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 4 is refined into CE [6] 
0.04/0.13	* CE 5 is refined into CE [7] 
0.04/0.13	* CE 3 is refined into CE [8] 
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 [8] --> Loop 6 
0.04/0.13	* CEs [6] --> Loop 7 
0.04/0.13	* CEs [7] --> Loop 8 
0.04/0.13	
0.04/0.13	### Ranking functions of CR eval_foo_bb1_in(V__02,V__01,B) 
0.04/0.13	* RF of phase [6]: [V__01,V__02]
0.04/0.13	
0.04/0.13	#### Partial ranking functions of CR eval_foo_bb1_in(V__02,V__01,B) 
0.04/0.13	* Partial RF of phase [6]:
0.04/0.13	  - RF of loop [6:1]:
0.04/0.13	    V__01
0.04/0.13	    V__02
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 2 is refined into CE [9,10,11,12] 
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 [11] --> Loop 9 
0.04/0.13	* CEs [12] --> Loop 10 
0.04/0.13	* CEs [9] --> Loop 11 
0.04/0.13	* CEs [10] --> Loop 12 
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 [13,14,15,16] 
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 [16] --> Loop 13 
0.04/0.13	* CEs [15] --> Loop 14 
0.04/0.13	* CEs [14] --> Loop 15 
0.04/0.13	* CEs [13] --> Loop 16 
0.04/0.13	
0.04/0.13	### Ranking functions of CR eval_foo_start(V_c,V_x,V_y,B) 
0.04/0.13	
0.04/0.13	#### Partial ranking functions of CR eval_foo_start(V_c,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__02,V__01,B):
0.04/0.13	* Chain [[6],8]: 1*it(6)+0
0.04/0.13	  Such that:it(6) =< V__02
0.04/0.13	
0.04/0.13	  with precondition: [B=2,V__02>=1,V__01>=V__02] 
0.04/0.13	
0.04/0.13	* Chain [[6],7]: 1*it(6)+0
0.04/0.13	  Such that:it(6) =< V__01
0.04/0.13	
0.04/0.13	  with precondition: [B=2,V__01>=1,V__02>=V__01] 
0.04/0.13	
0.04/0.13	* Chain [8]: 0
0.04/0.13	  with precondition: [B=2,0>=V__02] 
0.04/0.13	
0.04/0.13	* Chain [7]: 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 [12]: 0
0.04/0.13	  with precondition: [0>=V_x] 
0.04/0.13	
0.04/0.13	* Chain [11]: 0
0.04/0.13	  with precondition: [0>=V_y] 
0.04/0.13	
0.04/0.13	* Chain [10]: 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>=V_x] 
0.04/0.13	
0.04/0.13	* Chain [9]: 1*s(2)+0
0.04/0.13	  Such that:s(2) =< V_y
0.04/0.13	
0.04/0.13	  with precondition: [V_y>=1,V_x>=V_y] 
0.04/0.13	
0.04/0.13	
0.04/0.13	#### Cost of chains of eval_foo_start(V_c,V_x,V_y,B):
0.04/0.13	* Chain [16]: 0
0.04/0.13	  with precondition: [0>=V_x] 
0.04/0.13	
0.04/0.13	* Chain [15]: 0
0.04/0.13	  with precondition: [0>=V_y] 
0.04/0.13	
0.04/0.13	* Chain [14]: 1*s(3)+0
0.04/0.13	  Such that:s(3) =< V_x
0.04/0.13	
0.04/0.13	  with precondition: [V_x>=1,V_y>=V_x] 
0.04/0.13	
0.04/0.13	* Chain [13]: 1*s(4)+0
0.04/0.13	  Such that:s(4) =< V_y
0.04/0.13	
0.04/0.13	  with precondition: [V_y>=1,V_x>=V_y] 
0.04/0.13	
0.04/0.13	
0.04/0.13	Closed-form bounds of eval_foo_start(V_c,V_x,V_y,B): 
0.04/0.13	-------------------------------------
0.04/0.13	* Chain [16] with precondition: [0>=V_x] 
0.04/0.13	    - Upper bound: 0 
0.04/0.13	    - Complexity: constant 
0.04/0.13	* Chain [15] with precondition: [0>=V_y] 
0.04/0.13	    - Upper bound: 0 
0.04/0.13	    - Complexity: constant 
0.04/0.13	* Chain [14] with precondition: [V_x>=1,V_y>=V_x] 
0.04/0.13	    - Upper bound: V_x 
0.04/0.13	    - Complexity: n 
0.04/0.13	* Chain [13] with precondition: [V_y>=1,V_x>=V_y] 
0.04/0.13	    - Upper bound: V_y 
0.04/0.13	    - Complexity: n 
0.04/0.13	
0.04/0.13	### Maximum cost of eval_foo_start(V_c,V_x,V_y,B): max([nat(V_x),nat(V_y)]) 
0.04/0.13	Asymptotic class: n 
0.04/0.13	* Total analysis performed in 63 ms.
0.04/0.13	
0.04/0.23	EOF