0.05/0.22	WORST_CASE(?,O(n^1))  
0.05/0.22	
0.05/0.22	Preprocessing Cost Relations
0.05/0.22	=====================================
0.05/0.22	
0.05/0.22	#### Computed strongly connected components 
0.05/0.22	0. recursive  : [eval_Loopus2015_ex1_bb3_in/7,eval_Loopus2015_ex1_bb4_in/7]
0.05/0.22	1. recursive  : [eval_Loopus2015_ex1_2/5,eval_Loopus2015_ex1_3/6,eval_Loopus2015_ex1_bb1_in/3,eval_Loopus2015_ex1_bb2_in/3,eval_Loopus2015_ex1_bb3_in_loop_cont/4]
0.05/0.22	2. non_recursive  : [eval_Loopus2015_ex1_stop/1]
0.05/0.22	3. non_recursive  : [eval_Loopus2015_ex1_bb5_in/1]
0.05/0.22	4. non_recursive  : [eval_Loopus2015_ex1_bb1_in_loop_cont/2]
0.05/0.22	5. non_recursive  : [eval_Loopus2015_ex1_bb0_in/2]
0.05/0.22	6. non_recursive  : [eval_Loopus2015_ex1_start/2]
0.05/0.22	
0.05/0.22	#### Obtained direct recursion through partial evaluation 
0.05/0.22	0. SCC is partially evaluated into eval_Loopus2015_ex1_bb3_in/7
0.05/0.22	1. SCC is partially evaluated into eval_Loopus2015_ex1_bb1_in/3
0.05/0.22	2. SCC is completely evaluated into other SCCs
0.05/0.22	3. SCC is completely evaluated into other SCCs
0.05/0.22	4. SCC is completely evaluated into other SCCs
0.05/0.22	5. SCC is partially evaluated into eval_Loopus2015_ex1_bb0_in/2
0.05/0.22	6. SCC is partially evaluated into eval_Loopus2015_ex1_start/2
0.05/0.22	
0.05/0.22	Control-Flow Refinement of Cost Relations
0.05/0.22	=====================================
0.05/0.22	
0.05/0.22	### Specialization of cost equations eval_Loopus2015_ex1_bb3_in/7 
0.05/0.22	* CE 7 is refined into CE [8] 
0.05/0.22	* CE 6 is refined into CE [9] 
0.05/0.22	
0.05/0.22	
0.05/0.22	### Cost equations --> "Loop" of eval_Loopus2015_ex1_bb3_in/7 
0.05/0.22	* CEs [9] --> Loop 8 
0.05/0.22	* CEs [8] --> Loop 9 
0.05/0.22	
0.05/0.22	### Ranking functions of CR eval_Loopus2015_ex1_bb3_in(V_r_0,V_x_0,V_2,V_3,V_p_0,B,C) 
0.05/0.22	* RF of phase [8]: [V_p_0]
0.05/0.22	
0.05/0.22	#### Partial ranking functions of CR eval_Loopus2015_ex1_bb3_in(V_r_0,V_x_0,V_2,V_3,V_p_0,B,C) 
0.05/0.22	* Partial RF of phase [8]:
0.05/0.22	  - RF of loop [8:1]:
0.05/0.22	    V_p_0
0.05/0.22	
0.05/0.22	
0.05/0.22	### Specialization of cost equations eval_Loopus2015_ex1_bb1_in/3 
0.05/0.22	* CE 5 is refined into CE [10] 
0.05/0.22	* CE 4 is refined into CE [11,12] 
0.05/0.22	* CE 3 is refined into CE [13] 
0.05/0.22	
0.05/0.22	
0.05/0.22	### Cost equations --> "Loop" of eval_Loopus2015_ex1_bb1_in/3 
0.05/0.22	* CEs [13] --> Loop 10 
0.05/0.22	* CEs [12] --> Loop 11 
0.05/0.22	* CEs [11] --> Loop 12 
0.05/0.22	* CEs [10] --> Loop 13 
0.05/0.22	
0.05/0.22	### Ranking functions of CR eval_Loopus2015_ex1_bb1_in(V_r_0,V_x_0,B) 
0.05/0.22	* RF of phase [10,11,12]: [V_x_0]
0.05/0.22	
0.05/0.22	#### Partial ranking functions of CR eval_Loopus2015_ex1_bb1_in(V_r_0,V_x_0,B) 
0.05/0.22	
0.05/0.22	
0.05/0.22	### Specialization of cost equations eval_Loopus2015_ex1_bb0_in/2 
0.05/0.22	* CE 2 is refined into CE [14,15] 
0.05/0.22	
0.05/0.22	
0.05/0.22	### Cost equations --> "Loop" of eval_Loopus2015_ex1_bb0_in/2 
0.05/0.22	* CEs [15] --> Loop 14 
0.05/0.22	* CEs [14] --> Loop 15 
0.05/0.22	
0.05/0.22	### Ranking functions of CR eval_Loopus2015_ex1_bb0_in(V_n,B) 
0.05/0.22	
0.05/0.22	#### Partial ranking functions of CR eval_Loopus2015_ex1_bb0_in(V_n,B) 
0.05/0.22	
0.05/0.22	
0.05/0.22	### Specialization of cost equations eval_Loopus2015_ex1_start/2 
0.05/0.22	* CE 1 is refined into CE [16,17] 
0.05/0.22	
0.05/0.22	
0.05/0.22	### Cost equations --> "Loop" of eval_Loopus2015_ex1_start/2 
0.05/0.22	* CEs [17] --> Loop 16 
0.05/0.22	* CEs [16] --> Loop 17 
0.05/0.22	
0.05/0.22	### Ranking functions of CR eval_Loopus2015_ex1_start(V_n,B) 
0.05/0.22	
0.05/0.22	#### Partial ranking functions of CR eval_Loopus2015_ex1_start(V_n,B) 
0.05/0.22	
0.05/0.22	
0.05/0.22	Computing Bounds
0.05/0.22	=====================================
0.05/0.22	
0.05/0.22	#### Cost of chains of eval_Loopus2015_ex1_bb3_in(V_r_0,V_x_0,V_2,V_3,V_p_0,B,C):
0.05/0.22	* Chain [[8],9]: 1*it(8)+0
0.05/0.22	  Such that:it(8) =< V_p_0
0.05/0.22	
0.05/0.22	  with precondition: [B=2,C=0,V_r_0+1=V_2,V_x_0>=1,V_3>=1,V_p_0>=1,V_r_0+1>=V_p_0] 
0.05/0.22	
0.05/0.22	* Chain [9]: 0
0.05/0.22	  with precondition: [B=2,C=0,V_2=V_r_0+1,0>=V_p_0,V_x_0>=1,V_3>=1,V_2>=V_p_0] 
0.05/0.22	
0.05/0.22	
0.05/0.22	#### Cost of chains of eval_Loopus2015_ex1_bb1_in(V_r_0,V_x_0,B):
0.05/0.22	* Chain [[10,11,12],13]: 2*it(10)+1*s(3)+0
0.05/0.22	  Such that:s(3) =< V_r_0+V_x_0
0.05/0.22	aux(3) =< V_x_0
0.05/0.22	it(10) =< aux(3)
0.05/0.22	
0.05/0.22	  with precondition: [B=3,V_r_0>=0,V_x_0>=1] 
0.05/0.22	
0.05/0.22	* Chain [13]: 0
0.05/0.22	  with precondition: [B=3,0>=V_x_0,V_r_0>=0] 
0.05/0.22	
0.05/0.22	
0.05/0.22	#### Cost of chains of eval_Loopus2015_ex1_bb0_in(V_n,B):
0.05/0.22	* Chain [15]: 0
0.05/0.22	  with precondition: [0>=V_n] 
0.05/0.22	
0.05/0.22	* Chain [14]: 3*s(4)+0
0.05/0.22	  Such that:aux(4) =< V_n
0.05/0.22	s(4) =< aux(4)
0.05/0.22	
0.05/0.22	  with precondition: [V_n>=1] 
0.05/0.22	
0.05/0.22	
0.05/0.22	#### Cost of chains of eval_Loopus2015_ex1_start(V_n,B):
0.05/0.22	* Chain [17]: 0
0.05/0.22	  with precondition: [0>=V_n] 
0.05/0.22	
0.05/0.22	* Chain [16]: 3*s(8)+0
0.05/0.22	  Such that:s(7) =< V_n
0.05/0.22	s(8) =< s(7)
0.05/0.22	
0.05/0.22	  with precondition: [V_n>=1] 
0.05/0.22	
0.05/0.22	
0.05/0.22	Closed-form bounds of eval_Loopus2015_ex1_start(V_n,B): 
0.05/0.22	-------------------------------------
0.05/0.22	* Chain [17] with precondition: [0>=V_n] 
0.05/0.22	    - Upper bound: 0 
0.05/0.22	    - Complexity: constant 
0.05/0.22	* Chain [16] with precondition: [V_n>=1] 
0.05/0.22	    - Upper bound: 3*V_n 
0.05/0.22	    - Complexity: n 
0.05/0.22	
0.05/0.22	### Maximum cost of eval_Loopus2015_ex1_start(V_n,B): nat(V_n)*3 
0.05/0.22	Asymptotic class: n 
0.05/0.22	* Total analysis performed in 143 ms.
0.05/0.22	
0.05/0.32	EOF