0.05/0.15	WORST_CASE(?,O(n^1))  
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_foo_bb1_in/4,eval_foo_bb2_in/4]
0.05/0.15	1. non_recursive  : [eval_foo_stop/1]
0.05/0.15	2. non_recursive  : [eval_foo_bb3_in/1]
0.05/0.15	3. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
0.05/0.15	4. non_recursive  : [eval_foo_bb0_in/4]
0.05/0.15	5. non_recursive  : [eval_foo_start/5]
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_foo_bb1_in/4
0.05/0.15	1. SCC is completely evaluated into other SCCs
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 partially evaluated into eval_foo_bb0_in/4
0.05/0.15	5. SCC is partially evaluated into eval_foo_start/5
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_foo_bb1_in/4 
0.05/0.15	* CE 5 is refined into CE [6] 
0.05/0.15	* CE 4 is refined into CE [7] 
0.05/0.15	* CE 3 is refined into CE [8] 
0.05/0.15	
0.05/0.15	
0.05/0.15	### Cost equations --> "Loop" of eval_foo_bb1_in/4 
0.05/0.15	* CEs [7] --> Loop 6 
0.05/0.15	* CEs [8] --> Loop 7 
0.05/0.15	* CEs [6] --> Loop 8 
0.05/0.15	
0.05/0.15	### Ranking functions of CR eval_foo_bb1_in(V_y,V__01,V__0,B) 
0.05/0.15	
0.05/0.15	#### Partial ranking functions of CR eval_foo_bb1_in(V_y,V__01,V__0,B) 
0.05/0.15	* Partial RF of phase [6,7]:
0.05/0.15	  - RF of loop [6:1]:
0.05/0.15	    V__01-V__0 depends on loops [7:1] 
0.05/0.15	    V_y-V__0
0.05/0.15	  - RF of loop [7:1]:
0.05/0.15	    -V__01+V__0+1 depends on loops [6:1] 
0.05/0.15	    V_y-V__01
0.05/0.15	
0.05/0.15	
0.05/0.15	### Specialization of cost equations eval_foo_bb0_in/4 
0.05/0.15	* CE 2 is refined into CE [9,10] 
0.05/0.15	
0.05/0.15	
0.05/0.15	### Cost equations --> "Loop" of eval_foo_bb0_in/4 
0.05/0.15	* CEs [9] --> Loop 9 
0.05/0.15	* CEs [10] --> Loop 10 
0.05/0.15	
0.05/0.15	### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_z,B) 
0.05/0.15	
0.05/0.15	#### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_z,B) 
0.05/0.15	
0.05/0.15	
0.05/0.15	### Specialization of cost equations eval_foo_start/5 
0.05/0.15	* CE 1 is refined into CE [11,12] 
0.05/0.15	
0.05/0.15	
0.05/0.15	### Cost equations --> "Loop" of eval_foo_start/5 
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_foo_start(V_x,V_y,V_z,V_i,B) 
0.05/0.15	
0.05/0.15	#### Partial ranking functions of CR eval_foo_start(V_x,V_y,V_z,V_i,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_foo_bb1_in(V_y,V__01,V__0,B):
0.05/0.15	* Chain [[6,7],8]: 1*it(6)+1*it(7)+0
0.05/0.15	  Such that:it(7) =< V_y-V__01
0.05/0.15	it(6) =< V_y-V__0
0.05/0.15	
0.05/0.15	  with precondition: [B=2,V_y>=V__0+1] 
0.05/0.15	
0.05/0.15	* Chain [8]: 0
0.05/0.15	  with precondition: [B=2,V__0>=V_y] 
0.05/0.15	
0.05/0.15	
0.05/0.15	#### Cost of chains of eval_foo_bb0_in(V_x,V_y,V_z,B):
0.05/0.15	* Chain [10]: 1*s(1)+1*s(2)+0
0.05/0.15	  Such that:s(2) =< -V_x+V_y
0.05/0.15	s(1) =< V_y-V_z
0.05/0.15	
0.05/0.15	  with precondition: [V_y>=V_x+1] 
0.05/0.15	
0.05/0.15	* Chain [9]: 0
0.05/0.15	  with precondition: [V_x>=V_y] 
0.05/0.15	
0.05/0.15	
0.05/0.15	#### Cost of chains of eval_foo_start(V_x,V_y,V_z,V_i,B):
0.05/0.15	* Chain [12]: 1*s(3)+1*s(4)+0
0.05/0.15	  Such that:s(3) =< -V_x+V_y
0.05/0.15	s(4) =< V_y-V_z
0.05/0.15	
0.05/0.15	  with precondition: [V_y>=V_x+1] 
0.05/0.15	
0.05/0.15	* Chain [11]: 0
0.05/0.15	  with precondition: [V_x>=V_y] 
0.05/0.15	
0.05/0.15	
0.05/0.15	Closed-form bounds of eval_foo_start(V_x,V_y,V_z,V_i,B): 
0.05/0.15	-------------------------------------
0.05/0.15	* Chain [12] with precondition: [V_y>=V_x+1] 
0.05/0.15	    - Upper bound: -V_x+V_y+nat(V_y-V_z) 
0.05/0.15	    - Complexity: n 
0.05/0.15	* Chain [11] with precondition: [V_x>=V_y] 
0.05/0.15	    - Upper bound: 0 
0.05/0.15	    - Complexity: constant 
0.05/0.15	
0.05/0.15	### Maximum cost of eval_foo_start(V_x,V_y,V_z,V_i,B): nat(V_y-V_z)+nat(-V_x+V_y) 
0.05/0.15	Asymptotic class: n 
0.05/0.15	* Total analysis performed in 77 ms.
0.05/0.15	
0.05/0.25	EOF