0.05/0.20	WORST_CASE(?,O(n^1))  
0.05/0.20	
0.05/0.20	Preprocessing Cost Relations
0.05/0.20	=====================================
0.05/0.20	
0.05/0.20	#### Computed strongly connected components 
0.05/0.20	0. recursive  : [eval_foo_bb1_in/4,eval_foo_bb2_in/4,eval_foo_bb3_in/4]
0.05/0.20	1. non_recursive  : [eval_foo_stop/1]
0.05/0.20	2. non_recursive  : [eval_foo_bb4_in/1]
0.05/0.20	3. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
0.05/0.20	4. non_recursive  : [eval_foo_bb0_in/3]
0.05/0.20	5. non_recursive  : [eval_foo_start/5]
0.05/0.20	
0.05/0.20	#### Obtained direct recursion through partial evaluation 
0.05/0.20	0. SCC is partially evaluated into eval_foo_bb1_in/4
0.05/0.20	1. SCC is completely evaluated into other SCCs
0.05/0.20	2. SCC is completely evaluated into other SCCs
0.05/0.20	3. SCC is completely evaluated into other SCCs
0.05/0.20	4. SCC is partially evaluated into eval_foo_bb0_in/3
0.05/0.20	5. SCC is partially evaluated into eval_foo_start/5
0.05/0.20	
0.05/0.20	Control-Flow Refinement of Cost Relations
0.05/0.20	=====================================
0.05/0.20	
0.05/0.20	### Specialization of cost equations eval_foo_bb1_in/4 
0.05/0.20	* CE 7 is refined into CE [8] 
0.05/0.20	* CE 6 is refined into CE [9] 
0.05/0.20	* CE 5 is refined into CE [10] 
0.05/0.20	
0.05/0.20	
0.05/0.20	### Cost equations --> "Loop" of eval_foo_bb1_in/4 
0.05/0.20	* CEs [9] --> Loop 8 
0.05/0.20	* CEs [10] --> Loop 9 
0.05/0.20	* CEs [8] --> Loop 10 
0.05/0.20	
0.05/0.20	### Ranking functions of CR eval_foo_bb1_in(V_m,V__01,V__0,B) 
0.05/0.20	* RF of phase [8,9]: [V__01+2*V__0-1]
0.05/0.20	
0.05/0.20	#### Partial ranking functions of CR eval_foo_bb1_in(V_m,V__01,V__0,B) 
0.05/0.20	* Partial RF of phase [8,9]:
0.05/0.20	  - RF of loop [8:1]:
0.05/0.20	    V__0
0.05/0.20	    V_m-V__01 depends on loops [9:1] 
0.05/0.20	  - RF of loop [9:1]:
0.05/0.20	    V__01 depends on loops [8:1] 
0.05/0.20	    -V_m+V__01+1 depends on loops [8:1] 
0.05/0.20	
0.05/0.20	
0.05/0.20	### Specialization of cost equations eval_foo_bb0_in/3 
0.05/0.20	* CE 4 is refined into CE [11,12] 
0.05/0.20	* CE 2 is refined into CE [13] 
0.05/0.20	* CE 3 is refined into CE [14] 
0.05/0.20	
0.05/0.20	
0.05/0.20	### Cost equations --> "Loop" of eval_foo_bb0_in/3 
0.05/0.20	* CEs [12] --> Loop 11 
0.05/0.20	* CEs [13] --> Loop 12 
0.05/0.20	* CEs [14] --> Loop 13 
0.05/0.20	* CEs [11] --> Loop 14 
0.05/0.20	
0.05/0.20	### Ranking functions of CR eval_foo_bb0_in(V_m,V_n,B) 
0.05/0.20	
0.05/0.20	#### Partial ranking functions of CR eval_foo_bb0_in(V_m,V_n,B) 
0.05/0.20	
0.05/0.20	
0.05/0.20	### Specialization of cost equations eval_foo_start/5 
0.05/0.20	* CE 1 is refined into CE [15,16,17,18] 
0.05/0.20	
0.05/0.20	
0.05/0.20	### Cost equations --> "Loop" of eval_foo_start/5 
0.05/0.20	* CEs [18] --> Loop 15 
0.05/0.20	* CEs [17] --> Loop 16 
0.05/0.20	* CEs [16] --> Loop 17 
0.05/0.20	* CEs [15] --> Loop 18 
0.05/0.20	
0.05/0.20	### Ranking functions of CR eval_foo_start(V_m,V_n,V_v1,V_v2,B) 
0.05/0.20	
0.05/0.20	#### Partial ranking functions of CR eval_foo_start(V_m,V_n,V_v1,V_v2,B) 
0.05/0.20	
0.05/0.20	
0.05/0.20	Computing Bounds
0.05/0.20	=====================================
0.05/0.20	
0.05/0.20	#### Cost of chains of eval_foo_bb1_in(V_m,V__01,V__0,B):
0.05/0.20	* Chain [[8,9],10]: 1*it(8)+1*it(9)+0
0.05/0.20	  Such that:it(8) =< V__0
0.05/0.20	aux(20) =< V__01+2*V__0
0.05/0.20	it(8) =< aux(20)
0.05/0.20	it(9) =< aux(20)
0.05/0.20	
0.05/0.20	  with precondition: [B=2,V_m>=1,V__01>=0,V__0>=1] 
0.05/0.20	
0.05/0.20	* Chain [10]: 0
0.05/0.20	  with precondition: [V__0=0,B=2,V_m>=1,V__01>=0] 
0.05/0.20	
0.05/0.20	
0.05/0.20	#### Cost of chains of eval_foo_bb0_in(V_m,V_n,B):
0.05/0.20	* Chain [14]: 0
0.05/0.20	  with precondition: [V_n=0,V_m>=1] 
0.05/0.20	
0.05/0.20	* Chain [13]: 0
0.05/0.20	  with precondition: [0>=V_m] 
0.05/0.20	
0.05/0.20	* Chain [12]: 0
0.05/0.20	  with precondition: [0>=V_n+1] 
0.05/0.20	
0.05/0.20	* Chain [11]: 1*s(1)+1*s(3)+0
0.05/0.20	  Such that:s(1) =< V_n
0.05/0.20	s(2) =< 2*V_n
0.05/0.20	s(1) =< s(2)
0.05/0.20	s(3) =< s(2)
0.05/0.20	
0.05/0.20	  with precondition: [V_m>=1,V_n>=1] 
0.05/0.20	
0.05/0.20	
0.05/0.20	#### Cost of chains of eval_foo_start(V_m,V_n,V_v1,V_v2,B):
0.05/0.20	* Chain [18]: 0
0.05/0.20	  with precondition: [V_n=0,V_m>=1] 
0.05/0.20	
0.05/0.20	* Chain [17]: 0
0.05/0.20	  with precondition: [0>=V_m] 
0.05/0.20	
0.05/0.20	* Chain [16]: 0
0.05/0.20	  with precondition: [0>=V_n+1] 
0.05/0.20	
0.05/0.20	* Chain [15]: 1*s(4)+1*s(6)+0
0.05/0.20	  Such that:s(4) =< V_n
0.05/0.20	s(5) =< 2*V_n
0.05/0.20	s(4) =< s(5)
0.05/0.20	s(6) =< s(5)
0.05/0.20	
0.05/0.20	  with precondition: [V_m>=1,V_n>=1] 
0.05/0.20	
0.05/0.20	
0.05/0.20	Closed-form bounds of eval_foo_start(V_m,V_n,V_v1,V_v2,B): 
0.05/0.20	-------------------------------------
0.05/0.20	* Chain [18] with precondition: [V_n=0,V_m>=1] 
0.05/0.20	    - Upper bound: 0 
0.05/0.20	    - Complexity: constant 
0.05/0.20	* Chain [17] with precondition: [0>=V_m] 
0.05/0.20	    - Upper bound: 0 
0.05/0.20	    - Complexity: constant 
0.05/0.20	* Chain [16] with precondition: [0>=V_n+1] 
0.05/0.20	    - Upper bound: 0 
0.05/0.20	    - Complexity: constant 
0.05/0.20	* Chain [15] with precondition: [V_m>=1,V_n>=1] 
0.05/0.20	    - Upper bound: 3*V_n 
0.05/0.20	    - Complexity: n 
0.05/0.20	
0.05/0.20	### Maximum cost of eval_foo_start(V_m,V_n,V_v1,V_v2,B): nat(2*V_n)+nat(V_n) 
0.05/0.20	Asymptotic class: n 
0.05/0.20	* Total analysis performed in 121 ms.
0.05/0.20	
0.05/0.30	EOF