0.05/0.16	WORST_CASE(?,O(n^2))  
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_bb3_in/4,eval_foo_bb4_in/4]
0.05/0.16	1. recursive  : [eval_foo_bb1_in/2,eval_foo_bb2_in/2,eval_foo_bb3_in_loop_cont/5,eval_foo_bb5_in/4]
0.05/0.16	2. non_recursive  : [eval_foo_stop/1]
0.05/0.16	3. non_recursive  : [eval_foo_bb6_in/1]
0.05/0.16	4. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
0.05/0.16	5. non_recursive  : [eval_foo_bb0_in/2]
0.05/0.16	6. non_recursive  : [eval_foo_start/4]
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_bb3_in/4
0.05/0.16	1. SCC is partially evaluated into eval_foo_bb1_in/2
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 completely evaluated into other SCCs
0.05/0.16	5. SCC is partially evaluated into eval_foo_bb0_in/2
0.05/0.16	6. SCC is partially evaluated into eval_foo_start/4
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_bb3_in/4 
0.05/0.16	* CE 6 is refined into CE [7] 
0.05/0.16	* CE 5 is refined into CE [8] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_foo_bb3_in/4 
0.05/0.16	* CEs [8] --> Loop 7 
0.05/0.16	* CEs [7] --> Loop 8 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_foo_bb3_in(V_1,V__02,B,C) 
0.05/0.16	* RF of phase [7]: [V_1-V__02]
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_foo_bb3_in(V_1,V__02,B,C) 
0.05/0.16	* Partial RF of phase [7]:
0.05/0.16	  - RF of loop [7:1]:
0.05/0.16	    V_1-V__02
0.05/0.16	
0.05/0.16	
0.05/0.16	### Specialization of cost equations eval_foo_bb1_in/2 
0.05/0.16	* CE 4 is refined into CE [9] 
0.05/0.16	* CE 3 is refined into CE [10,11] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_foo_bb1_in/2 
0.05/0.16	* CEs [11] --> Loop 9 
0.05/0.16	* CEs [10] --> Loop 10 
0.05/0.16	* CEs [9] --> Loop 11 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_foo_bb1_in(V__01,B) 
0.05/0.16	* RF of phase [9]: [V__01]
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_foo_bb1_in(V__01,B) 
0.05/0.16	* Partial RF of phase [9]:
0.05/0.16	  - RF of loop [9:1]:
0.05/0.16	    V__01
0.05/0.16	
0.05/0.16	
0.05/0.16	### Specialization of cost equations eval_foo_bb0_in/2 
0.05/0.16	* CE 2 is refined into CE [12,13,14] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_foo_bb0_in/2 
0.05/0.16	* CEs [14] --> Loop 12 
0.05/0.16	* CEs [13] --> Loop 13 
0.05/0.16	* CEs [12] --> Loop 14 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_foo_bb0_in(V_x,B) 
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_foo_bb0_in(V_x,B) 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Specialization of cost equations eval_foo_start/4 
0.05/0.16	* CE 1 is refined into CE [15,16,17] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_foo_start/4 
0.05/0.16	* CEs [17] --> Loop 15 
0.05/0.16	* CEs [16] --> Loop 16 
0.05/0.16	* CEs [15] --> Loop 17 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_foo_start(V_c,V_x,V_y,B) 
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_foo_start(V_c,V_x,V_y,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_bb3_in(V_1,V__02,B,C):
0.05/0.16	* Chain [[7],8]: 1*it(7)+0
0.05/0.16	  Such that:it(7) =< -V__02+C
0.05/0.16	
0.05/0.16	  with precondition: [B=2,V_1=C,V__02>=1,V_1>=V__02+1] 
0.05/0.16	
0.05/0.16	* Chain [8]: 0
0.05/0.16	  with precondition: [B=2,V__02=V_1,V__02=C,V__02>=1] 
0.05/0.16	
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_foo_bb1_in(V__01,B):
0.05/0.16	* Chain [[9],10,11]: 1*it(9)+1*s(3)+1
0.05/0.16	  Such that:aux(3) =< V__01
0.05/0.16	it(9) =< aux(3)
0.05/0.16	s(3) =< it(9)*aux(3)
0.05/0.16	
0.05/0.16	  with precondition: [B=3,V__01>=1] 
0.05/0.16	
0.05/0.16	* Chain [11]: 0
0.05/0.16	  with precondition: [B=3,0>=V__01+1] 
0.05/0.16	
0.05/0.16	* Chain [10,11]: 1
0.05/0.16	  with precondition: [V__01=0,B=3] 
0.05/0.16	
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_foo_bb0_in(V_x,B):
0.05/0.16	* Chain [14]: 1
0.05/0.16	  with precondition: [V_x=0] 
0.05/0.16	
0.05/0.16	* Chain [13]: 0
0.05/0.16	  with precondition: [0>=V_x+1] 
0.05/0.16	
0.05/0.16	* Chain [12]: 1*s(5)+1*s(6)+1
0.05/0.16	  Such that:s(4) =< V_x
0.05/0.16	s(5) =< s(4)
0.05/0.16	s(6) =< s(5)*s(4)
0.05/0.16	
0.05/0.16	  with precondition: [V_x>=1] 
0.05/0.16	
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_foo_start(V_c,V_x,V_y,B):
0.05/0.16	* Chain [17]: 1
0.05/0.16	  with precondition: [V_x=0] 
0.05/0.16	
0.05/0.16	* Chain [16]: 0
0.05/0.16	  with precondition: [0>=V_x+1] 
0.05/0.16	
0.05/0.16	* Chain [15]: 1*s(8)+1*s(9)+1
0.05/0.16	  Such that:s(7) =< V_x
0.05/0.16	s(8) =< s(7)
0.05/0.16	s(9) =< s(8)*s(7)
0.05/0.16	
0.05/0.16	  with precondition: [V_x>=1] 
0.05/0.16	
0.05/0.16	
0.05/0.16	Closed-form bounds of eval_foo_start(V_c,V_x,V_y,B): 
0.05/0.16	-------------------------------------
0.05/0.16	* Chain [17] with precondition: [V_x=0] 
0.05/0.16	    - Upper bound: 1 
0.05/0.16	    - Complexity: constant 
0.05/0.16	* Chain [16] with precondition: [0>=V_x+1] 
0.05/0.16	    - Upper bound: 0 
0.05/0.16	    - Complexity: constant 
0.05/0.16	* Chain [15] with precondition: [V_x>=1] 
0.05/0.16	    - Upper bound: V_x+1+V_x*V_x 
0.05/0.16	    - Complexity: n^2 
0.05/0.16	
0.05/0.16	### Maximum cost of eval_foo_start(V_c,V_x,V_y,B): max([1,nat(V_x)+1+nat(V_x)*nat(V_x)]) 
0.05/0.16	Asymptotic class: n^2 
0.05/0.16	* Total analysis performed in 90 ms.
0.05/0.16	
0.05/0.26	EOF