0.05/0.17	WORST_CASE(?,O(n^2))  
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_jama_ex5_bb2_in/4,eval_jama_ex5_bb3_in/4]
0.05/0.17	1. recursive  : [eval_jama_ex5_bb1_in/3,eval_jama_ex5_bb2_in_loop_cont/5,eval_jama_ex5_bb4_in/4]
0.05/0.17	2. non_recursive  : [eval_jama_ex5_stop/1]
0.05/0.17	3. non_recursive  : [eval_jama_ex5_bb5_in/1]
0.05/0.17	4. non_recursive  : [eval_jama_ex5_bb1_in_loop_cont/2]
0.05/0.17	5. non_recursive  : [eval_jama_ex5_bb0_in/2]
0.05/0.17	6. non_recursive  : [eval_jama_ex5_start/2]
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_jama_ex5_bb2_in/4
0.05/0.17	1. SCC is partially evaluated into eval_jama_ex5_bb1_in/3
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 completely evaluated into other SCCs
0.05/0.17	5. SCC is partially evaluated into eval_jama_ex5_bb0_in/2
0.05/0.17	6. SCC is partially evaluated into eval_jama_ex5_start/2
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_jama_ex5_bb2_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	
0.05/0.17	
0.05/0.17	### Cost equations --> "Loop" of eval_jama_ex5_bb2_in/4 
0.05/0.17	* CEs [8] --> Loop 7 
0.05/0.17	* CEs [7] --> Loop 8 
0.05/0.17	
0.05/0.17	### Ranking functions of CR eval_jama_ex5_bb2_in(V_n,V_j_0,B,C) 
0.05/0.17	* RF of phase [7]: [V_n-V_j_0+1]
0.05/0.17	
0.05/0.17	#### Partial ranking functions of CR eval_jama_ex5_bb2_in(V_n,V_j_0,B,C) 
0.05/0.17	* Partial RF of phase [7]:
0.05/0.17	  - RF of loop [7:1]:
0.05/0.17	    V_n-V_j_0+1
0.05/0.17	
0.05/0.17	
0.05/0.17	### Specialization of cost equations eval_jama_ex5_bb1_in/3 
0.05/0.17	* CE 4 is refined into CE [9] 
0.05/0.17	* CE 3 is refined into CE [10] 
0.05/0.17	
0.05/0.17	
0.05/0.17	### Cost equations --> "Loop" of eval_jama_ex5_bb1_in/3 
0.05/0.17	* CEs [10] --> Loop 9 
0.05/0.17	* CEs [9] --> Loop 10 
0.05/0.17	
0.05/0.17	### Ranking functions of CR eval_jama_ex5_bb1_in(V_n,V_i_0,B) 
0.05/0.17	* RF of phase [9]: [V_n-V_i_0+1]
0.05/0.17	
0.05/0.17	#### Partial ranking functions of CR eval_jama_ex5_bb1_in(V_n,V_i_0,B) 
0.05/0.17	* Partial RF of phase [9]:
0.05/0.17	  - RF of loop [9:1]:
0.05/0.17	    V_n-V_i_0+1
0.05/0.17	
0.05/0.17	
0.05/0.17	### Specialization of cost equations eval_jama_ex5_bb0_in/2 
0.05/0.17	* CE 2 is refined into CE [11,12] 
0.05/0.17	
0.05/0.17	
0.05/0.17	### Cost equations --> "Loop" of eval_jama_ex5_bb0_in/2 
0.05/0.17	* CEs [12] --> Loop 11 
0.05/0.17	* CEs [11] --> Loop 12 
0.05/0.17	
0.05/0.17	### Ranking functions of CR eval_jama_ex5_bb0_in(V_n,B) 
0.05/0.17	
0.05/0.17	#### Partial ranking functions of CR eval_jama_ex5_bb0_in(V_n,B) 
0.05/0.17	
0.05/0.17	
0.05/0.17	### Specialization of cost equations eval_jama_ex5_start/2 
0.05/0.17	* CE 1 is refined into CE [13,14] 
0.05/0.17	
0.05/0.17	
0.05/0.17	### Cost equations --> "Loop" of eval_jama_ex5_start/2 
0.05/0.17	* CEs [14] --> Loop 13 
0.05/0.17	* CEs [13] --> Loop 14 
0.05/0.17	
0.05/0.17	### Ranking functions of CR eval_jama_ex5_start(V_n,B) 
0.05/0.17	
0.05/0.17	#### Partial ranking functions of CR eval_jama_ex5_start(V_n,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_jama_ex5_bb2_in(V_n,V_j_0,B,C):
0.05/0.17	* Chain [[7],8]: 1*it(7)+0
0.05/0.17	  Such that:it(7) =< V_n-V_j_0+1
0.05/0.17	
0.05/0.17	  with precondition: [B=2,V_j_0>=0,C>=V_n+1,C>=V_j_0+2,V_n+2>=C] 
0.05/0.17	
0.05/0.17	
0.05/0.17	#### Cost of chains of eval_jama_ex5_bb1_in(V_n,V_i_0,B):
0.05/0.17	* Chain [[9],10]: 1*it(9)+1*s(3)+0
0.05/0.17	  Such that:aux(1) =< V_n+1
0.05/0.17	it(9) =< V_n-V_i_0+1
0.05/0.17	s(3) =< it(9)*aux(1)
0.05/0.17	
0.05/0.17	  with precondition: [B=3,V_i_0>=0,V_n>=V_i_0] 
0.05/0.17	
0.05/0.17	* Chain [10]: 0
0.05/0.17	  with precondition: [B=3,V_i_0>=0,V_i_0>=V_n+1] 
0.05/0.17	
0.05/0.17	
0.05/0.17	#### Cost of chains of eval_jama_ex5_bb0_in(V_n,B):
0.05/0.17	* Chain [12]: 0
0.05/0.17	  with precondition: [0>=V_n+1] 
0.05/0.17	
0.05/0.17	* Chain [11]: 1*s(5)+1*s(6)+0
0.05/0.17	  Such that:aux(2) =< V_n+1
0.05/0.17	s(5) =< aux(2)
0.05/0.17	s(6) =< s(5)*aux(2)
0.05/0.17	
0.05/0.17	  with precondition: [V_n>=0] 
0.05/0.17	
0.05/0.17	
0.05/0.17	#### Cost of chains of eval_jama_ex5_start(V_n,B):
0.05/0.17	* Chain [14]: 0
0.05/0.17	  with precondition: [0>=V_n+1] 
0.05/0.17	
0.05/0.17	* Chain [13]: 1*s(8)+1*s(9)+0
0.05/0.17	  Such that:s(7) =< V_n+1
0.05/0.17	s(8) =< s(7)
0.05/0.17	s(9) =< s(8)*s(7)
0.05/0.17	
0.05/0.17	  with precondition: [V_n>=0] 
0.05/0.17	
0.05/0.17	
0.05/0.17	Closed-form bounds of eval_jama_ex5_start(V_n,B): 
0.05/0.17	-------------------------------------
0.05/0.17	* Chain [14] with precondition: [0>=V_n+1] 
0.05/0.17	    - Upper bound: 0 
0.05/0.17	    - Complexity: constant 
0.05/0.17	* Chain [13] with precondition: [V_n>=0] 
0.05/0.17	    - Upper bound: V_n+1+(V_n+1)*(V_n+1) 
0.05/0.17	    - Complexity: n^2 
0.05/0.17	
0.05/0.17	### Maximum cost of eval_jama_ex5_start(V_n,B): nat(V_n+1)*nat(V_n+1)+nat(V_n+1) 
0.05/0.17	Asymptotic class: n^2 
0.05/0.17	* Total analysis performed in 93 ms.
0.05/0.17	
0.05/0.27	EOF