0.05/0.15	WORST_CASE(?,O(n^2))  
0.05/0.15	
0.05/0.15	Preprocessing Cost Relations
0.05/0.15	=====================================
0.05/0.15	
0.05/0.15	#### Computed strongly connected components 
0.05/0.15	0. recursive  : [eval_while2_bb2_in/3,eval_while2_bb3_in/3]
0.05/0.15	1. recursive  : [eval_while2_bb1_in/3,eval_while2_bb2_in_loop_cont/5,eval_while2_bb4_in/4]
0.05/0.15	2. non_recursive  : [eval_while2_stop/1]
0.05/0.15	3. non_recursive  : [eval_while2_bb5_in/1]
0.05/0.15	4. non_recursive  : [eval_while2_bb1_in_loop_cont/2]
0.05/0.15	5. non_recursive  : [eval_while2_bb0_in/2]
0.05/0.15	6. non_recursive  : [eval_while2_start/2]
0.05/0.15	
0.05/0.15	#### Obtained direct recursion through partial evaluation 
0.05/0.15	0. SCC is partially evaluated into eval_while2_bb2_in/3
0.05/0.15	1. SCC is partially evaluated into eval_while2_bb1_in/3
0.05/0.15	2. SCC is completely evaluated into other SCCs
0.05/0.15	3. SCC is completely evaluated into other SCCs
0.05/0.15	4. SCC is completely evaluated into other SCCs
0.05/0.15	5. SCC is partially evaluated into eval_while2_bb0_in/2
0.05/0.15	6. SCC is partially evaluated into eval_while2_start/2
0.05/0.15	
0.05/0.15	Control-Flow Refinement of Cost Relations
0.05/0.15	=====================================
0.05/0.15	
0.05/0.15	### Specialization of cost equations eval_while2_bb2_in/3 
0.05/0.15	* CE 6 is refined into CE [7] 
0.05/0.15	* CE 5 is refined into CE [8] 
0.05/0.15	
0.05/0.15	
0.05/0.15	### Cost equations --> "Loop" of eval_while2_bb2_in/3 
0.05/0.15	* CEs [8] --> Loop 7 
0.05/0.15	* CEs [7] --> Loop 8 
0.05/0.15	
0.05/0.15	### Ranking functions of CR eval_while2_bb2_in(V_j_0,B,C) 
0.05/0.15	* RF of phase [7]: [V_j_0]
0.05/0.15	
0.05/0.15	#### Partial ranking functions of CR eval_while2_bb2_in(V_j_0,B,C) 
0.05/0.15	* Partial RF of phase [7]:
0.05/0.15	  - RF of loop [7:1]:
0.05/0.15	    V_j_0
0.05/0.15	
0.05/0.15	
0.05/0.15	### Specialization of cost equations eval_while2_bb1_in/3 
0.05/0.15	* CE 4 is refined into CE [9] 
0.05/0.15	* CE 3 is refined into CE [10] 
0.05/0.15	
0.05/0.15	
0.05/0.15	### Cost equations --> "Loop" of eval_while2_bb1_in/3 
0.05/0.15	* CEs [10] --> Loop 9 
0.05/0.15	* CEs [9] --> Loop 10 
0.05/0.15	
0.05/0.15	### Ranking functions of CR eval_while2_bb1_in(V_N,V_i_0,B) 
0.05/0.15	* RF of phase [9]: [V_i_0]
0.05/0.15	
0.05/0.15	#### Partial ranking functions of CR eval_while2_bb1_in(V_N,V_i_0,B) 
0.05/0.15	* Partial RF of phase [9]:
0.05/0.15	  - RF of loop [9:1]:
0.05/0.15	    V_i_0
0.05/0.15	
0.05/0.15	
0.05/0.15	### Specialization of cost equations eval_while2_bb0_in/2 
0.05/0.15	* CE 2 is refined into CE [11,12] 
0.05/0.15	
0.05/0.15	
0.05/0.15	### Cost equations --> "Loop" of eval_while2_bb0_in/2 
0.05/0.15	* CEs [12] --> Loop 11 
0.05/0.15	* CEs [11] --> Loop 12 
0.05/0.15	
0.05/0.15	### Ranking functions of CR eval_while2_bb0_in(V_N,B) 
0.05/0.15	
0.05/0.15	#### Partial ranking functions of CR eval_while2_bb0_in(V_N,B) 
0.05/0.15	
0.05/0.15	
0.05/0.15	### Specialization of cost equations eval_while2_start/2 
0.05/0.15	* CE 1 is refined into CE [13,14] 
0.05/0.15	
0.05/0.15	
0.05/0.15	### Cost equations --> "Loop" of eval_while2_start/2 
0.05/0.15	* CEs [14] --> Loop 13 
0.05/0.15	* CEs [13] --> Loop 14 
0.05/0.15	
0.05/0.15	### Ranking functions of CR eval_while2_start(V_N,B) 
0.05/0.15	
0.05/0.15	#### Partial ranking functions of CR eval_while2_start(V_N,B) 
0.05/0.15	
0.05/0.15	
0.05/0.15	Computing Bounds
0.05/0.15	=====================================
0.05/0.15	
0.05/0.15	#### Cost of chains of eval_while2_bb2_in(V_j_0,B,C):
0.05/0.15	* Chain [[7],8]: 1*it(7)+0
0.05/0.15	  Such that:it(7) =< V_j_0
0.05/0.15	
0.05/0.15	  with precondition: [B=2,C=0,V_j_0>=1] 
0.05/0.15	
0.05/0.15	
0.05/0.15	#### Cost of chains of eval_while2_bb1_in(V_N,V_i_0,B):
0.05/0.15	* Chain [[9],10]: 1*it(9)+1*s(3)+0
0.05/0.15	  Such that:aux(1) =< V_N
0.05/0.15	it(9) =< V_i_0
0.05/0.15	s(3) =< it(9)*aux(1)
0.05/0.15	
0.05/0.15	  with precondition: [B=3,V_i_0>=1,V_N>=V_i_0] 
0.05/0.15	
0.05/0.15	* Chain [10]: 0
0.05/0.15	  with precondition: [B=3,0>=V_i_0,V_N>=V_i_0] 
0.05/0.15	
0.05/0.15	
0.05/0.15	#### Cost of chains of eval_while2_bb0_in(V_N,B):
0.05/0.15	* Chain [12]: 0
0.05/0.15	  with precondition: [0>=V_N] 
0.05/0.15	
0.05/0.15	* Chain [11]: 1*s(5)+1*s(6)+0
0.05/0.15	  Such that:aux(2) =< V_N
0.05/0.15	s(5) =< aux(2)
0.05/0.15	s(6) =< s(5)*aux(2)
0.05/0.15	
0.05/0.15	  with precondition: [V_N>=1] 
0.05/0.15	
0.05/0.15	
0.05/0.15	#### Cost of chains of eval_while2_start(V_N,B):
0.05/0.15	* Chain [14]: 0
0.05/0.15	  with precondition: [0>=V_N] 
0.05/0.15	
0.05/0.15	* Chain [13]: 1*s(8)+1*s(9)+0
0.05/0.15	  Such that:s(7) =< V_N
0.05/0.15	s(8) =< s(7)
0.05/0.15	s(9) =< s(8)*s(7)
0.05/0.15	
0.05/0.15	  with precondition: [V_N>=1] 
0.05/0.15	
0.05/0.15	
0.05/0.15	Closed-form bounds of eval_while2_start(V_N,B): 
0.05/0.15	-------------------------------------
0.05/0.15	* Chain [14] with precondition: [0>=V_N] 
0.05/0.15	    - Upper bound: 0 
0.05/0.15	    - Complexity: constant 
0.05/0.15	* Chain [13] with precondition: [V_N>=1] 
0.05/0.15	    - Upper bound: V_N*V_N+V_N 
0.05/0.15	    - Complexity: n^2 
0.05/0.15	
0.05/0.15	### Maximum cost of eval_while2_start(V_N,B): nat(V_N)*nat(V_N)+nat(V_N) 
0.05/0.15	Asymptotic class: n^2 
0.05/0.15	* Total analysis performed in 78 ms.
0.05/0.15	
0.05/0.25	EOF