0.05/0.27	WORST_CASE(?,O(n^1))  
0.05/0.27	
0.05/0.27	Preprocessing Cost Relations
0.05/0.27	=====================================
0.05/0.27	
0.05/0.27	#### Computed strongly connected components 
0.05/0.27	0. recursive  : [eval_Loopus2011_ex1_2/6,eval_Loopus2011_ex1_3/7,eval_Loopus2011_ex1_bb3_in/6,eval_Loopus2011_ex1_bb4_in/6,eval_Loopus2011_ex1_bb5_in/7]
0.05/0.27	1. recursive  : [eval_Loopus2011_ex1__critedge_in/5,eval_Loopus2011_ex1_bb1_in/3,eval_Loopus2011_ex1_bb2_in/3,eval_Loopus2011_ex1_bb3_in_loop_cont/6]
0.05/0.27	2. non_recursive  : [eval_Loopus2011_ex1_stop/1]
0.05/0.27	3. non_recursive  : [eval_Loopus2011_ex1_bb6_in/1]
0.05/0.28	4. non_recursive  : [eval_Loopus2011_ex1_bb1_in_loop_cont/2]
0.05/0.28	5. non_recursive  : [eval_Loopus2011_ex1_bb0_in/2]
0.05/0.28	6. non_recursive  : [eval_Loopus2011_ex1_start/2]
0.05/0.28	
0.05/0.28	#### Obtained direct recursion through partial evaluation 
0.05/0.28	0. SCC is partially evaluated into eval_Loopus2011_ex1_bb3_in/6
0.05/0.28	1. SCC is partially evaluated into eval_Loopus2011_ex1_bb1_in/3
0.05/0.28	2. SCC is completely evaluated into other SCCs
0.05/0.28	3. SCC is completely evaluated into other SCCs
0.05/0.28	4. SCC is completely evaluated into other SCCs
0.05/0.28	5. SCC is partially evaluated into eval_Loopus2011_ex1_bb0_in/2
0.05/0.28	6. SCC is partially evaluated into eval_Loopus2011_ex1_start/2
0.05/0.28	
0.05/0.28	Control-Flow Refinement of Cost Relations
0.05/0.28	=====================================
0.05/0.28	
0.05/0.28	### Specialization of cost equations eval_Loopus2011_ex1_bb3_in/6 
0.05/0.28	* CE 6 is refined into CE [9] 
0.05/0.28	* CE 8 is refined into CE [10] 
0.05/0.28	* CE 7 is refined into CE [11] 
0.05/0.28	
0.05/0.28	
0.05/0.28	### Cost equations --> "Loop" of eval_Loopus2011_ex1_bb3_in/6 
0.05/0.28	* CEs [11] --> Loop 8 
0.05/0.28	* CEs [9] --> Loop 9 
0.05/0.28	* CEs [10] --> Loop 10 
0.05/0.28	
0.05/0.28	### Ranking functions of CR eval_Loopus2011_ex1_bb3_in(V_n,V_j_0,V_i_1,B,C,D) 
0.05/0.28	* RF of phase [8]: [V_n-V_i_1]
0.05/0.28	
0.05/0.28	#### Partial ranking functions of CR eval_Loopus2011_ex1_bb3_in(V_n,V_j_0,V_i_1,B,C,D) 
0.05/0.28	* Partial RF of phase [8]:
0.05/0.28	  - RF of loop [8:1]:
0.05/0.28	    V_n-V_i_1
0.05/0.28	
0.05/0.28	
0.05/0.28	### Specialization of cost equations eval_Loopus2011_ex1_bb1_in/3 
0.05/0.28	* CE 5 is refined into CE [12] 
0.05/0.28	* CE 3 is refined into CE [13,14] 
0.05/0.28	* CE 4 is refined into CE [15,16] 
0.05/0.28	
0.05/0.28	
0.05/0.28	### Cost equations --> "Loop" of eval_Loopus2011_ex1_bb1_in/3 
0.05/0.28	* CEs [16] --> Loop 11 
0.05/0.28	* CEs [15] --> Loop 12 
0.05/0.28	* CEs [14] --> Loop 13 
0.05/0.28	* CEs [13] --> Loop 14 
0.05/0.28	* CEs [12] --> Loop 15 
0.05/0.28	
0.05/0.28	### Ranking functions of CR eval_Loopus2011_ex1_bb1_in(V_n,V_i_0,B) 
0.05/0.28	* RF of phase [11,13]: [V_n-V_i_0-1]
0.05/0.28	
0.05/0.28	#### Partial ranking functions of CR eval_Loopus2011_ex1_bb1_in(V_n,V_i_0,B) 
0.05/0.28	* Partial RF of phase [11,13]:
0.05/0.28	  - RF of loop [11:1]:
0.05/0.28	    V_n-V_i_0-2
0.05/0.28	  - RF of loop [13:1]:
0.05/0.28	    V_n-V_i_0-1
0.05/0.28	
0.05/0.28	
0.05/0.28	### Specialization of cost equations eval_Loopus2011_ex1_bb0_in/2 
0.05/0.28	* CE 2 is refined into CE [17,18,19,20] 
0.05/0.28	
0.05/0.28	
0.05/0.28	### Cost equations --> "Loop" of eval_Loopus2011_ex1_bb0_in/2 
0.05/0.28	* CEs [20] --> Loop 16 
0.05/0.28	* CEs [19] --> Loop 17 
0.05/0.28	* CEs [18] --> Loop 18 
0.05/0.28	* CEs [17] --> Loop 19 
0.05/0.28	
0.05/0.28	### Ranking functions of CR eval_Loopus2011_ex1_bb0_in(V_n,B) 
0.05/0.28	
0.05/0.28	#### Partial ranking functions of CR eval_Loopus2011_ex1_bb0_in(V_n,B) 
0.05/0.28	
0.05/0.28	
0.05/0.28	### Specialization of cost equations eval_Loopus2011_ex1_start/2 
0.05/0.28	* CE 1 is refined into CE [21,22,23,24] 
0.05/0.28	
0.05/0.28	
0.05/0.28	### Cost equations --> "Loop" of eval_Loopus2011_ex1_start/2 
0.05/0.28	* CEs [24] --> Loop 20 
0.05/0.28	* CEs [23] --> Loop 21 
0.05/0.28	* CEs [22] --> Loop 22 
0.05/0.28	* CEs [21] --> Loop 23 
0.05/0.28	
0.05/0.28	### Ranking functions of CR eval_Loopus2011_ex1_start(V_n,B) 
0.05/0.28	
0.05/0.28	#### Partial ranking functions of CR eval_Loopus2011_ex1_start(V_n,B) 
0.05/0.28	
0.05/0.28	
0.05/0.28	Computing Bounds
0.05/0.28	=====================================
0.05/0.28	
0.05/0.28	#### Cost of chains of eval_Loopus2011_ex1_bb3_in(V_n,V_j_0,V_i_1,B,C,D):
0.05/0.28	* Chain [[8],10]: 1*it(8)+0
0.05/0.28	  Such that:it(8) =< V_n-V_i_1
0.05/0.28	
0.05/0.28	  with precondition: [B=2,V_n=D,V_j_0+V_n=V_i_1+C,V_j_0>=0,V_n>=V_i_1+1] 
0.05/0.28	
0.05/0.28	* Chain [[8],9]: 1*it(8)+0
0.05/0.28	  Such that:it(8) =< -V_i_1+D
0.05/0.28	
0.05/0.28	  with precondition: [B=2,V_i_1+C=V_j_0+D,V_j_0>=0,C>=V_j_0+1,V_j_0+V_n>=V_i_1+C+1] 
0.05/0.28	
0.05/0.28	* Chain [10]: 0
0.05/0.28	  with precondition: [B=2,V_i_1=V_n,V_j_0=C,V_i_1=D,V_j_0>=0] 
0.05/0.28	
0.05/0.28	* Chain [9]: 0
0.05/0.28	  with precondition: [B=2,V_j_0=C,V_i_1=D,V_j_0>=0,V_n>=V_i_1+1] 
0.05/0.28	
0.05/0.28	
0.05/0.28	#### Cost of chains of eval_Loopus2011_ex1_bb1_in(V_n,V_i_0,B):
0.05/0.28	* Chain [[11,13],14,15]: 3*it(11)+1
0.05/0.28	  Such that:aux(3) =< V_n-V_i_0
0.05/0.28	it(11) =< aux(3)
0.05/0.28	
0.05/0.28	  with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+2] 
0.05/0.28	
0.05/0.28	* Chain [[11,13],12,14,15]: 4*it(11)+2
0.05/0.28	  Such that:aux(4) =< V_n-V_i_0
0.05/0.28	it(11) =< aux(4)
0.05/0.28	
0.05/0.28	  with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+3] 
0.05/0.28	
0.05/0.28	* Chain [15]: 0
0.05/0.28	  with precondition: [B=3,V_i_0>=0,V_i_0>=V_n] 
0.05/0.28	
0.05/0.28	* Chain [14,15]: 1
0.05/0.28	  with precondition: [B=3,V_i_0+1=V_n,V_i_0>=0] 
0.05/0.28	
0.05/0.28	* Chain [12,14,15]: 1*s(4)+2
0.05/0.28	  Such that:s(4) =< V_n-V_i_0
0.05/0.28	
0.05/0.28	  with precondition: [B=3,V_i_0>=0,V_n>=V_i_0+2] 
0.05/0.28	
0.05/0.28	
0.05/0.28	#### Cost of chains of eval_Loopus2011_ex1_bb0_in(V_n,B):
0.05/0.28	* Chain [19]: 1
0.05/0.28	  with precondition: [V_n=1] 
0.05/0.28	
0.05/0.28	* Chain [18]: 0
0.05/0.28	  with precondition: [0>=V_n] 
0.05/0.28	
0.05/0.28	* Chain [17]: 4*s(9)+2
0.05/0.28	  Such that:s(8) =< V_n
0.05/0.28	s(9) =< s(8)
0.05/0.28	
0.05/0.28	  with precondition: [V_n>=2] 
0.05/0.28	
0.05/0.28	* Chain [16]: 4*s(11)+2
0.05/0.28	  Such that:s(10) =< V_n
0.05/0.28	s(11) =< s(10)
0.05/0.28	
0.05/0.28	  with precondition: [V_n>=3] 
0.05/0.28	
0.05/0.28	
0.05/0.28	#### Cost of chains of eval_Loopus2011_ex1_start(V_n,B):
0.05/0.28	* Chain [23]: 1
0.05/0.28	  with precondition: [V_n=1] 
0.05/0.28	
0.05/0.28	* Chain [22]: 0
0.05/0.28	  with precondition: [0>=V_n] 
0.05/0.28	
0.05/0.28	* Chain [21]: 4*s(13)+2
0.05/0.28	  Such that:s(12) =< V_n
0.05/0.28	s(13) =< s(12)
0.05/0.28	
0.05/0.28	  with precondition: [V_n>=2] 
0.05/0.28	
0.05/0.28	* Chain [20]: 4*s(15)+2
0.05/0.28	  Such that:s(14) =< V_n
0.05/0.28	s(15) =< s(14)
0.05/0.28	
0.05/0.28	  with precondition: [V_n>=3] 
0.05/0.28	
0.05/0.28	
0.05/0.28	Closed-form bounds of eval_Loopus2011_ex1_start(V_n,B): 
0.05/0.28	-------------------------------------
0.05/0.28	* Chain [23] with precondition: [V_n=1] 
0.05/0.28	    - Upper bound: 1 
0.05/0.28	    - Complexity: constant 
0.05/0.28	* Chain [22] with precondition: [0>=V_n] 
0.05/0.28	    - Upper bound: 0 
0.05/0.28	    - Complexity: constant 
0.05/0.28	* Chain [21] with precondition: [V_n>=2] 
0.05/0.28	    - Upper bound: 4*V_n+2 
0.05/0.28	    - Complexity: n 
0.05/0.28	* Chain [20] with precondition: [V_n>=3] 
0.05/0.28	    - Upper bound: 4*V_n+2 
0.05/0.28	    - Complexity: n 
0.05/0.28	
0.05/0.28	### Maximum cost of eval_Loopus2011_ex1_start(V_n,B): max([1,nat(V_n)*4+2]) 
0.05/0.28	Asymptotic class: n 
0.05/0.28	* Total analysis performed in 193 ms.
0.05/0.28	
0.05/0.38	EOF