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_speedpldi4_bb1_in/3,eval_speedpldi4_bb2_in/3]
0.05/0.16	1. non_recursive  : [eval_speedpldi4_stop/1]
0.05/0.16	2. non_recursive  : [eval_speedpldi4_bb3_in/1]
0.05/0.16	3. non_recursive  : [eval_speedpldi4_bb1_in_loop_cont/2]
0.05/0.16	4. non_recursive  : [eval_speedpldi4_bb0_in/3]
0.05/0.16	5. non_recursive  : [eval_speedpldi4_start/3]
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_speedpldi4_bb1_in/3
0.05/0.16	1. SCC is completely evaluated into other SCCs
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 partially evaluated into eval_speedpldi4_bb0_in/3
0.05/0.16	5. SCC is partially evaluated into eval_speedpldi4_start/3
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_speedpldi4_bb1_in/3 
0.05/0.16	* CE 7 is refined into CE [8] 
0.05/0.16	* CE 5 is refined into CE [9] 
0.05/0.16	* CE 6 is refined into CE [10] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_speedpldi4_bb1_in/3 
0.05/0.16	* CEs [9] --> Loop 8 
0.05/0.16	* CEs [10] --> Loop 9 
0.05/0.16	* CEs [8] --> Loop 10 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_speedpldi4_bb1_in(V_m,V_i_0,B) 
0.05/0.16	* RF of phase [8]: [V_i_0,-V_m+V_i_0+1]
0.05/0.16	* RF of phase [9]: [V_i_0]
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_speedpldi4_bb1_in(V_m,V_i_0,B) 
0.05/0.16	* Partial RF of phase [8]:
0.05/0.16	  - RF of loop [8:1]:
0.05/0.16	    V_i_0
0.05/0.16	    -V_m+V_i_0+1
0.05/0.16	* Partial RF of phase [9]:
0.05/0.16	  - RF of loop [9:1]:
0.05/0.16	    V_i_0
0.05/0.16	
0.05/0.16	
0.05/0.16	### Specialization of cost equations eval_speedpldi4_bb0_in/3 
0.05/0.16	* CE 3 is refined into CE [11] 
0.05/0.16	* CE 4 is refined into CE [12,13] 
0.05/0.16	* CE 2 is refined into CE [14] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_speedpldi4_bb0_in/3 
0.05/0.16	* CEs [11] --> Loop 11 
0.05/0.16	* CEs [13] --> Loop 12 
0.05/0.16	* CEs [12] --> Loop 13 
0.05/0.16	* CEs [14] --> Loop 14 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_speedpldi4_bb0_in(V_m,V_n,B) 
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_speedpldi4_bb0_in(V_m,V_n,B) 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Specialization of cost equations eval_speedpldi4_start/3 
0.05/0.16	* CE 1 is refined into CE [15,16,17,18] 
0.05/0.16	
0.05/0.16	
0.05/0.16	### Cost equations --> "Loop" of eval_speedpldi4_start/3 
0.05/0.16	* CEs [18] --> Loop 15 
0.05/0.16	* CEs [17] --> Loop 16 
0.05/0.16	* CEs [16] --> Loop 17 
0.05/0.16	* CEs [15] --> Loop 18 
0.05/0.16	
0.05/0.16	### Ranking functions of CR eval_speedpldi4_start(V_m,V_n,B) 
0.05/0.16	
0.05/0.16	#### Partial ranking functions of CR eval_speedpldi4_start(V_m,V_n,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_speedpldi4_bb1_in(V_m,V_i_0,B):
0.05/0.16	* Chain [[8],[9],10]: 1*it(8)+1*it(9)+0
0.05/0.16	  Such that:it(9) =< -V_m+V_i_0
0.05/0.16	it(8) =< -V_m+V_i_0+1
0.05/0.16	it(9) =< V_m
0.05/0.16	
0.05/0.16	  with precondition: [B=2,V_m>=2,V_i_0>=V_m+1] 
0.05/0.16	
0.05/0.16	* Chain [[8],10]: 1*it(8)+0
0.05/0.16	  Such that:it(8) =< -V_m+V_i_0+1
0.05/0.16	
0.05/0.16	  with precondition: [B=2,V_m>=1,V_i_0>=V_m] 
0.05/0.16	
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_speedpldi4_bb0_in(V_m,V_n,B):
0.05/0.16	* Chain [14]: 0
0.05/0.16	  with precondition: [0>=V_m] 
0.05/0.16	
0.05/0.16	* Chain [13]: 1*s(1)+0
0.05/0.16	  Such that:s(1) =< -V_m+V_n+1
0.05/0.16	
0.05/0.16	  with precondition: [V_m>=1,V_n>=V_m+1] 
0.05/0.16	
0.05/0.16	* Chain [12]: 1*s(2)+1*s(3)+0
0.05/0.16	  Such that:s(2) =< -V_m+V_n
0.05/0.16	s(3) =< -V_m+V_n+1
0.05/0.16	s(2) =< V_m
0.05/0.16	
0.05/0.16	  with precondition: [V_m>=2,V_n>=V_m+1] 
0.05/0.16	
0.05/0.16	* Chain [11]: 0
0.05/0.16	  with precondition: [V_m>=V_n] 
0.05/0.16	
0.05/0.16	
0.05/0.16	#### Cost of chains of eval_speedpldi4_start(V_m,V_n,B):
0.05/0.16	* Chain [18]: 0
0.05/0.16	  with precondition: [0>=V_m] 
0.05/0.16	
0.05/0.16	* Chain [17]: 1*s(4)+0
0.05/0.16	  Such that:s(4) =< -V_m+V_n+1
0.05/0.16	
0.05/0.16	  with precondition: [V_m>=1,V_n>=V_m+1] 
0.05/0.16	
0.05/0.16	* Chain [16]: 1*s(5)+1*s(6)+0
0.05/0.16	  Such that:s(5) =< -V_m+V_n
0.05/0.16	s(6) =< -V_m+V_n+1
0.05/0.16	s(5) =< V_m
0.05/0.16	
0.05/0.16	  with precondition: [V_m>=2,V_n>=V_m+1] 
0.05/0.16	
0.05/0.16	* Chain [15]: 0
0.05/0.16	  with precondition: [V_m>=V_n] 
0.05/0.16	
0.05/0.16	
0.05/0.16	Closed-form bounds of eval_speedpldi4_start(V_m,V_n,B): 
0.05/0.16	-------------------------------------
0.05/0.16	* Chain [18] with precondition: [0>=V_m] 
0.05/0.16	    - Upper bound: 0 
0.05/0.16	    - Complexity: constant 
0.05/0.16	* Chain [17] with precondition: [V_m>=1,V_n>=V_m+1] 
0.05/0.16	    - Upper bound: -V_m+V_n+1 
0.05/0.16	    - Complexity: n 
0.05/0.16	* Chain [16] with precondition: [V_m>=2,V_n>=V_m+1] 
0.05/0.16	    - Upper bound: -2*V_m+2*V_n+1 
0.05/0.16	    - Complexity: n 
0.05/0.16	* Chain [15] with precondition: [V_m>=V_n] 
0.05/0.16	    - Upper bound: 0 
0.05/0.16	    - Complexity: constant 
0.05/0.16	
0.05/0.16	### Maximum cost of eval_speedpldi4_start(V_m,V_n,B): nat(-V_m+V_n+1)+nat(-V_m+V_n) 
0.05/0.16	Asymptotic class: n 
0.05/0.16	* Total analysis performed in 94 ms.
0.05/0.16	
0.05/0.27	EOF