0.04/0.13	WORST_CASE(?,O(n^1))  
0.04/0.13	
0.04/0.13	Preprocessing Cost Relations
0.04/0.13	=====================================
0.04/0.13	
0.04/0.13	#### Computed strongly connected components 
0.04/0.13	0. recursive  : [eval_foo_bb1_in/3,eval_foo_bb2_in/3]
0.04/0.13	1. non_recursive  : [eval_foo_stop/1]
0.04/0.13	2. non_recursive  : [eval_foo_bb3_in/1]
0.04/0.13	3. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
0.04/0.13	4. non_recursive  : [eval_foo_bb0_in/3]
0.04/0.13	5. non_recursive  : [eval_foo_start/4]
0.04/0.13	
0.04/0.13	#### Obtained direct recursion through partial evaluation 
0.04/0.13	0. SCC is partially evaluated into eval_foo_bb1_in/3
0.04/0.13	1. SCC is completely evaluated into other SCCs
0.04/0.13	2. SCC is completely evaluated into other SCCs
0.04/0.13	3. SCC is completely evaluated into other SCCs
0.04/0.13	4. SCC is partially evaluated into eval_foo_bb0_in/3
0.04/0.13	5. SCC is partially evaluated into eval_foo_start/4
0.04/0.13	
0.04/0.13	Control-Flow Refinement of Cost Relations
0.04/0.13	=====================================
0.04/0.13	
0.04/0.13	### Specialization of cost equations eval_foo_bb1_in/3 
0.04/0.13	* CE 6 is refined into CE [8] 
0.04/0.13	* CE 7 is refined into CE [9] 
0.04/0.13	* CE 5 is refined into CE [10] 
0.04/0.13	
0.04/0.13	
0.04/0.13	### Cost equations --> "Loop" of eval_foo_bb1_in/3 
0.04/0.13	* CEs [10] --> Loop 8 
0.04/0.13	* CEs [8] --> Loop 9 
0.04/0.13	* CEs [9] --> Loop 10 
0.04/0.13	
0.04/0.13	### Ranking functions of CR eval_foo_bb1_in(V_y,V__01,B) 
0.04/0.13	* RF of phase [8]: [V__01]
0.04/0.13	
0.04/0.13	#### Partial ranking functions of CR eval_foo_bb1_in(V_y,V__01,B) 
0.04/0.13	* Partial RF of phase [8]:
0.04/0.13	  - RF of loop [8:1]:
0.04/0.13	    V__01
0.04/0.13	
0.04/0.13	
0.04/0.13	### Specialization of cost equations eval_foo_bb0_in/3 
0.04/0.13	* CE 4 is refined into CE [11,12] 
0.04/0.13	* CE 3 is refined into CE [13,14] 
0.04/0.13	* CE 2 is refined into CE [15] 
0.04/0.13	
0.04/0.13	
0.04/0.13	### Cost equations --> "Loop" of eval_foo_bb0_in/3 
0.04/0.13	* CEs [12] --> Loop 11 
0.04/0.13	* CEs [11] --> Loop 12 
0.04/0.13	* CEs [13] --> Loop 13 
0.04/0.13	* CEs [14] --> Loop 14 
0.04/0.13	* CEs [15] --> Loop 15 
0.04/0.13	
0.04/0.13	### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 
0.04/0.13	
0.04/0.13	#### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,B) 
0.04/0.13	
0.04/0.13	
0.04/0.13	### Specialization of cost equations eval_foo_start/4 
0.04/0.13	* CE 1 is refined into CE [16,17,18,19,20] 
0.04/0.13	
0.04/0.13	
0.04/0.13	### Cost equations --> "Loop" of eval_foo_start/4 
0.04/0.13	* CEs [20] --> Loop 16 
0.04/0.13	* CEs [19] --> Loop 17 
0.04/0.13	* CEs [18] --> Loop 18 
0.04/0.13	* CEs [17] --> Loop 19 
0.04/0.13	* CEs [16] --> Loop 20 
0.04/0.13	
0.04/0.13	### Ranking functions of CR eval_foo_start(V_i,V_x,V_y,B) 
0.04/0.13	
0.04/0.13	#### Partial ranking functions of CR eval_foo_start(V_i,V_x,V_y,B) 
0.04/0.13	
0.04/0.13	
0.04/0.13	Computing Bounds
0.04/0.13	=====================================
0.04/0.13	
0.04/0.13	#### Cost of chains of eval_foo_bb1_in(V_y,V__01,B):
0.04/0.13	* Chain [[8],9]: 1*it(8)+0
0.04/0.13	  Such that:it(8) =< V__01
0.04/0.13	
0.04/0.13	  with precondition: [B=2,V_y>=1,V__01>=1] 
0.04/0.13	
0.04/0.13	* Chain [10]: 0
0.04/0.13	  with precondition: [B=2,0>=V_y] 
0.04/0.13	
0.04/0.13	* Chain [9]: 0
0.04/0.13	  with precondition: [B=2,0>=V__01] 
0.04/0.13	
0.04/0.13	
0.04/0.13	#### Cost of chains of eval_foo_bb0_in(V_x,V_y,B):
0.04/0.13	* Chain [15]: 0
0.04/0.13	  with precondition: [V_x=0] 
0.04/0.13	
0.04/0.13	* Chain [14]: 0
0.04/0.13	  with precondition: [0>=V_x+1] 
0.04/0.13	
0.04/0.13	* Chain [13]: 0
0.04/0.13	  with precondition: [0>=V_x+1,0>=V_y] 
0.04/0.13	
0.04/0.13	* Chain [12]: 0
0.04/0.13	  with precondition: [0>=V_y,V_x>=1] 
0.04/0.13	
0.04/0.13	* Chain [11]: 1*s(1)+0
0.04/0.13	  Such that:s(1) =< V_x
0.04/0.13	
0.04/0.13	  with precondition: [V_x>=1,V_y>=1] 
0.04/0.13	
0.04/0.13	
0.04/0.13	#### Cost of chains of eval_foo_start(V_i,V_x,V_y,B):
0.04/0.13	* Chain [20]: 0
0.04/0.13	  with precondition: [V_x=0] 
0.04/0.13	
0.04/0.13	* Chain [19]: 0
0.04/0.13	  with precondition: [0>=V_x+1] 
0.04/0.13	
0.04/0.13	* Chain [18]: 0
0.04/0.13	  with precondition: [0>=V_x+1,0>=V_y] 
0.04/0.13	
0.04/0.13	* Chain [17]: 0
0.04/0.13	  with precondition: [0>=V_y,V_x>=1] 
0.04/0.13	
0.04/0.13	* Chain [16]: 1*s(2)+0
0.04/0.13	  Such that:s(2) =< V_x
0.04/0.13	
0.04/0.13	  with precondition: [V_x>=1,V_y>=1] 
0.04/0.13	
0.04/0.13	
0.04/0.13	Closed-form bounds of eval_foo_start(V_i,V_x,V_y,B): 
0.04/0.13	-------------------------------------
0.04/0.13	* Chain [20] with precondition: [V_x=0] 
0.04/0.13	    - Upper bound: 0 
0.04/0.13	    - Complexity: constant 
0.04/0.13	* Chain [19] with precondition: [0>=V_x+1] 
0.04/0.13	    - Upper bound: 0 
0.04/0.13	    - Complexity: constant 
0.04/0.13	* Chain [18] with precondition: [0>=V_x+1,0>=V_y] 
0.04/0.13	    - Upper bound: 0 
0.04/0.13	    - Complexity: constant 
0.04/0.13	* Chain [17] with precondition: [0>=V_y,V_x>=1] 
0.04/0.13	    - Upper bound: 0 
0.04/0.13	    - Complexity: constant 
0.04/0.13	* Chain [16] with precondition: [V_x>=1,V_y>=1] 
0.04/0.13	    - Upper bound: V_x 
0.04/0.13	    - Complexity: n 
0.04/0.13	
0.04/0.13	### Maximum cost of eval_foo_start(V_i,V_x,V_y,B): nat(V_x) 
0.04/0.13	Asymptotic class: n 
0.04/0.13	* Total analysis performed in 62 ms.
0.04/0.13	
0.04/0.23	EOF