0.05/0.14	WORST_CASE(?,O(n^1))  
0.05/0.14	
0.05/0.14	Preprocessing Cost Relations
0.05/0.14	=====================================
0.05/0.14	
0.05/0.14	#### Computed strongly connected components 
0.05/0.14	0. recursive  : [eval_foo_bb1_in/3,eval_foo_bb2_in/3]
0.05/0.14	1. non_recursive  : [eval_foo_stop/1]
0.05/0.14	2. non_recursive  : [eval_foo_bb3_in/1]
0.05/0.14	3. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
0.05/0.14	4. non_recursive  : [eval_foo_bb0_in/3]
0.05/0.14	5. non_recursive  : [eval_foo_start/3]
0.05/0.14	
0.05/0.14	#### Obtained direct recursion through partial evaluation 
0.05/0.14	0. SCC is partially evaluated into eval_foo_bb1_in/3
0.05/0.14	1. SCC is completely evaluated into other SCCs
0.05/0.14	2. SCC is completely evaluated into other SCCs
0.05/0.14	3. SCC is completely evaluated into other SCCs
0.05/0.14	4. SCC is partially evaluated into eval_foo_bb0_in/3
0.05/0.14	5. SCC is partially evaluated into eval_foo_start/3
0.05/0.14	
0.05/0.14	Control-Flow Refinement of Cost Relations
0.05/0.14	=====================================
0.05/0.14	
0.05/0.14	### Specialization of cost equations eval_foo_bb1_in/3 
0.05/0.14	* CE 5 is refined into CE [6] 
0.05/0.14	* CE 4 is refined into CE [7] 
0.05/0.14	* CE 3 is refined into CE [8] 
0.05/0.14	
0.05/0.14	
0.05/0.14	### Cost equations --> "Loop" of eval_foo_bb1_in/3 
0.05/0.14	* CEs [7] --> Loop 6 
0.05/0.14	* CEs [8] --> Loop 7 
0.05/0.14	* CEs [6] --> Loop 8 
0.05/0.14	
0.05/0.14	### Ranking functions of CR eval_foo_bb1_in(V_K,V__0,B) 
0.05/0.14	* RF of phase [6]: [-V_K+V__0]
0.05/0.14	* RF of phase [7]: [V_K-V__0]
0.05/0.14	
0.05/0.14	#### Partial ranking functions of CR eval_foo_bb1_in(V_K,V__0,B) 
0.05/0.14	* Partial RF of phase [6]:
0.05/0.14	  - RF of loop [6:1]:
0.05/0.14	    -V_K+V__0
0.05/0.14	* Partial RF of phase [7]:
0.05/0.14	  - RF of loop [7:1]:
0.05/0.14	    V_K-V__0
0.05/0.14	
0.05/0.14	
0.05/0.14	### Specialization of cost equations eval_foo_bb0_in/3 
0.05/0.14	* CE 2 is refined into CE [9,10,11] 
0.05/0.14	
0.05/0.14	
0.05/0.14	### Cost equations --> "Loop" of eval_foo_bb0_in/3 
0.05/0.14	* CEs [11] --> Loop 9 
0.05/0.14	* CEs [10] --> Loop 10 
0.05/0.14	* CEs [9] --> Loop 11 
0.05/0.14	
0.05/0.14	### Ranking functions of CR eval_foo_bb0_in(V_K,V_x,B) 
0.05/0.14	
0.05/0.14	#### Partial ranking functions of CR eval_foo_bb0_in(V_K,V_x,B) 
0.05/0.14	
0.05/0.14	
0.05/0.14	### Specialization of cost equations eval_foo_start/3 
0.05/0.14	* CE 1 is refined into CE [12,13,14] 
0.05/0.14	
0.05/0.14	
0.05/0.14	### Cost equations --> "Loop" of eval_foo_start/3 
0.05/0.14	* CEs [14] --> Loop 12 
0.05/0.14	* CEs [13] --> Loop 13 
0.05/0.14	* CEs [12] --> Loop 14 
0.05/0.14	
0.05/0.14	### Ranking functions of CR eval_foo_start(V_K,V_x,B) 
0.05/0.14	
0.05/0.14	#### Partial ranking functions of CR eval_foo_start(V_K,V_x,B) 
0.05/0.14	
0.05/0.14	
0.05/0.14	Computing Bounds
0.05/0.14	=====================================
0.05/0.14	
0.05/0.14	#### Cost of chains of eval_foo_bb1_in(V_K,V__0,B):
0.05/0.14	* Chain [[7],8]: 1*it(7)+0
0.05/0.14	  Such that:it(7) =< V_K-V__0
0.05/0.14	
0.05/0.14	  with precondition: [B=2,V_K>=V__0+1] 
0.05/0.14	
0.05/0.14	* Chain [[6],8]: 1*it(6)+0
0.05/0.14	  Such that:it(6) =< -V_K+V__0
0.05/0.14	
0.05/0.14	  with precondition: [B=2,V__0>=V_K+1] 
0.05/0.14	
0.05/0.14	* Chain [8]: 0
0.05/0.14	  with precondition: [B=2,V__0=V_K] 
0.05/0.14	
0.05/0.14	
0.05/0.14	#### Cost of chains of eval_foo_bb0_in(V_K,V_x,B):
0.05/0.14	* Chain [11]: 0
0.05/0.14	  with precondition: [V_x=V_K] 
0.05/0.14	
0.05/0.14	* Chain [10]: 1*s(1)+0
0.05/0.14	  Such that:s(1) =< -V_K+V_x
0.05/0.14	
0.05/0.14	  with precondition: [V_x>=V_K+1] 
0.05/0.14	
0.05/0.14	* Chain [9]: 1*s(2)+0
0.05/0.14	  Such that:s(2) =< V_K-V_x
0.05/0.14	
0.05/0.14	  with precondition: [V_K>=V_x+1] 
0.05/0.14	
0.05/0.14	
0.05/0.14	#### Cost of chains of eval_foo_start(V_K,V_x,B):
0.05/0.14	* Chain [14]: 0
0.05/0.14	  with precondition: [V_x=V_K] 
0.05/0.14	
0.05/0.14	* Chain [13]: 1*s(3)+0
0.05/0.14	  Such that:s(3) =< -V_K+V_x
0.05/0.14	
0.05/0.14	  with precondition: [V_x>=V_K+1] 
0.05/0.14	
0.05/0.14	* Chain [12]: 1*s(4)+0
0.05/0.14	  Such that:s(4) =< V_K-V_x
0.05/0.14	
0.05/0.14	  with precondition: [V_K>=V_x+1] 
0.05/0.14	
0.05/0.14	
0.05/0.14	Closed-form bounds of eval_foo_start(V_K,V_x,B): 
0.05/0.14	-------------------------------------
0.05/0.14	* Chain [14] with precondition: [V_x=V_K] 
0.05/0.14	    - Upper bound: 0 
0.05/0.14	    - Complexity: constant 
0.05/0.14	* Chain [13] with precondition: [V_x>=V_K+1] 
0.05/0.14	    - Upper bound: -V_K+V_x 
0.05/0.14	    - Complexity: n 
0.05/0.14	* Chain [12] with precondition: [V_K>=V_x+1] 
0.05/0.14	    - Upper bound: V_K-V_x 
0.05/0.14	    - Complexity: n 
0.05/0.14	
0.05/0.14	### Maximum cost of eval_foo_start(V_K,V_x,B): max([nat(-V_K+V_x),nat(V_K-V_x)]) 
0.05/0.14	Asymptotic class: n 
0.05/0.14	* Total analysis performed in 68 ms.
0.05/0.14	
0.05/0.24	EOF