 is refined into CE [5] 
0.04/0.11	* CE 3 is refined into CE [6] 
0.04/0.11	
0.04/0.11	
0.04/0.11	### Cost equations --> "Loop" of eval_foo_bb1_in/3 
0.04/0.11	* CEs [6] --> Loop 5 
0.04/0.11	* CEs [5] --> Loop 6 
0.04/0.11	
0.04/0.11	### Ranking functions of CR eval_foo_bb1_in(V__02,V__01,B) 
0.04/0.11	* RF of phase [5]: [-V__02/2+V__01/2]
0.04/0.11	
0.04/0.11	#### Partial ranking functions of CR eval_foo_bb1_in(V__02,V__01,B) 
0.04/0.11	* Partial RF of phase [5]:
0.04/0.11	  - RF of loop [5:1]:
0.04/0.11	    -V__02/2+V__01/2
0.04/0.11	
0.04/0.11	
0.04/0.11	### Specialization of cost equations eval_foo_bb0_in/3 
0.04/0.11	* CE 2 is refined into CE [7,8] 
0.04/0.11	
0.04/0.11	
0.04/0.11	### Cost equations --> "Loop" of eval_foo_bb0_in/3 
0.04/0.11	* CEs [7] --> Loop 7 
0.04/0.11	* CEs [8] --> Loop 8 
0.04/0.11	
0.04/0.11	### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 
0.04/0.11	
0.04/0.11	#### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 
0.04/0.11	
0.04/0.11	
0.04/0.11	### Specialization of cost equations eval_foo_start/4 
0.04/0.11	* CE 1 is refined into CE [9,10] 
0.04/0.11	
0.04/0.11	
0.04/0.11	### Cost equations --> "Loop" of eval_foo_start/4 
0.04/0.11	* CEs [10] --> Loop 9 
0.04/0.11	* CEs [9] --> Loop 10 
0.04/0.11	
0.04/0.11	### Ranking functions of CR eval_foo_start(V_c,V_x,V_y,B) 
0.04/0.11	
0.04/0.11	#### Partial ranking functions of CR eval_foo_start(V_c,V_x,V_y,B) 
0.04/0.11	
0.04/0.11	
0.04/0.11	Computing Bounds
0.04/0.11	=====================================
0.04/0.11	
0.04/0.11	#### Cost of chains of eval_foo_bb1_in(V__02,V__01,B):
0.04/0.11	* Chain [[5],6]: 1*it(5)+0
0.04/0.11	  Such that:it(5) =< -V__02/2+V__01/2
0.04/0.11	
0.04/0.11	  with precondition: [B=2,V__01>=V__02+1] 
0.04/0.11	
0.04/0.11	* Chain [6]: 0
0.04/0.11	  with precondition: [B=2,V__02>=V__01] 
0.04/0.11	
0.04/0.11	
0.04/0.11	#### Cost of chains of eval_foo_bb0_in(V_x,V_y,B):
0.04/0.11	* Chain [8]: 0
0.04/0.11	  with precondition: [V_y>=V_x] 
0.04/0.11	
0.04/0.11	* Chain [7]: 1*s(1)+0
0.04/0.11	  Such that:s(1) =< V_x/2-V_y/2
0.04/0.11	
0.04/0.11	  with precondition: [V_x>=V_y+1] 
0.04/0.11	
0.04/0.11	
0.04/0.11	#### Cost of chains of eval_foo_start(V_c,V_x,V_y,B):
0.04/0.11	* Chain [10]: 0
0.04/0.11	  with precondition: [V_y>=V_x] 
0.04/0.11	
0.04/0.11	* Chain [9]: 1*s(2)+0
0.04/0.11	  Such that:s(2) =< V_x/2-V_y/2
0.04/0.11	
0.04/0.11	  with precondition: [V_x>=V_y+1] 
0.04/0.11	
0.04/0.11	
0.04/0.11	Closed-form bounds of eval_foo_start(V_c,V_x,V_y,B): 
0.04/0.11	-------------------------------------
0.04/0.11	* Chain [10] with precondition: [V_y>=V_x] 
0.04/0.11	    - Upper bound: 0 
0.04/0.11	    - Complexity: constant 
0.04/0.11	* Chain [9] with precondition: [V_x>=V_y+1] 
0.04/0.11	    - Upper bound: V_x/2-V_y/2 
0.04/0.11	    - Complexity: n 
0.04/0.11	
0.04/0.11	### Maximum cost of eval_foo_start(V_c,V_x,V_y,B): nat(V_x/2-V_y/2) 
0.04/0.11	Asymptotic class: n 
0.04/0.11	* Total analysis performed in 42 ms.
0.04/0.11	
0.04/0.21	EOF