0.04/0.15	WORST_CASE(?,O(n^1))  
0.04/0.15	
0.04/0.15	Preprocessing Cost Relations
0.04/0.15	=====================================
0.04/0.15	
0.04/0.15	#### Computed strongly connected components 
0.04/0.15	0. recursive  : [eval_foo_bb1_in/4,eval_foo_bb2_in/4]
0.04/0.15	1. non_recursive  : [eval_foo_stop/1]
0.04/0.15	2. non_recursive  : [eval_foo_bb3_in/1]
0.04/0.15	3. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
0.04/0.15	4. non_recursive  : [eval_foo_bb0_in/4]
0.04/0.15	5. non_recursive  : [eval_foo_start/5]
0.04/0.15	
0.04/0.15	#### Obtained direct recursion through partial evaluation 
0.04/0.15	0. SCC is partially evaluated into eval_foo_bb1_in/4
0.04/0.15	1. SCC is completely evaluated into other SCCs
0.04/0.15	2. SCC is completely evaluated into other SCCs
0.04/0.15	3. SCC is completely evaluated into other SCCs
0.04/0.15	4. SCC is partially evaluated into eval_foo_bb0_in/4
0.04/0.15	5. SCC is partially evaluated into eval_foo_start/5
0.04/0.15	
0.04/0.15	Control-Flow Refinement of Cost Relations
0.04/0.15	=====================================
0.04/0.15	
0.04/0.15	### Specialization of cost equations eval_foo_bb1_in/4 
0.04/0.15	* CE 5 is refined into CE [6] 
0.04/0.15	* CE 4 is refined into CE [7] 
0.04/0.15	* CE 3 is refined into CE [8] 
0.04/0.15	
0.04/0.15	
0.04/0.15	### Cost equations --> "Loop" of eval_foo_bb1_in/4 
0.04/0.15	* CEs [8] --> Loop 6 
0.04/0.15	* CEs [6] --> Loop 7 
0.04/0.15	* CEs [7] --> Loop 8 
0.04/0.15	
0.04/0.15	### Ranking functions of CR eval_foo_bb1_in(V__02,V__01,V__0,B) 
0.04/0.15	* RF of phase [6]: [-V__02/2-V__01/2+V__0/2+101/2]
0.04/0.15	
0.04/0.15	#### Partial ranking functions of CR eval_foo_bb1_in(V__02,V__01,V__0,B) 
0.04/0.15	* Partial RF of phase [6]:
0.04/0.15	  - RF of loop [6:1]:
0.04/0.15	    -V__02/2-V__01/2+V__0/2+101/2
0.04/0.15	
0.04/0.15	
0.04/0.15	### Specialization of cost equations eval_foo_bb0_in/4 
0.04/0.15	* CE 2 is refined into CE [9,10,11,12] 
0.04/0.15	
0.04/0.15	
0.04/0.15	### Cost equations --> "Loop" of eval_foo_bb0_in/4 
0.04/0.15	* CEs [12] --> Loop 9 
0.04/0.15	* CEs [11] --> Loop 10 
0.04/0.15	* CEs [10] --> Loop 11 
0.04/0.15	* CEs [9] --> Loop 12 
0.04/0.15	
0.04/0.15	### Ranking functions of CR eval_foo_bb0_in(V_k,V_i,V_j,B) 
0.04/0.15	
0.04/0.15	#### Partial ranking functions of CR eval_foo_bb0_in(V_k,V_i,V_j,B) 
0.04/0.15	
0.04/0.15	
0.04/0.15	### Specialization of cost equations eval_foo_start/5 
0.04/0.15	* CE 1 is refined into CE [13,14,15,16] 
0.04/0.15	
0.04/0.15	
0.04/0.15	### Cost equations --> "Loop" of eval_foo_start/5 
0.04/0.15	* CEs [16] --> Loop 13 
0.04/0.15	* CEs [15] --> Loop 14 
0.04/0.15	* CEs [14] --> Loop 15 
0.04/0.15	* CEs [13] --> Loop 16 
0.04/0.15	
0.04/0.15	### Ranking functions of CR eval_foo_start(V_k,V_i,V_j,V_tmp,B) 
0.04/0.15	
0.04/0.15	#### Partial ranking functions of CR eval_foo_start(V_k,V_i,V_j,V_tmp,B) 
0.04/0.15	
0.04/0.15	
0.04/0.15	Computing Bounds
0.04/0.15	=====================================
0.04/0.15	
0.04/0.15	#### Cost of chains of eval_foo_bb1_in(V__02,V__01,V__0,B):
0.04/0.15	* Chain [[6],8]: 1*it(6)+0
0.04/0.15	  Such that:it(6) =< -V__02/2-V__01/2+V__0/2+101/2
0.04/0.15	it(6) =< V__0
0.04/0.15	
0.04/0.15	  with precondition: [B=2,100>=V__01,V__0>=101,V__0>=V__02] 
0.04/0.15	
0.04/0.15	* Chain [[6],7]: 1*it(6)+0
0.04/0.15	  Such that:it(6) =< -V__02/2-V__01/2+V__0/2+101/2
0.04/0.15	
0.04/0.15	  with precondition: [B=2,100>=V__01,V__0>=V__02] 
0.04/0.15	
0.04/0.15	* Chain [8]: 0
0.04/0.15	  with precondition: [B=2,V__01>=101] 
0.04/0.15	
0.04/0.15	* Chain [7]: 0
0.04/0.15	  with precondition: [B=2,V__02>=V__0+1] 
0.04/0.15	
0.04/0.15	
0.04/0.15	#### Cost of chains of eval_foo_bb0_in(V_k,V_i,V_j,B):
0.04/0.15	* Chain [12]: 1*s(1)+0
0.04/0.15	  Such that:s(1) =< V_k
0.04/0.15	s(1) =< V_k/2-V_i/2-V_j/2+101/2
0.04/0.15	
0.04/0.15	  with precondition: [100>=V_i,V_k>=101,V_k>=V_j] 
0.04/0.15	
0.04/0.15	* Chain [11]: 1*s(2)+0
0.04/0.15	  Such that:s(2) =< V_k/2-V_i/2-V_j/2+101/2
0.04/0.15	
0.04/0.15	  with precondition: [100>=V_i,V_k>=V_j] 
0.04/0.15	
0.04/0.15	* Chain [10]: 0
0.04/0.15	  with precondition: [V_i>=101] 
0.04/0.15	
0.04/0.15	* Chain [9]: 0
0.04/0.15	  with precondition: [V_j>=V_k+1] 
0.04/0.15	
0.04/0.15	
0.04/0.15	#### Cost of chains of eval_foo_start(V_k,V_i,V_j,V_tmp,B):
0.04/0.15	* Chain [16]: 1*s(3)+0
0.04/0.15	  Such that:s(3) =< V_k
0.04/0.15	s(3) =< V_k/2-V_i/2-V_j/2+101/2
0.04/0.15	
0.04/0.15	  with precondition: [100>=V_i,V_k>=101,V_k>=V_j] 
0.04/0.15	
0.04/0.15	* Chain [15]: 1*s(4)+0
0.04/0.15	  Such that:s(4) =< V_k/2-V_i/2-V_j/2+101/2
0.04/0.15	
0.04/0.15	  with precondition: [100>=V_i,V_k>=V_j] 
0.04/0.15	
0.04/0.15	* Chain [14]: 0
0.04/0.15	  with precondition: [V_i>=101] 
0.04/0.15	
0.04/0.15	* Chain [13]: 0
0.04/0.15	  with precondition: [V_j>=V_k+1] 
0.04/0.15	
0.04/0.15	
0.04/0.15	Closed-form bounds of eval_foo_start(V_k,V_i,V_j,V_tmp,B): 
0.04/0.15	-------------------------------------
0.04/0.15	* Chain [16] with precondition: [100>=V_i,V_k>=101,V_k>=V_j] 
0.04/0.15	    - Upper bound: V_k 
0.04/0.15	    - Complexity: n 
0.04/0.15	* Chain [15] with precondition: [100>=V_i,V_k>=V_j] 
0.04/0.15	    - Upper bound: V_k/2-V_i/2-V_j/2+101/2 
0.04/0.15	    - Complexity: n 
0.04/0.15	* Chain [14] with precondition: [V_i>=101] 
0.04/0.15	    - Upper bound: 0 
0.04/0.15	    - Complexity: constant 
0.04/0.15	* Chain [13] with precondition: [V_j>=V_k+1] 
0.04/0.15	    - Upper bound: 0 
0.04/0.15	    - Complexity: constant 
0.04/0.15	
0.04/0.15	### Maximum cost of eval_foo_start(V_k,V_i,V_j,V_tmp,B): max([nat(V_k),nat(V_k/2-V_i/2-V_j/2+101/2)]) 
0.04/0.15	Asymptotic class: n 
0.04/0.15	* Total analysis performed in 79 ms.
0.04/0.15	
0.04/0.25	EOF