0.71/0.76	WORST_CASE(?,O(n^2))  
0.71/0.76	
0.71/0.76	Preprocessing Cost Relations
0.71/0.76	=====================================
0.71/0.76	
0.71/0.76	#### Computed strongly connected components 
0.71/0.76	0. recursive  : [eval_perfectg_bb3_in/4,eval_perfectg_bb5_in/4]
0.71/0.76	1. recursive  : [eval_perfectg_10/14,eval_perfectg_9/14,eval_perfectg_bb1_in/14,eval_perfectg_bb3_in_loop_cont/15,eval_perfectg_bb4_in/14]
0.71/0.76	2. non_recursive  : [eval_perfectg_stop/9]
0.71/0.76	3. non_recursive  : [eval_perfectg_bb2_in/9]
0.71/0.76	4. non_recursive  : [exit_location/1]
0.71/0.76	5. non_recursive  : [eval_perfectg_bb1_in_loop_cont/10]
0.71/0.76	6. non_recursive  : [eval_perfectg_3/9]
0.71/0.76	7. non_recursive  : [eval_perfectg_2/9]
0.71/0.76	8. non_recursive  : [eval_perfectg_1/9]
0.71/0.76	9. non_recursive  : [eval_perfectg_bb0_in/9]
0.71/0.76	10. non_recursive  : [eval_perfectg_start/9]
0.71/0.76	
0.71/0.76	#### Obtained direct recursion through partial evaluation 
0.71/0.76	0. SCC is partially evaluated into eval_perfectg_bb3_in/4
0.71/0.76	1. SCC is partially evaluated into eval_perfectg_bb1_in/14
0.71/0.76	2. SCC is completely evaluated into other SCCs
0.71/0.76	3. SCC is partially evaluated into eval_perfectg_bb2_in/9
0.71/0.76	4. SCC is completely evaluated into other SCCs
0.71/0.76	5. SCC is partially evaluated into eval_perfectg_bb1_in_loop_cont/10
0.71/0.76	6. SCC is partially evaluated into eval_perfectg_3/9
0.71/0.76	7. SCC is completely evaluated into other SCCs
0.71/0.76	8. SCC is completely evaluated into other SCCs
0.71/0.76	9. SCC is completely evaluated into other SCCs
0.71/0.76	10. SCC is partially evaluated into eval_perfectg_start/9
0.71/0.76	
0.71/0.76	Control-Flow Refinement of Cost Relations
0.71/0.76	=====================================
0.71/0.76	
0.71/0.76	### Specialization of cost equations eval_perfectg_bb3_in/4 
0.71/0.76	* CE 21 is refined into CE [22] 
0.71/0.76	* CE 20 is refined into CE [23] 
0.71/0.76	* CE 19 is refined into CE [24] 
0.71/0.76	
0.71/0.76	
0.71/0.76	### Cost equations --> "Loop" of eval_perfectg_bb3_in/4 
0.71/0.76	* CEs [24] --> Loop 22 
0.71/0.76	* CEs [22] --> Loop 23 
0.71/0.76	* CEs [23] --> Loop 24 
0.71/0.76	
0.71/0.76	### Ranking functions of CR eval_perfectg_bb3_in(V_2,V_y2_1,B,C) 
0.71/0.76	* RF of phase [22]: [-V_2+V_y2_1+1,V_y2_1]
0.71/0.76	
0.71/0.76	#### Partial ranking functions of CR eval_perfectg_bb3_in(V_2,V_y2_1,B,C) 
0.71/0.76	* Partial RF of phase [22]:
0.71/0.76	  - RF of loop [22:1]:
0.71/0.76	    -V_2+V_y2_1+1
0.71/0.76	    V_y2_1
0.71/0.76	
0.71/0.76	
0.71/0.76	### Specialization of cost equations eval_perfectg_bb1_in/14 
0.71/0.76	* CE 13 is refined into CE [25,26] 
0.71/0.76	* CE 14 is discarded (unfeasible) 
0.71/0.76	* CE 16 is refined into CE [27] 
0.71/0.76	* CE 15 is refined into CE [28] 
0.71/0.76	* CE 9 is refined into CE [29] 
0.71/0.76	* CE 11 is discarded (unfeasible) 
0.71/0.76	* CE 10 is discarded (unfeasible) 
0.71/0.76	* CE 12 is discarded (unfeasible) 
0.71/0.76	* CE 7 is refined into CE [30] 
0.71/0.76	* CE 8 is discarded (unfeasible) 
0.71/0.76	
0.71/0.76	
0.71/0.76	### Cost equations --> "Loop" of eval_perfectg_bb1_in/14 
0.71/0.76	* CEs [29] --> Loop 25 
0.71/0.76	* CEs [30] --> Loop 26 
0.71/0.76	* CEs [25,26] --> Loop 27 
0.71/0.76	* CEs [27] --> Loop 28 
0.71/0.76	* CEs [28] --> Loop 29 
0.71/0.76	
0.71/0.76	### Ranking functions of CR eval_perfectg_bb1_in(V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B,C,D,E,F,G,H) 
0.71/0.76	* RF of phase [25,26]: [V_y1_0-1]
0.71/0.76	
0.71/0.76	#### Partial ranking functions of CR eval_perfectg_bb1_in(V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B,C,D,E,F,G,H) 
0.71/0.76	* Partial RF of phase [25,26]:
0.71/0.76	  - RF of loop [25:1]:
0.71/0.76	    V_y1_0-2
0.71/0.76	  - RF of loop [26:1]:
0.71/0.76	    V_y1_0-1
0.71/0.76	
0.71/0.76	
0.71/0.76	### Specialization of cost equations eval_perfectg_bb2_in/9 
0.71/0.76	* CE 5 is refined into CE [31] 
0.71/0.76	* CE 4 is refined into CE [32] 
0.71/0.76	* CE 6 is refined into CE [33] 
0.71/0.76	
0.71/0.76	
0.71/0.76	### Cost equations --> "Loop" of eval_perfectg_bb2_in/9 
0.71/0.76	* CEs [31] --> Loop 30 
0.71/0.76	* CEs [32] --> Loop 31 
0.71/0.76	* CEs [33] --> Loop 32 
0.71/0.76	
0.71/0.76	### Ranking functions of CR eval_perfectg_bb2_in(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B) 
0.71/0.76	
0.71/0.76	#### Partial ranking functions of CR eval_perfectg_bb2_in(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B) 
0.71/0.76	
0.71/0.76	
0.71/0.76	### Specialization of cost equations eval_perfectg_bb1_in_loop_cont/10 
0.71/0.76	* CE 17 is refined into CE [34,35,36] 
0.71/0.76	* CE 18 is refined into CE [37] 
0.71/0.76	
0.71/0.76	
0.71/0.76	### Cost equations --> "Loop" of eval_perfectg_bb1_in_loop_cont/10 
0.71/0.76	* CEs [36] --> Loop 33 
0.71/0.76	* CEs [35] --> Loop 34 
0.71/0.76	* CEs [34] --> Loop 35 
0.71/0.76	* CEs [37] --> Loop 36 
0.71/0.76	
0.71/0.76	### Ranking functions of CR eval_perfectg_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 
0.71/0.76	
0.71/0.76	#### Partial ranking functions of CR eval_perfectg_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J) 
0.71/0.76	
0.71/0.76	
0.71/0.76	### Specialization of cost equations eval_perfectg_3/9 
0.71/0.76	* CE 3 is refined into CE [38,39,40,41,42,43] 
0.71/0.76	* CE 2 is refined into CE [44,45,46] 
0.71/0.76	
0.71/0.76	
0.71/0.76	### Cost equations --> "Loop" of eval_perfectg_3/9 
0.71/0.76	* CEs [40] --> Loop 37 
0.71/0.76	* CEs [38,39,41,42,43] --> Loop 38 
0.71/0.76	* CEs [46] --> Loop 39 
0.71/0.76	* CEs [45] --> Loop 40 
0.71/0.76	* CEs [44] --> Loop 41 
0.71/0.76	
0.71/0.76	### Ranking functions of CR eval_perfectg_3(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B) 
0.71/0.76	
0.71/0.76	#### Partial ranking functions of CR eval_perfectg_3(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B) 
0.71/0.76	
0.71/0.76	
0.71/0.76	### Specialization of cost equations eval_perfectg_start/9 
0.71/0.76	* CE 1 is refined into CE [47,48,49,50,51] 
0.71/0.76	
0.71/0.76	
0.71/0.76	### Cost equations --> "Loop" of eval_perfectg_start/9 
0.71/0.76	* CEs [51] --> Loop 42 
0.71/0.76	* CEs [50] --> Loop 43 
0.71/0.76	* CEs [47,48,49] --> Loop 44 
0.71/0.76	
0.71/0.76	### Ranking functions of CR eval_perfectg_start(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B) 
0.71/0.76	
0.71/0.76	#### Partial ranking functions of CR eval_perfectg_start(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B) 
0.71/0.76	
0.71/0.76	
0.71/0.76	Computing Bounds
0.71/0.76	=====================================
0.71/0.76	
0.71/0.76	#### Cost of chains of eval_perfectg_bb3_in(V_2,V_y2_1,B,C):
0.71/0.76	* Chain [[22],24]: 1*it(22)+0
0.71/0.76	  Such that:it(22) =< -V_2+V_y2_1+1
0.71/0.76	
0.71/0.76	  with precondition: [B=2,C>=0,V_2>=C+1,V_y2_1>=V_2+C] 
0.71/0.76	
0.71/0.76	* Chain [[22],23]: 1*it(22)+0
0.71/0.76	  Such that:it(22) =< -V_2+V_y2_1+1
0.71/0.76	
0.71/0.76	  with precondition: [B=3,V_2>=1,V_y2_1>=V_2] 
0.71/0.76	
0.71/0.76	* Chain [23]: 0
0.71/0.76	  with precondition: [B=3,V_2>=1] 
0.71/0.76	
0.71/0.76	
0.71/0.76	#### Cost of chains of eval_perfectg_bb1_in(V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B,C,D,E,F,G,H):
0.71/0.76	* Chain [[25,26],29]: 2*it(25)+1*s(5)+1*s(6)+0
0.71/0.76	  Such that:aux(1) =< V_x
0.71/0.76	aux(5) =< V_y1_0
0.71/0.76	it(25) =< aux(5)
0.71/0.76	aux(2) =< aux(1)
0.71/0.76	s(5) =< it(25)*aux(1)
0.71/0.76	s(6) =< it(25)*aux(2)
0.71/0.76	
0.71/0.76	  with precondition: [B=4,C=1,E=1,F=0,D=G,D=H,V_y1_0>=2,V_x>=V_y1_0,V_x>=V_y3_0,V_y3_0>=D+1] 
0.71/0.76	
0.71/0.76	* Chain [[25,26],28]: 2*it(25)+1*s(5)+1*s(6)+0
0.71/0.76	  Such that:aux(1) =< V_x
0.71/0.76	aux(6) =< V_y1_0
0.71/0.76	it(25) =< aux(6)
0.71/0.76	aux(2) =< aux(1)
0.71/0.76	s(5) =< it(25)*aux(1)
0.71/0.76	s(6) =< it(25)*aux(2)
0.71/0.76	
0.71/0.76	  with precondition: [B=3,V_y1_0>=2,V_x>=V_y1_0,V_x>=V_y3_0] 
0.71/0.76	
0.71/0.76	* Chain [[25,26],27]: 2*it(25)+1*s(5)+1*s(6)+1*s(7)+0
0.71/0.76	  Such that:aux(7) =< V_x
0.71/0.76	aux(8) =< V_y1_0
0.71/0.76	s(7) =< aux(7)
0.71/0.76	it(25) =< aux(8)
0.71/0.76	aux(2) =< aux(7)
0.71/0.76	s(5) =< it(25)*aux(7)
0.71/0.76	s(6) =< it(25)*aux(2)
0.71/0.76	
0.71/0.76	  with precondition: [B=3,V_y1_0>=3,V_x>=V_y1_0,V_x>=V_y3_0] 
0.71/0.76	
0.71/0.76	* Chain [28]: 0
0.71/0.76	  with precondition: [B=3,V_x>=2,V_x>=V_y1_0,V_x>=V_y3_0,V_x+V_y1_0>=V_y3_0+2] 
0.71/0.76	
0.71/0.76	* Chain [27]: 1*s(7)+0
0.71/0.76	  Such that:s(7) =< V_x-V_y1_0+2
0.71/0.76	
0.71/0.76	  with precondition: [B=3,V_y1_0>=2,V_x>=V_y1_0,V_x>=V_y3_0] 
0.71/0.76	
0.71/0.76	
0.71/0.76	#### Cost of chains of eval_perfectg_bb2_in(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B):
0.71/0.76	* Chain [32]: 0
0.71/0.76	  with precondition: [V_y3_2=0] 
0.71/0.76	
0.71/0.76	* Chain [31]: 0
0.71/0.76	  with precondition: [0>=V_y3_2+1] 
0.71/0.76	
0.71/0.76	* Chain [30]: 0
0.71/0.76	  with precondition: [V_y3_2>=1] 
0.71/0.76	
0.71/0.76	
0.71/0.76	#### Cost of chains of eval_perfectg_bb1_in_loop_cont(A,B,C,D,E,F,G,H,I,J):
0.71/0.76	* Chain [36]: 0
0.71/0.76	  with precondition: [A=3,E>=2] 
0.71/0.76	
0.71/0.76	* Chain [35]: 0
0.71/0.76	  with precondition: [A=4,I=0,E>=2] 
0.71/0.76	
0.71/0.76	* Chain [34]: 0
0.71/0.76	  with precondition: [A=4,0>=I+1,E>=2] 
0.71/0.76	
0.71/0.76	* Chain [33]: 0
0.71/0.76	  with precondition: [A=4,E>=2,I>=1] 
0.71/0.76	
0.71/0.76	
0.71/0.76	#### Cost of chains of eval_perfectg_3(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B):
0.71/0.76	* Chain [41]: 0
0.71/0.76	  with precondition: [V_0=0,1>=V_x] 
0.71/0.76	
0.71/0.76	* Chain [40]: 0
0.71/0.76	  with precondition: [0>=V_0+1,1>=V_x] 
0.71/0.76	
0.71/0.76	* Chain [39]: 0
0.71/0.76	  with precondition: [1>=V_x,V_0>=1] 
0.71/0.76	
0.71/0.76	* Chain [38]: 1*s(16)+8*s(18)+4*s(20)+4*s(21)+0
0.71/0.76	  Such that:s(16) =< 2
0.71/0.76	aux(13) =< V_x
0.71/0.76	s(18) =< aux(13)
0.71/0.76	s(19) =< aux(13)
0.71/0.76	s(20) =< s(18)*aux(13)
0.71/0.76	s(21) =< s(18)*s(19)
0.71/0.76	
0.71/0.76	  with precondition: [V_x>=2] 
0.71/0.76	
0.71/0.76	* Chain [37]: 3*s(42)+1*s(45)+1*s(46)+0
0.71/0.76	  Such that:aux(14) =< V_x
0.71/0.76	s(42) =< aux(14)
0.71/0.76	s(44) =< aux(14)
0.71/0.76	s(45) =< s(42)*aux(14)
0.71/0.76	s(46) =< s(42)*s(44)
0.71/0.76	
0.71/0.76	  with precondition: [V_x>=3] 
0.71/0.76	
0.71/0.76	
0.71/0.76	#### Cost of chains of eval_perfectg_start(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B):
0.71/0.76	* Chain [44]: 0
0.71/0.76	  with precondition: [1>=V_x] 
0.71/0.76	
0.71/0.76	* Chain [43]: 1*s(47)+8*s(49)+4*s(51)+4*s(52)+0
0.71/0.76	  Such that:s(47) =< 2
0.71/0.76	s(48) =< V_x
0.71/0.76	s(49) =< s(48)
0.71/0.76	s(50) =< s(48)
0.71/0.76	s(51) =< s(49)*s(48)
0.71/0.76	s(52) =< s(49)*s(50)
0.71/0.76	
0.71/0.76	  with precondition: [V_x>=2] 
0.71/0.76	
0.71/0.76	* Chain [42]: 3*s(54)+1*s(56)+1*s(57)+0
0.71/0.76	  Such that:s(53) =< V_x
0.71/0.76	s(54) =< s(53)
0.71/0.76	s(55) =< s(53)
0.71/0.76	s(56) =< s(54)*s(53)
0.71/0.76	s(57) =< s(54)*s(55)
0.71/0.76	
0.71/0.76	  with precondition: [V_x>=3] 
0.71/0.76	
0.71/0.76	
0.71/0.76	Closed-form bounds of eval_perfectg_start(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B): 
0.71/0.76	-------------------------------------
0.71/0.76	* Chain [44] with precondition: [1>=V_x] 
0.71/0.76	    - Upper bound: 0 
0.71/0.76	    - Complexity: constant 
0.71/0.76	* Chain [43] with precondition: [V_x>=2] 
0.71/0.76	    - Upper bound: 8*V_x+2+8*V_x*V_x 
0.71/0.76	    - Complexity: n^2 
0.71/0.76	* Chain [42] with precondition: [V_x>=3] 
0.71/0.76	    - Upper bound: 2*V_x*V_x+3*V_x 
0.71/0.76	    - Complexity: n^2 
0.71/0.76	
0.71/0.76	### Maximum cost of eval_perfectg_start(V_0,V_2,V_8,V_x,V_y1_0,V_y2_1,V_y3_0,V_y3_2,B): nat(V_x)*5+2+nat(V_x)*6*nat(V_x)+(nat(V_x)*2*nat(V_x)+nat(V_x)*3) 
0.71/0.76	Asymptotic class: n^2 
0.71/0.76	* Total analysis performed in 644 ms.
0.71/0.76	
0.77/0.86	EOF