0.05/0.24	WORST_CASE(?,O(n^2))  
0.05/0.24	
0.05/0.24	Preprocessing Cost Relations
0.05/0.24	=====================================
0.05/0.24	
0.05/0.24	#### Computed strongly connected components 
0.05/0.24	0. recursive  : [eval_foo_bb1_in/5,eval_foo_bb2_in/5]
0.05/0.24	1. non_recursive  : [eval_foo_stop/1]
0.05/0.24	2. non_recursive  : [eval_foo_bb3_in/1]
0.05/0.24	3. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
0.05/0.24	4. non_recursive  : [eval_foo_bb0_in/3]
0.05/0.24	5. non_recursive  : [eval_foo_start/5]
0.05/0.24	
0.05/0.24	#### Obtained direct recursion through partial evaluation 
0.05/0.24	0. SCC is partially evaluated into eval_foo_bb1_in/5
0.05/0.24	1. SCC is completely evaluated into other SCCs
0.05/0.24	2. SCC is completely evaluated into other SCCs
0.05/0.24	3. SCC is completely evaluated into other SCCs
0.05/0.24	4. SCC is partially evaluated into eval_foo_bb0_in/3
0.05/0.24	5. SCC is partially evaluated into eval_foo_start/5
0.05/0.24	
0.05/0.24	Control-Flow Refinement of Cost Relations
0.05/0.24	=====================================
0.05/0.24	
0.05/0.24	### Specialization of cost equations eval_foo_bb1_in/5 
0.05/0.24	* CE 7 is refined into CE [8] 
0.05/0.24	* CE 6 is refined into CE [9] 
0.05/0.24	* CE 5 is refined into CE [10] 
0.05/0.24	
0.05/0.24	
0.05/0.24	### Cost equations --> "Loop" of eval_foo_bb1_in/5 
0.05/0.24	* CEs [9] --> Loop 8 
0.05/0.24	* CEs [10] --> Loop 9 
0.05/0.24	* CEs [8] --> Loop 10 
0.05/0.24	
0.05/0.24	### Ranking functions of CR eval_foo_bb1_in(V_m,V_n,V__01,V__0,B) 
0.05/0.24	
0.05/0.24	#### Partial ranking functions of CR eval_foo_bb1_in(V_m,V_n,V__01,V__0,B) 
0.05/0.24	* Partial RF of phase [8,9]:
0.05/0.24	  - RF of loop [8:1]:
0.05/0.24	    V_m-V__01 depends on loops [9:1] 
0.05/0.24	    V_n-V__01-1 depends on loops [9:1] 
0.05/0.24	  - RF of loop [9:1]:
0.05/0.24	    V__01 depends on loops [8:1] 
0.05/0.24	    -V_m+V__01+1 depends on loops [8:1] 
0.05/0.24	    V_n-V__0
0.05/0.24	
0.05/0.24	
0.05/0.24	### Specialization of cost equations eval_foo_bb0_in/3 
0.05/0.24	* CE 3 is refined into CE [11] 
0.05/0.24	* CE 4 is refined into CE [12] 
0.05/0.24	* CE 2 is refined into CE [13] 
0.05/0.24	
0.05/0.24	
0.05/0.24	### Cost equations --> "Loop" of eval_foo_bb0_in/3 
0.05/0.24	* CEs [11] --> Loop 11 
0.05/0.24	* CEs [12] --> Loop 12 
0.05/0.24	* CEs [13] --> Loop 13 
0.05/0.24	
0.05/0.24	### Ranking functions of CR eval_foo_bb0_in(V_m,V_n,B) 
0.05/0.24	
0.05/0.24	#### Partial ranking functions of CR eval_foo_bb0_in(V_m,V_n,B) 
0.05/0.24	
0.05/0.24	
0.05/0.24	### Specialization of cost equations eval_foo_start/5 
0.05/0.24	* CE 1 is refined into CE [14,15,16] 
0.05/0.24	
0.05/0.24	
0.05/0.24	### Cost equations --> "Loop" of eval_foo_start/5 
0.05/0.24	* CEs [16] --> Loop 14 
0.05/0.24	* CEs [15] --> Loop 15 
0.05/0.24	* CEs [14] --> Loop 16 
0.05/0.24	
0.05/0.24	### Ranking functions of CR eval_foo_start(V_i,V_j,V_m,V_n,B) 
0.05/0.24	
0.05/0.24	#### Partial ranking functions of CR eval_foo_start(V_i,V_j,V_m,V_n,B) 
0.05/0.24	
0.05/0.24	
0.05/0.24	Computing Bounds
0.05/0.24	=====================================
0.05/0.24	
0.05/0.24	#### Cost of chains of eval_foo_bb1_in(V_m,V_n,V__01,V__0,B):
0.05/0.24	* Chain [[8,9],10]: 1*it(8)+1*it(9)+0
0.05/0.24	  Such that:aux(19) =< V_n
0.05/0.24	aux(4) =< V_n-V__01
0.05/0.24	it(9) =< V_n-V__0
0.05/0.24	aux(3) =< it(9)*aux(19)
0.05/0.24	it(8) =< aux(3)+aux(4)
0.05/0.24	
0.05/0.24	  with precondition: [B=2,V_m>=1,V__01>=0,V__0>=0,V_n>=V_m+1,V_n>=V__0+1] 
0.05/0.24	
0.05/0.24	
0.05/0.24	#### Cost of chains of eval_foo_bb0_in(V_m,V_n,B):
0.05/0.24	* Chain [13]: 0
0.05/0.24	  with precondition: [0>=V_m] 
0.05/0.24	
0.05/0.24	* Chain [12]: 1*s(3)+1*s(5)+0
0.05/0.24	  Such that:aux(22) =< V_n
0.05/0.24	s(3) =< aux(22)
0.05/0.24	s(4) =< s(3)*aux(22)
0.05/0.24	s(5) =< s(4)+aux(22)
0.05/0.24	
0.05/0.24	  with precondition: [V_m>=1,V_n>=V_m+1] 
0.05/0.24	
0.05/0.24	* Chain [11]: 0
0.05/0.24	  with precondition: [V_m>=V_n] 
0.05/0.24	
0.05/0.24	
0.05/0.24	#### Cost of chains of eval_foo_start(V_i,V_j,V_m,V_n,B):
0.05/0.24	* Chain [16]: 0
0.05/0.24	  with precondition: [0>=V_m] 
0.05/0.24	
0.05/0.24	* Chain [15]: 1*s(7)+1*s(9)+0
0.05/0.24	  Such that:s(6) =< V_n
0.05/0.24	s(7) =< s(6)
0.05/0.24	s(8) =< s(7)*s(6)
0.05/0.24	s(9) =< s(8)+s(6)
0.05/0.24	
0.05/0.24	  with precondition: [V_m>=1,V_n>=V_m+1] 
0.05/0.24	
0.05/0.24	* Chain [14]: 0
0.05/0.24	  with precondition: [V_m>=V_n] 
0.05/0.24	
0.05/0.24	
0.05/0.24	Closed-form bounds of eval_foo_start(V_i,V_j,V_m,V_n,B): 
0.05/0.24	-------------------------------------
0.05/0.24	* Chain [16] with precondition: [0>=V_m] 
0.05/0.24	    - Upper bound: 0 
0.05/0.24	    - Complexity: constant 
0.05/0.24	* Chain [15] with precondition: [V_m>=1,V_n>=V_m+1] 
0.05/0.24	    - Upper bound: 2*V_n+V_n*V_n 
0.05/0.24	    - Complexity: n^2 
0.05/0.24	* Chain [14] with precondition: [V_m>=V_n] 
0.05/0.24	    - Upper bound: 0 
0.05/0.24	    - Complexity: constant 
0.05/0.24	
0.05/0.24	### Maximum cost of eval_foo_start(V_i,V_j,V_m,V_n,B): nat(V_n)*nat(V_n)+nat(V_n)*2 
0.05/0.24	Asymptotic class: n^2 
0.05/0.24	* Total analysis performed in 163 ms.
0.05/0.24	
0.05/0.35	EOF