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_0/4,eval_foo_1/5,eval_foo_bb1_in/4,eval_foo_bb2_in/4,eval_foo_bb3_in/5,eval_foo_bb4_in/5]
0.05/0.16	1. non_recursive  : [eval_foo_stop/1]
0.05/0.16	2. non_recursive  : [eval_foo_bb5_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/4]
0.05/0.16	5. 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_bb1_in/4
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/4
0.05/0.16	5. 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_bb1_in/4 
0.05/0.16	* CE 5 is refined into CE [7] 
0.05/0.16	* CE 6 is refined into CE [8] 
0.05/0.16	* CE 4 is refined into CE [9] 
0.05/0.16	* CE 3 is refined into CE [10] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_foo_bb1_in/4 
0.05/0.16	* CEs [9] --> Loop 7 
0.05/0.16	* CEs [10] --> Loop 8 
0.05/0.16	* CEs [7] --> Loop 9 
0.05/0.16	* CEs [8] --> Loop 10 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_foo_bb1_in(V_tx,V__01,V__0,B) 
0.05/0.16	* RF of phase [7,8]: [-V__01+V__0+1]
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_foo_bb1_in(V_tx,V__01,V__0,B) 
0.05/0.16	* Partial RF of phase [7,8]:
0.05/0.16	  - RF of loop [7:1,8:1]:
0.05/0.16	    -V__01+V__0+1
0.05/0.16	
0.05/0.16	
0.05/0.16	### Specialization of cost equations eval_foo_bb0_in/4 
0.05/0.16	* CE 2 is refined into CE [11,12,13] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_foo_bb0_in/4 
0.05/0.16	* CEs [13] --> Loop 11 
0.05/0.16	* CEs [12] --> Loop 12 
0.05/0.16	* CEs [11] --> Loop 13 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_tx,B) 
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_foo_bb0_in(V_x,V_y,V_tx,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 [14,15,16] 
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 [16] --> Loop 14 
0.05/0.16	* CEs [15] --> Loop 15 
0.05/0.16	* CEs [14] --> Loop 16 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_foo_start(V_x,V_y,V_tx,B) 
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_foo_start(V_x,V_y,V_tx,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_tx,V__01,V__0,B):
0.05/0.16	* Chain [[7,8],9]: 2*it(7)+0
0.05/0.16	  Such that:aux(2) =< V_tx-V__01+V__0+1
0.05/0.16	aux(1) =< -V__01+V__0+1
0.05/0.16	it(7) =< aux(1)
0.05/0.16	it(7) =< aux(2)
0.05/0.16	
0.05/0.16	  with precondition: [B=2,V_tx>=0,V__0>=V__01] 
0.05/0.16	
0.05/0.16	* Chain [10]: 0
0.05/0.16	  with precondition: [B=2,0>=V_tx+1] 
0.05/0.16	
0.05/0.16	* Chain [9]: 0
0.05/0.16	  with precondition: [B=2,V__01>=V__0+1] 
0.05/0.16	
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_foo_bb0_in(V_x,V_y,V_tx,B):
0.05/0.16	* Chain [13]: 0
0.05/0.16	  with precondition: [0>=V_tx+1] 
0.05/0.16	
0.05/0.16	* Chain [12]: 2*s(3)+0
0.05/0.16	  Such that:s(2) =< V_x-V_y+1
0.05/0.16	s(1) =< V_x-V_y+V_tx+1
0.05/0.16	s(3) =< s(2)
0.05/0.16	s(3) =< s(1)
0.05/0.16	
0.05/0.16	  with precondition: [V_tx>=0,V_x>=V_y] 
0.05/0.16	
0.05/0.16	* Chain [11]: 0
0.05/0.16	  with precondition: [V_y>=V_x+1] 
0.05/0.16	
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_foo_start(V_x,V_y,V_tx,B):
0.05/0.16	* Chain [16]: 0
0.05/0.16	  with precondition: [0>=V_tx+1] 
0.05/0.16	
0.05/0.16	* Chain [15]: 2*s(6)+0
0.05/0.16	  Such that:s(4) =< V_x-V_y+1
0.05/0.16	s(5) =< V_x-V_y+V_tx+1
0.05/0.16	s(6) =< s(4)
0.05/0.16	s(6) =< s(5)
0.05/0.16	
0.05/0.16	  with precondition: [V_tx>=0,V_x>=V_y] 
0.05/0.16	
0.05/0.16	* Chain [14]: 0
0.05/0.16	  with precondition: [V_y>=V_x+1] 
0.05/0.16	
0.05/0.16	
0.05/0.16	Closed-form bounds of eval_foo_start(V_x,V_y,V_tx,B): 
0.05/0.16	-------------------------------------
0.05/0.16	* Chain [16] with precondition: [0>=V_tx+1] 
0.05/0.16	    - Upper bound: 0 
0.05/0.16	    - Complexity: constant 
0.05/0.16	* Chain [15] with precondition: [V_tx>=0,V_x>=V_y] 
0.05/0.16	    - Upper bound: 2*V_x-2*V_y+2 
0.05/0.16	    - Complexity: n 
0.05/0.16	* Chain [14] with precondition: [V_y>=V_x+1] 
0.05/0.16	    - Upper bound: 0 
0.05/0.16	    - Complexity: constant 
0.05/0.16	
0.05/0.16	### Maximum cost of eval_foo_start(V_x,V_y,V_tx,B): nat(V_x-V_y+1)*2 
0.05/0.16	Asymptotic class: n 
0.05/0.16	* Total analysis performed in 91 ms.
0.05/0.16	
0.05/0.27	EOF