0.05/0.13	WORST_CASE(?,O(n^1))  
0.05/0.13	
0.05/0.13	Preprocessing Cost Relations
0.05/0.13	=====================================
0.05/0.13	
0.05/0.13	#### Computed strongly connected components 
0.05/0.13	0. recursive  : [eval_foo_bb1_in/3,eval_foo_bb2_in/3]
0.05/0.13	1. non_recursive  : [eval_foo_stop/1]
0.05/0.13	2. non_recursive  : [eval_foo_bb3_in/1]
0.05/0.13	3. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
0.05/0.13	4. non_recursive  : [eval_foo_bb0_in/3]
0.05/0.13	5. non_recursive  : [eval_foo_start/4]
0.05/0.13	
0.05/0.13	#### Obtained direct recursion through partial evaluation 
0.05/0.13	0. SCC is partially evaluated into eval_foo_bb1_in/3
0.05/0.13	1. SCC is completely evaluated into other SCCs
0.05/0.13	2. SCC is completely evaluated into other SCCs
0.05/0.13	3. SCC is completely evaluated into other SCCs
0.05/0.13	4. SCC is partially evaluated into eval_foo_bb0_in/3
0.05/0.13	5. SCC is partially evaluated into eval_foo_start/4
0.05/0.13	
0.05/0.13	Control-Flow Refinement of Cost Relations
0.05/0.13	=====================================
0.05/0.13	
0.05/0.13	### Specialization of cost equations eval_foo_bb1_in/3 
0.05/0.13	* CE 4 is refined into CE [6] 
0.05/0.13	* CE 5 is refined into CE [7] 
0.05/0.13	* CE 3 is refined into CE [8] 
0.05/0.13	
0.05/0.13	
0.05/0.13	### Cost equations --> "Loop" of eval_foo_bb1_in/3 
0.05/0.13	* CEs [8] --> Loop 6 
0.05/0.13	* CEs [6] --> Loop 7 
0.05/0.13	* CEs [7] --> Loop 8 
0.05/0.13	
0.05/0.13	### Ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 
0.05/0.13	* RF of phase [6]: [V__01/2+V__0/2+1/2]
0.05/0.13	
0.05/0.13	#### Partial ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 
0.05/0.13	* Partial RF of phase [6]:
0.05/0.13	  - RF of loop [6:1]:
0.05/0.13	    V__01/2+V__0/2+1/2
0.05/0.13	
0.05/0.13	
0.05/0.13	### Specialization of cost equations eval_foo_bb0_in/3 
0.05/0.13	* CE 2 is refined into CE [9,10,11] 
0.05/0.13	
0.05/0.13	
0.05/0.13	### Cost equations --> "Loop" of eval_foo_bb0_in/3 
0.05/0.13	* CEs [11] --> Loop 9 
0.05/0.13	* CEs [9] --> Loop 10 
0.05/0.13	* CEs [10] --> Loop 11 
0.05/0.13	
0.05/0.13	### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 
0.05/0.13	
0.05/0.13	#### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 
0.05/0.13	
0.05/0.13	
0.05/0.13	### Specialization of cost equations eval_foo_start/4 
0.05/0.13	* CE 1 is refined into CE [12,13,14] 
0.05/0.13	
0.05/0.13	
0.05/0.13	### Cost equations --> "Loop" of eval_foo_start/4 
0.05/0.13	* CEs [14] --> Loop 12 
0.05/0.13	* CEs [13] --> Loop 13 
0.05/0.13	* CEs [12] --> Loop 14 
0.05/0.13	
0.05/0.13	### Ranking functions of CR eval_foo_start(V_x,V_y,V_oldx,B) 
0.05/0.13	
0.05/0.13	#### Partial ranking functions of CR eval_foo_start(V_x,V_y,V_oldx,B) 
0.05/0.13	
0.05/0.13	
0.05/0.13	Computing Bounds
0.05/0.13	=====================================
0.05/0.13	
0.05/0.13	#### Cost of chains of eval_foo_bb1_in(V__01,V__0,B):
0.05/0.13	* Chain [[6],8]: 1*it(6)+0
0.05/0.13	  Such that:it(6) =< V__01/2+V__0/2+1/2
0.05/0.13	
0.05/0.13	  with precondition: [B=2,V__01>=0,V__0>=0] 
0.05/0.13	
0.05/0.13	* Chain [[6],7]: 1*it(6)+0
0.05/0.13	  Such that:it(6) =< V__01/2+V__0/2+1/2
0.05/0.13	
0.05/0.13	  with precondition: [B=2,V__01>=0,V__0>=0] 
0.05/0.13	
0.05/0.13	* Chain [8]: 0
0.05/0.13	  with precondition: [B=2,0>=V__01+1] 
0.05/0.13	
0.05/0.13	* Chain [7]: 0
0.05/0.13	  with precondition: [B=2,0>=V__0+1] 
0.05/0.13	
0.05/0.13	
0.05/0.13	#### Cost of chains of eval_foo_bb0_in(V_x,V_y,B):
0.05/0.13	* Chain [11]: 0
0.05/0.13	  with precondition: [0>=V_x+1] 
0.05/0.13	
0.05/0.13	* Chain [10]: 0
0.05/0.13	  with precondition: [0>=V_y+1] 
0.05/0.13	
0.05/0.13	* Chain [9]: 2*s(4)+0
0.05/0.13	  Such that:s(3) =< V_x/2+V_y/2+1/2
0.05/0.13	s(4) =< s(3)
0.05/0.13	
0.05/0.13	  with precondition: [V_x>=0,V_y>=0] 
0.05/0.13	
0.05/0.13	
0.05/0.13	#### Cost of chains of eval_foo_start(V_x,V_y,V_oldx,B):
0.05/0.13	* Chain [14]: 0
0.05/0.13	  with precondition: [0>=V_x+1] 
0.05/0.13	
0.05/0.13	* Chain [13]: 0
0.05/0.13	  with precondition: [0>=V_y+1] 
0.05/0.13	
0.05/0.13	* Chain [12]: 2*s(6)+0
0.05/0.13	  Such that:s(5) =< V_x/2+V_y/2+1/2
0.05/0.13	s(6) =< s(5)
0.05/0.13	
0.05/0.13	  with precondition: [V_x>=0,V_y>=0] 
0.05/0.13	
0.05/0.13	
0.05/0.13	Closed-form bounds of eval_foo_start(V_x,V_y,V_oldx,B): 
0.05/0.13	-------------------------------------
0.05/0.13	* Chain [14] with precondition: [0>=V_x+1] 
0.05/0.13	    - Upper bound: 0 
0.05/0.13	    - Complexity: constant 
0.05/0.13	* Chain [13] with precondition: [0>=V_y+1] 
0.05/0.13	    - Upper bound: 0 
0.05/0.13	    - Complexity: constant 
0.05/0.13	* Chain [12] with precondition: [V_x>=0,V_y>=0] 
0.05/0.13	    - Upper bound: V_x+V_y+1 
0.05/0.13	    - Complexity: n 
0.05/0.13	
0.05/0.13	### Maximum cost of eval_foo_start(V_x,V_y,V_oldx,B): nat(V_x/2+V_y/2+1/2)*2 
0.05/0.13	Asymptotic class: n 
0.05/0.13	* Total analysis performed in 56 ms.
0.05/0.13	
0.05/0.23	EOF