0.05/0.17	WORST_CASE(?,O(n^1))  
0.05/0.17	
0.05/0.17	Preprocessing Cost Relations
0.05/0.17	=====================================
0.05/0.17	
0.05/0.17	#### Computed strongly connected components 
0.05/0.17	0. recursive  : [eval_ex_paper1_bb1_in/4,eval_ex_paper1_bb2_in/4]
0.05/0.17	1. non_recursive  : [eval_ex_paper1_stop/1]
0.05/0.17	2. non_recursive  : [eval_ex_paper1_bb3_in/1]
0.05/0.17	3. non_recursive  : [eval_ex_paper1_bb1_in_loop_cont/2]
0.05/0.17	4. non_recursive  : [eval_ex_paper1_bb0_in/4]
0.05/0.17	5. non_recursive  : [eval_ex_paper1_start/4]
0.05/0.17	
0.05/0.17	#### Obtained direct recursion through partial evaluation 
0.05/0.17	0. SCC is partially evaluated into eval_ex_paper1_bb1_in/4
0.05/0.17	1. SCC is completely evaluated into other SCCs
0.05/0.17	2. SCC is completely evaluated into other SCCs
0.05/0.17	3. SCC is completely evaluated into other SCCs
0.05/0.17	4. SCC is partially evaluated into eval_ex_paper1_bb0_in/4
0.05/0.17	5. SCC is partially evaluated into eval_ex_paper1_start/4
0.05/0.17	
0.05/0.17	Control-Flow Refinement of Cost Relations
0.05/0.17	=====================================
0.05/0.17	
0.05/0.17	### Specialization of cost equations eval_ex_paper1_bb1_in/4 
0.05/0.17	* CE 6 is refined into CE [7] 
0.05/0.17	* CE 5 is refined into CE [8] 
0.05/0.17	* CE 3 is refined into CE [9] 
0.05/0.17	* CE 4 is refined into CE [10] 
0.05/0.17	
0.05/0.17	
0.05/0.17	### Cost equations --> "Loop" of eval_ex_paper1_bb1_in/4 
0.05/0.17	* CEs [9] --> Loop 7 
0.05/0.17	* CEs [10] --> Loop 8 
0.05/0.17	* CEs [7] --> Loop 9 
0.05/0.17	* CEs [8] --> Loop 10 
0.05/0.17	
0.05/0.17	### Ranking functions of CR eval_ex_paper1_bb1_in(V_n,V_fwd,V__0,B) 
0.05/0.17	* RF of phase [7]: [V__0]
0.05/0.17	* RF of phase [8]: [V_n-V__0]
0.05/0.17	
0.05/0.17	#### Partial ranking functions of CR eval_ex_paper1_bb1_in(V_n,V_fwd,V__0,B) 
0.05/0.17	* Partial RF of phase [7]:
0.05/0.17	  - RF of loop [7:1]:
0.05/0.17	    V__0
0.05/0.17	* Partial RF of phase [8]:
0.05/0.17	  - RF of loop [8:1]:
0.05/0.17	    V_n-V__0
0.05/0.17	
0.05/0.17	
0.05/0.17	### Specialization of cost equations eval_ex_paper1_bb0_in/4 
0.05/0.17	* CE 2 is refined into CE [11,12,13,14] 
0.05/0.17	
0.05/0.17	
0.05/0.17	### Cost equations --> "Loop" of eval_ex_paper1_bb0_in/4 
0.05/0.17	* CEs [14] --> Loop 11 
0.05/0.17	* CEs [13] --> Loop 12 
0.05/0.17	* CEs [11] --> Loop 13 
0.05/0.17	* CEs [12] --> Loop 14 
0.05/0.17	
0.05/0.17	### Ranking functions of CR eval_ex_paper1_bb0_in(V_i,V_n,V_fwd,B) 
0.05/0.17	
0.05/0.17	#### Partial ranking functions of CR eval_ex_paper1_bb0_in(V_i,V_n,V_fwd,B) 
0.05/0.17	
0.05/0.17	
0.05/0.17	### Specialization of cost equations eval_ex_paper1_start/4 
0.05/0.17	* CE 1 is refined into CE [15,16,17,18] 
0.05/0.17	
0.05/0.17	
0.05/0.17	### Cost equations --> "Loop" of eval_ex_paper1_start/4 
0.05/0.17	* CEs [18] --> Loop 15 
0.05/0.17	* CEs [17] --> Loop 16 
0.05/0.17	* CEs [16] --> Loop 17 
0.05/0.17	* CEs [15] --> Loop 18 
0.05/0.17	
0.05/0.17	### Ranking functions of CR eval_ex_paper1_start(V_i,V_n,V_fwd,B) 
0.05/0.17	
0.05/0.17	#### Partial ranking functions of CR eval_ex_paper1_start(V_i,V_n,V_fwd,B) 
0.05/0.17	
0.05/0.17	
0.05/0.17	Computing Bounds
0.05/0.17	=====================================
0.05/0.17	
0.05/0.17	#### Cost of chains of eval_ex_paper1_bb1_in(V_n,V_fwd,V__0,B):
0.05/0.17	* Chain [[8],9]: 1*it(8)+0
0.05/0.17	  Such that:it(8) =< V_n-V__0
0.05/0.17	
0.05/0.17	  with precondition: [B=2,V_fwd>=1,V__0>=1,V_n>=V__0+1] 
0.05/0.17	
0.05/0.17	* Chain [[7],10]: 1*it(7)+0
0.05/0.17	  Such that:it(7) =< V__0
0.05/0.17	
0.05/0.17	  with precondition: [B=2,0>=V_fwd,V__0>=1,V_n>=V__0+1] 
0.05/0.17	
0.05/0.17	* Chain [10]: 0
0.05/0.17	  with precondition: [B=2,0>=V__0] 
0.05/0.17	
0.05/0.17	* Chain [9]: 0
0.05/0.17	  with precondition: [B=2,V__0>=V_n] 
0.05/0.17	
0.05/0.17	
0.05/0.17	#### Cost of chains of eval_ex_paper1_bb0_in(V_i,V_n,V_fwd,B):
0.05/0.17	* Chain [14]: 0
0.05/0.17	  with precondition: [0>=V_i] 
0.05/0.17	
0.05/0.17	* Chain [13]: 1*s(1)+0
0.05/0.17	  Such that:s(1) =< V_i
0.05/0.17	
0.05/0.17	  with precondition: [0>=V_fwd,V_i>=1,V_n>=V_i+1] 
0.05/0.17	
0.05/0.17	* Chain [12]: 1*s(2)+0
0.05/0.17	  Such that:s(2) =< -V_i+V_n
0.05/0.17	
0.05/0.17	  with precondition: [V_i>=1,V_fwd>=1,V_n>=V_i+1] 
0.05/0.17	
0.05/0.17	* Chain [11]: 0
0.05/0.17	  with precondition: [V_i>=V_n] 
0.05/0.17	
0.05/0.17	
0.05/0.17	#### Cost of chains of eval_ex_paper1_start(V_i,V_n,V_fwd,B):
0.05/0.17	* Chain [18]: 0
0.05/0.17	  with precondition: [0>=V_i] 
0.05/0.17	
0.05/0.17	* Chain [17]: 1*s(3)+0
0.05/0.17	  Such that:s(3) =< V_i
0.05/0.17	
0.05/0.17	  with precondition: [0>=V_fwd,V_i>=1,V_n>=V_i+1] 
0.05/0.17	
0.05/0.17	* Chain [16]: 1*s(4)+0
0.05/0.17	  Such that:s(4) =< -V_i+V_n
0.05/0.17	
0.05/0.17	  with precondition: [V_i>=1,V_fwd>=1,V_n>=V_i+1] 
0.05/0.17	
0.05/0.17	* Chain [15]: 0
0.05/0.17	  with precondition: [V_i>=V_n] 
0.05/0.17	
0.05/0.17	
0.05/0.17	Closed-form bounds of eval_ex_paper1_start(V_i,V_n,V_fwd,B): 
0.05/0.17	-------------------------------------
0.05/0.17	* Chain [18] with precondition: [0>=V_i] 
0.05/0.17	    - Upper bound: 0 
0.05/0.17	    - Complexity: constant 
0.05/0.17	* Chain [17] with precondition: [0>=V_fwd,V_i>=1,V_n>=V_i+1] 
0.05/0.17	    - Upper bound: V_i 
0.05/0.17	    - Complexity: n 
0.05/0.17	* Chain [16] with precondition: [V_i>=1,V_fwd>=1,V_n>=V_i+1] 
0.05/0.17	    - Upper bound: -V_i+V_n 
0.05/0.17	    - Complexity: n 
0.05/0.17	* Chain [15] with precondition: [V_i>=V_n] 
0.05/0.17	    - Upper bound: 0 
0.05/0.17	    - Complexity: constant 
0.05/0.17	
0.05/0.17	### Maximum cost of eval_ex_paper1_start(V_i,V_n,V_fwd,B): max([nat(V_i),nat(-V_i+V_n)]) 
0.05/0.17	Asymptotic class: n 
0.05/0.17	* Total analysis performed in 94 ms.
0.05/0.17	
0.05/0.27	EOF