0.05/0.16	WORST_CASE(?,O(n^1))  
0.05/0.16	
0.05/0.16	Preprocessing Cost Relations
0.05/0.16	=====================================
0.05/0.16	
0.05/0.16	#### Computed strongly connected components 
0.05/0.16	0. recursive  : [eval_foo_bb1_in/3,eval_foo_bb2_in/3,eval_foo_bb3_in/3,eval_foo_bb4_in/3]
0.05/0.16	1. non_recursive  : [eval_foo_stop/1]
0.05/0.16	2. non_recursive  : [eval_foo__critedge_in/1]
0.05/0.16	3. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
0.05/0.16	4. non_recursive  : [eval_foo_bb0_in/3]
0.05/0.16	5. non_recursive  : [eval_foo_start/3]
0.05/0.16	
0.05/0.16	#### Obtained direct recursion through partial evaluation 
0.05/0.16	0. SCC is partially evaluated into eval_foo_bb1_in/3
0.05/0.16	1. SCC is completely evaluated into other SCCs
0.05/0.16	2. SCC is completely evaluated into other SCCs
0.05/0.16	3. SCC is completely evaluated into other SCCs
0.05/0.16	4. SCC is partially evaluated into eval_foo_bb0_in/3
0.05/0.16	5. SCC is partially evaluated into eval_foo_start/3
0.05/0.16	
0.05/0.16	Control-Flow Refinement of Cost Relations
0.05/0.16	=====================================
0.05/0.16	
0.05/0.16	### Specialization of cost equations eval_foo_bb1_in/3 
0.05/0.16	* CE 6 is refined into CE [8] 
0.05/0.16	* CE 5 is refined into CE [9] 
0.05/0.16	* CE 7 is refined into CE [10] 
0.05/0.16	* CE 3 is refined into CE [11] 
0.05/0.16	* CE 4 is refined into CE [12] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_foo_bb1_in/3 
0.05/0.16	* CEs [11] --> Loop 8 
0.05/0.16	* CEs [12] --> Loop 9 
0.05/0.16	* CEs [8] --> Loop 10 
0.05/0.16	* CEs [9] --> Loop 11 
0.05/0.16	* CEs [10] --> Loop 12 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 
0.05/0.16	* RF of phase [8]: [V__01]
0.05/0.16	* RF of phase [9]: [V__0]
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_foo_bb1_in(V__01,V__0,B) 
0.05/0.16	* Partial RF of phase [8]:
0.05/0.16	  - RF of loop [8:1]:
0.05/0.16	    V__01
0.05/0.16	* Partial RF of phase [9]:
0.05/0.16	  - RF of loop [9:1]:
0.05/0.16	    V__0
0.05/0.16	
0.05/0.16	
0.05/0.16	### Specialization of cost equations eval_foo_bb0_in/3 
0.05/0.16	* CE 2 is refined into CE [13,14,15,16,17] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_foo_bb0_in/3 
0.05/0.16	* CEs [16] --> Loop 13 
0.05/0.16	* CEs [17] --> Loop 14 
0.05/0.16	* CEs [14] --> Loop 15 
0.05/0.16	* CEs [15] --> Loop 16 
0.05/0.16	* CEs [13] --> Loop 17 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_foo_bb0_in(V_p,V_q,B) 
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_foo_bb0_in(V_p,V_q,B) 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Specialization of cost equations eval_foo_start/3 
0.05/0.16	* CE 1 is refined into CE [18,19,20,21,22] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_foo_start/3 
0.05/0.16	* CEs [22] --> Loop 18 
0.05/0.16	* CEs [21] --> Loop 19 
0.05/0.16	* CEs [20] --> Loop 20 
0.05/0.16	* CEs [19] --> Loop 21 
0.05/0.16	* CEs [18] --> Loop 22 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_foo_start(V_p,V_q,B) 
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_foo_start(V_p,V_q,B) 
0.05/0.16	
0.05/0.16	
0.05/0.16	Computing Bounds
0.05/0.16	=====================================
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_foo_bb1_in(V__01,V__0,B):
0.05/0.16	* Chain [[9],10]: 1*it(9)+0
0.05/0.16	  Such that:it(9) =< V__0
0.05/0.16	
0.05/0.16	  with precondition: [B=2,V__0>=1,V__01>=V__0+1] 
0.05/0.16	
0.05/0.16	* Chain [[8],11]: 1*it(8)+0
0.05/0.16	  Such that:it(8) =< V__01
0.05/0.16	
0.05/0.16	  with precondition: [B=2,V__01>=1,V__0>=V__01+1] 
0.05/0.16	
0.05/0.16	* Chain [12]: 0
0.05/0.16	  with precondition: [B=2,V__0=V__01] 
0.05/0.16	
0.05/0.16	* Chain [11]: 0
0.05/0.16	  with precondition: [B=2,0>=V__01] 
0.05/0.16	
0.05/0.16	* Chain [10]: 0
0.05/0.16	  with precondition: [B=2,0>=V__0] 
0.05/0.16	
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_foo_bb0_in(V_p,V_q,B):
0.05/0.16	* Chain [17]: 0
0.05/0.16	  with precondition: [V_q=V_p] 
0.05/0.16	
0.05/0.16	* Chain [16]: 0
0.05/0.16	  with precondition: [0>=V_p] 
0.05/0.16	
0.05/0.16	* Chain [15]: 0
0.05/0.16	  with precondition: [0>=V_q] 
0.05/0.16	
0.05/0.16	* Chain [14]: 1*s(1)+0
0.05/0.16	  Such that:s(1) =< V_p
0.05/0.16	
0.05/0.16	  with precondition: [V_p>=1,V_q>=V_p+1] 
0.05/0.16	
0.05/0.16	* Chain [13]: 1*s(2)+0
0.05/0.16	  Such that:s(2) =< V_q
0.05/0.16	
0.05/0.16	  with precondition: [V_q>=1,V_p>=V_q+1] 
0.05/0.16	
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_foo_start(V_p,V_q,B):
0.05/0.16	* Chain [22]: 0
0.05/0.16	  with precondition: [V_q=V_p] 
0.05/0.16	
0.05/0.16	* Chain [21]: 0
0.05/0.16	  with precondition: [0>=V_p] 
0.05/0.16	
0.05/0.16	* Chain [20]: 0
0.05/0.16	  with precondition: [0>=V_q] 
0.05/0.16	
0.05/0.16	* Chain [19]: 1*s(3)+0
0.05/0.16	  Such that:s(3) =< V_p
0.05/0.16	
0.05/0.16	  with precondition: [V_p>=1,V_q>=V_p+1] 
0.05/0.16	
0.05/0.16	* Chain [18]: 1*s(4)+0
0.05/0.16	  Such that:s(4) =< V_q
0.05/0.16	
0.05/0.16	  with precondition: [V_q>=1,V_p>=V_q+1] 
0.05/0.16	
0.05/0.16	
0.05/0.16	Closed-form bounds of eval_foo_start(V_p,V_q,B): 
0.05/0.16	-------------------------------------
0.05/0.16	* Chain [22] with precondition: [V_q=V_p] 
0.05/0.16	    - Upper bound: 0 
0.05/0.16	    - Complexity: constant 
0.05/0.16	* Chain [21] with precondition: [0>=V_p] 
0.05/0.16	    - Upper bound: 0 
0.05/0.16	    - Complexity: constant 
0.05/0.16	* Chain [20] with precondition: [0>=V_q] 
0.05/0.16	    - Upper bound: 0 
0.05/0.16	    - Complexity: constant 
0.05/0.16	* Chain [19] with precondition: [V_p>=1,V_q>=V_p+1] 
0.05/0.16	    - Upper bound: V_p 
0.05/0.16	    - Complexity: n 
0.05/0.16	* Chain [18] with precondition: [V_q>=1,V_p>=V_q+1] 
0.05/0.16	    - Upper bound: V_q 
0.05/0.16	    - Complexity: n 
0.05/0.16	
0.05/0.16	### Maximum cost of eval_foo_start(V_p,V_q,B): max([nat(V_p),nat(V_q)]) 
0.05/0.16	Asymptotic class: n 
0.05/0.16	* Total analysis performed in 92 ms.
0.05/0.16	
0.05/0.26	EOF