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_bb3_in/3,eval_foo_bb4_in/3]
0.05/0.16	1. recursive  : [eval_foo_bb1_in/2,eval_foo_bb2_in/2,eval_foo_bb3_in_loop_cont/4,eval_foo_bb5_in/3]
0.05/0.16	2. non_recursive  : [eval_foo_stop/1]
0.05/0.16	3. non_recursive  : [eval_foo_bb6_in/1]
0.05/0.16	4. non_recursive  : [eval_foo_bb1_in_loop_cont/2]
0.05/0.16	5. non_recursive  : [eval_foo_bb0_in/2]
0.05/0.16	6. non_recursive  : [eval_foo_start/5]
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_bb3_in/3
0.05/0.16	1. SCC is partially evaluated into eval_foo_bb1_in/2
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 completely evaluated into other SCCs
0.05/0.16	5. SCC is partially evaluated into eval_foo_bb0_in/2
0.05/0.16	6. SCC is partially evaluated into eval_foo_start/5
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_bb3_in/3 
0.05/0.16	* CE 6 is refined into CE [7] 
0.05/0.16	* CE 5 is refined into CE [8] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_foo_bb3_in/3 
0.05/0.16	* CEs [8] --> Loop 7 
0.05/0.16	* CEs [7] --> Loop 8 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_foo_bb3_in(V__01,B,C) 
0.05/0.16	* RF of phase [7]: [V__01-1]
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_foo_bb3_in(V__01,B,C) 
0.05/0.16	* Partial RF of phase [7]:
0.05/0.16	  - RF of loop [7:1]:
0.05/0.16	    V__01-1
0.05/0.16	
0.05/0.16	
0.05/0.16	### Specialization of cost equations eval_foo_bb1_in/2 
0.05/0.16	* CE 4 is refined into CE [9] 
0.05/0.16	* CE 3 is refined into CE [10,11] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_foo_bb1_in/2 
0.05/0.16	* CEs [11] --> Loop 9 
0.05/0.16	* CEs [10] --> Loop 10 
0.05/0.16	* CEs [9] --> Loop 11 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_foo_bb1_in(V__0,B) 
0.05/0.16	* RF of phase [10]: [V__0-1]
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_foo_bb1_in(V__0,B) 
0.05/0.16	* Partial RF of phase [10]:
0.05/0.16	  - RF of loop [10:1]:
0.05/0.16	    V__0-1
0.05/0.16	
0.05/0.16	
0.05/0.16	### Specialization of cost equations eval_foo_bb0_in/2 
0.05/0.16	* CE 2 is refined into CE [12,13,14,15] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_foo_bb0_in/2 
0.05/0.16	* CEs [15] --> Loop 12 
0.05/0.16	* CEs [14] --> Loop 13 
0.05/0.16	* CEs [13] --> Loop 14 
0.05/0.16	* CEs [12] --> Loop 15 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_foo_bb0_in(V_x,B) 
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_foo_bb0_in(V_x,B) 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Specialization of cost equations eval_foo_start/5 
0.05/0.16	* CE 1 is refined into CE [16,17,18,19] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_foo_start/5 
0.05/0.16	* CEs [19] --> Loop 16 
0.05/0.16	* CEs [18] --> Loop 17 
0.05/0.16	* CEs [17] --> Loop 18 
0.05/0.16	* CEs [16] --> Loop 19 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_foo_start(V_x,V_xtmp,V_res,V_restmp,B) 
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_foo_start(V_x,V_xtmp,V_res,V_restmp,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_bb3_in(V__01,B,C):
0.05/0.16	* Chain [[7],8]: 1*it(7)+0
0.05/0.16	  Such that:it(7) =< V__01-C
0.05/0.16	
0.05/0.16	  with precondition: [B=2,1>=C,C>=0,V__01>=C+2] 
0.05/0.16	
0.05/0.16	* Chain [8]: 0
0.05/0.16	  with precondition: [B=2,V__01=C,1>=V__01,V__01>=0] 
0.05/0.16	
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_foo_bb1_in(V__0,B):
0.05/0.16	* Chain [[10],11]: 1*it(10)+0
0.05/0.16	  Such that:it(10) =< V__0
0.05/0.16	
0.05/0.16	  with precondition: [B=3,3>=V__0,V__0>=2] 
0.05/0.16	
0.05/0.16	* Chain [11]: 0
0.05/0.16	  with precondition: [B=3,1>=V__0] 
0.05/0.16	
0.05/0.16	* Chain [9,[10],11]: 1*it(10)+1*s(1)+1
0.05/0.16	  Such that:it(10) =< 2
0.05/0.16	s(1) =< V__0
0.05/0.16	
0.05/0.16	  with precondition: [B=3,V__0>=5] 
0.05/0.16	
0.05/0.16	* Chain [9,11]: 1*s(1)+1
0.05/0.16	  Such that:s(1) =< V__0
0.05/0.16	
0.05/0.16	  with precondition: [B=3,V__0>=4] 
0.05/0.16	
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_foo_bb0_in(V_x,B):
0.05/0.16	* Chain [15]: 1*s(2)+0
0.05/0.16	  Such that:s(2) =< V_x
0.05/0.16	
0.05/0.16	  with precondition: [3>=V_x,V_x>=2] 
0.05/0.16	
0.05/0.16	* Chain [14]: 0
0.05/0.16	  with precondition: [1>=V_x] 
0.05/0.16	
0.05/0.16	* Chain [13]: 1*s(3)+1
0.05/0.16	  Such that:s(3) =< V_x
0.05/0.16	
0.05/0.16	  with precondition: [V_x>=4] 
0.05/0.16	
0.05/0.16	* Chain [12]: 1*s(4)+1*s(5)+1
0.05/0.16	  Such that:s(4) =< 2
0.05/0.16	s(5) =< V_x
0.05/0.16	
0.05/0.16	  with precondition: [V_x>=5] 
0.05/0.16	
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_foo_start(V_x,V_xtmp,V_res,V_restmp,B):
0.05/0.16	* Chain [19]: 1*s(6)+0
0.05/0.16	  Such that:s(6) =< V_x
0.05/0.16	
0.05/0.16	  with precondition: [3>=V_x,V_x>=2] 
0.05/0.16	
0.05/0.16	* Chain [18]: 0
0.05/0.16	  with precondition: [1>=V_x] 
0.05/0.16	
0.05/0.16	* Chain [17]: 1*s(7)+1
0.05/0.16	  Such that:s(7) =< V_x
0.05/0.16	
0.05/0.16	  with precondition: [V_x>=4] 
0.05/0.16	
0.05/0.16	* Chain [16]: 1*s(8)+1*s(9)+1
0.05/0.16	  Such that:s(8) =< 2
0.05/0.16	s(9) =< V_x
0.05/0.16	
0.05/0.16	  with precondition: [V_x>=5] 
0.05/0.16	
0.05/0.16	
0.05/0.16	Closed-form bounds of eval_foo_start(V_x,V_xtmp,V_res,V_restmp,B): 
0.05/0.16	-------------------------------------
0.05/0.16	* Chain [19] with precondition: [3>=V_x,V_x>=2] 
0.05/0.16	    - Upper bound: V_x 
0.05/0.16	    - Complexity: n 
0.05/0.16	* Chain [18] with precondition: [1>=V_x] 
0.05/0.16	    - Upper bound: 0 
0.05/0.16	    - Complexity: constant 
0.05/0.16	* Chain [17] with precondition: [V_x>=4] 
0.05/0.16	    - Upper bound: V_x+1 
0.05/0.16	    - Complexity: n 
0.05/0.16	* Chain [16] with precondition: [V_x>=5] 
0.05/0.16	    - Upper bound: V_x+3 
0.05/0.16	    - Complexity: n 
0.05/0.16	
0.05/0.16	### Maximum cost of eval_foo_start(V_x,V_xtmp,V_res,V_restmp,B): nat(V_x)+3 
0.05/0.16	Asymptotic class: n 
0.05/0.16	* Total analysis performed in 88 ms.
0.05/0.16	
0.05/0.26	EOF