0.05/0.25	WORST_CASE(?,O(n^1))  
0.05/0.25	
0.05/0.25	Preprocessing Cost Relations
0.05/0.25	=====================================
0.05/0.25	
0.05/0.25	#### Computed strongly connected components 
0.05/0.25	0. recursive  : [eval_speed_popl10_nested_single_2/6,eval_speed_popl10_nested_single_3/7,eval_speed_popl10_nested_single_bb2_in/5,eval_speed_popl10_nested_single_bb3_in/6]
0.05/0.25	1. recursive  : [eval_speed_popl10_nested_single_bb1_in/3,eval_speed_popl10_nested_single_bb2_in_loop_cont/4]
0.05/0.25	2. non_recursive  : [eval_speed_popl10_nested_single_stop/1]
0.05/0.25	3. non_recursive  : [eval_speed_popl10_nested_single_bb4_in/1]
0.05/0.25	4. non_recursive  : [eval_speed_popl10_nested_single_bb1_in_loop_cont/2]
0.05/0.25	5. non_recursive  : [eval_speed_popl10_nested_single_bb0_in/2]
0.05/0.25	6. non_recursive  : [eval_speed_popl10_nested_single_start/2]
0.05/0.25	
0.05/0.25	#### Obtained direct recursion through partial evaluation 
0.05/0.25	0. SCC is partially evaluated into eval_speed_popl10_nested_single_bb2_in/5
0.05/0.25	1. SCC is partially evaluated into eval_speed_popl10_nested_single_bb1_in/3
0.05/0.25	2. SCC is completely evaluated into other SCCs
0.05/0.25	3. SCC is completely evaluated into other SCCs
0.05/0.25	4. SCC is completely evaluated into other SCCs
0.05/0.25	5. SCC is partially evaluated into eval_speed_popl10_nested_single_bb0_in/2
0.05/0.25	6. SCC is partially evaluated into eval_speed_popl10_nested_single_start/2
0.05/0.25	
0.05/0.25	Control-Flow Refinement of Cost Relations
0.05/0.25	=====================================
0.05/0.25	
0.05/0.25	### Specialization of cost equations eval_speed_popl10_nested_single_bb2_in/5 
0.05/0.25	* CE 6 is refined into CE [8] 
0.05/0.25	* CE 7 is refined into CE [9] 
0.05/0.25	* CE 5 is refined into CE [10] 
0.05/0.25	
0.05/0.25	
0.05/0.25	### Cost equations --> "Loop" of eval_speed_popl10_nested_single_bb2_in/5 
0.05/0.25	* CEs [10] --> Loop 8 
0.05/0.25	* CEs [8] --> Loop 9 
0.05/0.25	* CEs [9] --> Loop 10 
0.05/0.25	
0.05/0.25	### Ranking functions of CR eval_speed_popl10_nested_single_bb2_in(V_n,V_x_0,V_x_0_sink,B,C) 
0.05/0.25	* RF of phase [8]: [V_n-V_x_0_sink-1]
0.05/0.25	
0.05/0.25	#### Partial ranking functions of CR eval_speed_popl10_nested_single_bb2_in(V_n,V_x_0,V_x_0_sink,B,C) 
0.05/0.25	* Partial RF of phase [8]:
0.05/0.25	  - RF of loop [8:1]:
0.05/0.25	    V_n-V_x_0_sink-1
0.05/0.25	
0.05/0.25	
0.05/0.25	### Specialization of cost equations eval_speed_popl10_nested_single_bb1_in/3 
0.05/0.25	* CE 4 is refined into CE [11] 
0.05/0.25	* CE 3 is refined into CE [12,13,14,15] 
0.05/0.25	
0.05/0.25	
0.05/0.25	### Cost equations --> "Loop" of eval_speed_popl10_nested_single_bb1_in/3 
0.05/0.25	* CEs [15] --> Loop 11 
0.05/0.25	* CEs [14] --> Loop 12 
0.05/0.25	* CEs [13] --> Loop 13 
0.05/0.25	* CEs [12] --> Loop 14 
0.05/0.25	* CEs [11] --> Loop 15 
0.05/0.25	
0.05/0.25	### Ranking functions of CR eval_speed_popl10_nested_single_bb1_in(V_n,V_x_0,B) 
0.05/0.25	* RF of phase [11,12]: [V_n-V_x_0-1]
0.05/0.25	
0.05/0.25	#### Partial ranking functions of CR eval_speed_popl10_nested_single_bb1_in(V_n,V_x_0,B) 
0.05/0.25	* Partial RF of phase [11,12]:
0.05/0.25	  - RF of loop [11:1]:
0.05/0.25	    V_n/2-V_x_0/2-1
0.05/0.25	  - RF of loop [12:1]:
0.05/0.25	    V_n-V_x_0-1
0.05/0.25	
0.05/0.25	
0.05/0.25	### Specialization of cost equations eval_speed_popl10_nested_single_bb0_in/2 
0.05/0.25	* CE 2 is refined into CE [16,17,18,19] 
0.05/0.25	
0.05/0.25	
0.05/0.25	### Cost equations --> "Loop" of eval_speed_popl10_nested_single_bb0_in/2 
0.05/0.25	* CEs [19] --> Loop 16 
0.05/0.25	* CEs [18] --> Loop 17 
0.05/0.25	* CEs [17] --> Loop 18 
0.05/0.25	* CEs [16] --> Loop 19 
0.05/0.25	
0.05/0.25	### Ranking functions of CR eval_speed_popl10_nested_single_bb0_in(V_n,B) 
0.05/0.25	
0.05/0.25	#### Partial ranking functions of CR eval_speed_popl10_nested_single_bb0_in(V_n,B) 
0.05/0.25	
0.05/0.25	
0.05/0.25	### Specialization of cost equations eval_speed_popl10_nested_single_start/2 
0.05/0.25	* CE 1 is refined into CE [20,21,22,23] 
0.05/0.25	
0.05/0.25	
0.05/0.25	### Cost equations --> "Loop" of eval_speed_popl10_nested_single_start/2 
0.05/0.25	* CEs [23] --> Loop 20 
0.05/0.25	* CEs [22] --> Loop 21 
0.05/0.25	* CEs [21] --> Loop 22 
0.05/0.25	* CEs [20] --> Loop 23 
0.05/0.25	
0.05/0.25	### Ranking functions of CR eval_speed_popl10_nested_single_start(V_n,B) 
0.05/0.25	
0.05/0.25	#### Partial ranking functions of CR eval_speed_popl10_nested_single_start(V_n,B) 
0.05/0.25	
0.05/0.25	
0.05/0.25	Computing Bounds
0.05/0.25	=====================================
0.05/0.25	
0.05/0.25	#### Cost of chains of eval_speed_popl10_nested_single_bb2_in(V_n,V_x_0,V_x_0_sink,B,C):
0.05/0.25	* Chain [[8],10]: 1*it(8)+0
0.05/0.25	  Such that:it(8) =< V_n-V_x_0_sink
0.05/0.25	
0.05/0.25	  with precondition: [B=2,V_n=C,V_x_0_sink>=V_x_0,V_n>=V_x_0_sink+2] 
0.05/0.25	
0.05/0.25	* Chain [[8],9]: 1*it(8)+0
0.05/0.25	  Such that:it(8) =< -V_x_0_sink+C
0.05/0.25	
0.05/0.25	  with precondition: [B=2,V_x_0_sink>=V_x_0,C>=V_x_0_sink+2,V_n>=C+1] 
0.05/0.25	
0.05/0.25	* Chain [10]: 0
0.05/0.25	  with precondition: [B=2,V_x_0_sink+1=V_n,V_x_0_sink+1=C,V_x_0_sink>=V_x_0] 
0.05/0.25	
0.05/0.25	* Chain [9]: 0
0.05/0.25	  with precondition: [B=2,V_x_0_sink+1=C,V_x_0_sink>=V_x_0,V_n>=V_x_0_sink+2] 
0.05/0.25	
0.05/0.25	
0.05/0.25	#### Cost of chains of eval_speed_popl10_nested_single_bb1_in(V_n,V_x_0,B):
0.05/0.25	* Chain [[11,12],14,15]: 1*it(11)+2*it(12)+1
0.05/0.25	  Such that:it(11) =< V_n/2-V_x_0/2
0.05/0.25	aux(3) =< V_n-V_x_0
0.05/0.25	it(11) =< aux(3)
0.05/0.25	it(12) =< aux(3)
0.05/0.25	
0.05/0.25	  with precondition: [B=3,V_x_0>=0,V_n>=V_x_0+2] 
0.05/0.25	
0.05/0.25	* Chain [[11,12],13,15]: 1*it(11)+3*it(12)+1
0.05/0.25	  Such that:it(11) =< V_n/2-V_x_0/2
0.05/0.25	aux(4) =< V_n-V_x_0
0.05/0.25	it(11) =< aux(4)
0.05/0.25	it(12) =< aux(4)
0.05/0.25	
0.05/0.25	  with precondition: [B=3,V_x_0>=0,V_n>=V_x_0+3] 
0.05/0.25	
0.05/0.25	* Chain [15]: 0
0.05/0.25	  with precondition: [B=3,V_x_0>=0,V_x_0>=V_n] 
0.05/0.25	
0.05/0.25	* Chain [14,15]: 1
0.05/0.25	  with precondition: [B=3,V_x_0+1=V_n,V_x_0>=0] 
0.05/0.25	
0.05/0.25	* Chain [13,15]: 1*s(4)+1
0.05/0.25	  Such that:s(4) =< V_n-V_x_0
0.05/0.25	
0.05/0.25	  with precondition: [B=3,V_x_0>=0,V_n>=V_x_0+2] 
0.05/0.25	
0.05/0.25	
0.05/0.25	#### Cost of chains of eval_speed_popl10_nested_single_bb0_in(V_n,B):
0.05/0.25	* Chain [19]: 1
0.05/0.25	  with precondition: [V_n=1] 
0.05/0.25	
0.05/0.25	* Chain [18]: 0
0.05/0.25	  with precondition: [0>=V_n] 
0.05/0.25	
0.05/0.25	* Chain [17]: 1*s(9)+3*s(11)+1
0.05/0.25	  Such that:s(10) =< V_n
0.05/0.25	s(9) =< V_n/2
0.05/0.25	s(11) =< s(10)
0.05/0.25	s(9) =< s(10)
0.05/0.25	
0.05/0.25	  with precondition: [V_n>=2] 
0.05/0.25	
0.05/0.25	* Chain [16]: 1*s(12)+3*s(14)+1
0.05/0.25	  Such that:s(13) =< V_n
0.05/0.25	s(12) =< V_n/2
0.05/0.25	s(12) =< s(13)
0.05/0.25	s(14) =< s(13)
0.05/0.25	
0.05/0.25	  with precondition: [V_n>=3] 
0.05/0.25	
0.05/0.25	
0.05/0.25	#### Cost of chains of eval_speed_popl10_nested_single_start(V_n,B):
0.05/0.25	* Chain [23]: 1
0.05/0.25	  with precondition: [V_n=1] 
0.05/0.25	
0.05/0.25	* Chain [22]: 0
0.05/0.25	  with precondition: [0>=V_n] 
0.05/0.25	
0.05/0.25	* Chain [21]: 1*s(16)+3*s(17)+1
0.05/0.25	  Such that:s(15) =< V_n
0.05/0.25	s(16) =< V_n/2
0.05/0.25	s(17) =< s(15)
0.05/0.25	s(16) =< s(15)
0.05/0.25	
0.05/0.25	  with precondition: [V_n>=2] 
0.05/0.25	
0.05/0.25	* Chain [20]: 1*s(19)+3*s(20)+1
0.05/0.25	  Such that:s(18) =< V_n
0.05/0.25	s(19) =< V_n/2
0.05/0.25	s(19) =< s(18)
0.05/0.25	s(20) =< s(18)
0.05/0.25	
0.05/0.25	  with precondition: [V_n>=3] 
0.05/0.25	
0.05/0.25	
0.05/0.25	Closed-form bounds of eval_speed_popl10_nested_single_start(V_n,B): 
0.05/0.25	-------------------------------------
0.05/0.25	* Chain [23] with precondition: [V_n=1] 
0.05/0.25	    - Upper bound: 1 
0.05/0.25	    - Complexity: constant 
0.05/0.25	* Chain [22] with precondition: [0>=V_n] 
0.05/0.25	    - Upper bound: 0 
0.05/0.25	    - Complexity: constant 
0.05/0.25	* Chain [21] with precondition: [V_n>=2] 
0.05/0.25	    - Upper bound: 7/2*V_n+1 
0.05/0.25	    - Complexity: n 
0.05/0.25	* Chain [20] with precondition: [V_n>=3] 
0.05/0.25	    - Upper bound: 7/2*V_n+1 
0.05/0.25	    - Complexity: n 
0.05/0.25	
0.05/0.25	### Maximum cost of eval_speed_popl10_nested_single_start(V_n,B): max([1,nat(V_n)*3+1+nat(V_n/2)]) 
0.05/0.25	Asymptotic class: n 
0.05/0.25	* Total analysis performed in 170 ms.
0.05/0.25	
0.05/0.35	EOF