0.04/0.42	WORST_CASE(?,O(n^2))  
0.04/0.42	
0.04/0.42	Preprocessing Cost Relations
0.04/0.42	=====================================
0.04/0.42	
0.04/0.42	#### Computed strongly connected components 
0.04/0.42	0. recursive  : [evalrealbubblebb1in/8,evalrealbubblebb2in/8,evalrealbubblebb3in/8,evalrealbubblebb4in/8]
0.04/0.42	1. recursive  : [evalrealbubblebb4in_loop_cont/10,evalrealbubblebb5in/9,evalrealbubblebb6in/9,evalrealbubblebb7in/9]
0.04/0.42	2. non_recursive  : [evalrealbubblestop/5]
0.04/0.42	3. non_recursive  : [evalrealbubblereturnin/5]
0.04/0.42	4. non_recursive  : [exit_location/1]
0.04/0.42	5. non_recursive  : [evalrealbubblebb7in_loop_cont/6]
0.04/0.42	6. non_recursive  : [evalrealbubbleentryin/5]
0.04/0.42	7. non_recursive  : [evalrealbubblestart/5]
0.04/0.42	
0.04/0.42	#### Obtained direct recursion through partial evaluation 
0.04/0.42	0. SCC is partially evaluated into evalrealbubblebb4in/8
0.04/0.42	1. SCC is partially evaluated into evalrealbubblebb7in/9
0.04/0.42	2. SCC is completely evaluated into other SCCs
0.04/0.42	3. SCC is completely evaluated into other SCCs
0.04/0.42	4. SCC is completely evaluated into other SCCs
0.04/0.42	5. SCC is partially evaluated into evalrealbubblebb7in_loop_cont/6
0.04/0.42	6. SCC is partially evaluated into evalrealbubbleentryin/5
0.04/0.42	7. SCC is partially evaluated into evalrealbubblestart/5
0.04/0.42	
0.04/0.42	Control-Flow Refinement of Cost Relations
0.04/0.42	=====================================
0.04/0.42	
0.04/0.42	### Specialization of cost equations evalrealbubblebb4in/8 
0.04/0.42	* CE 14 is refined into CE [15] 
0.04/0.42	* CE 13 is refined into CE [16] 
0.04/0.42	* CE 11 is refined into CE [17] 
0.04/0.42	* CE 12 is refined into CE [18] 
0.04/0.42	
0.04/0.42	
0.04/0.42	### Cost equations --> "Loop" of evalrealbubblebb4in/8 
0.04/0.42	* CEs [17] --> Loop 15 
0.04/0.42	* CEs [18] --> Loop 16 
0.04/0.42	* CEs [15] --> Loop 17 
0.04/0.42	* CEs [16] --> Loop 18 
0.04/0.42	
0.04/0.42	### Ranking functions of CR evalrealbubblebb4in(A,B,C,D,G,H,I,J) 
0.04/0.42	* RF of phase [15,16]: [A-B]
0.04/0.42	
0.04/0.42	#### Partial ranking functions of CR evalrealbubblebb4in(A,B,C,D,G,H,I,J) 
0.04/0.42	* Partial RF of phase [15,16]:
0.04/0.42	  - RF of loop [15:1,16:1]:
0.04/0.42	    A-B
0.04/0.42	
0.04/0.42	
0.04/0.42	### Specialization of cost equations evalrealbubblebb7in/9 
0.04/0.42	* CE 7 is refined into CE [19] 
0.04/0.42	* CE 3 is refined into CE [20] 
0.04/0.42	* CE 6 is refined into CE [21,22] 
0.04/0.42	* CE 8 is refined into CE [23] 
0.04/0.42	* CE 5 is refined into CE [24] 
0.04/0.42	* CE 4 is discarded (unfeasible) 
0.04/0.42	
0.04/0.42	
0.04/0.42	### Cost equations --> "Loop" of evalrealbubblebb7in/9 
0.04/0.42	* CEs [24] --> Loop 19 
0.04/0.42	* CEs [19] --> Loop 20 
0.04/0.42	* CEs [20] --> Loop 21 
0.04/0.42	* CEs [21,22] --> Loop 22 
0.04/0.42	* CEs [23] --> Loop 23 
0.04/0.42	
0.04/0.42	### Ranking functions of CR evalrealbubblebb7in(A,B,C,D,G,H,I,J,K) 
0.04/0.42	* RF of phase [19]: [A]
0.04/0.42	
0.04/0.42	#### Partial ranking functions of CR evalrealbubblebb7in(A,B,C,D,G,H,I,J,K) 
0.04/0.42	* Partial RF of phase [19]:
0.04/0.42	  - RF of loop [19:1]:
0.04/0.42	    A
0.04/0.42	
0.04/0.42	
0.04/0.42	### Specialization of cost equations evalrealbubblebb7in_loop_cont/6 
0.04/0.42	* CE 9 is refined into CE [25] 
0.04/0.42	* CE 10 is refined into CE [26] 
0.04/0.42	
0.04/0.42	
0.04/0.42	### Cost equations --> "Loop" of evalrealbubblebb7in_loop_cont/6 
0.04/0.42	* CEs [25] --> Loop 24 
0.04/0.42	* CEs [26] --> Loop 25 
0.04/0.42	
0.04/0.42	### Ranking functions of CR evalrealbubblebb7in_loop_cont(A,B,C,D,E,F) 
0.04/0.42	
0.04/0.42	#### Partial ranking functions of CR evalrealbubblebb7in_loop_cont(A,B,C,D,E,F) 
0.04/0.42	
0.04/0.42	
0.04/0.42	### Specialization of cost equations evalrealbubbleentryin/5 
0.04/0.42	* CE 2 is refined into CE [27,28,29,30,31,32,33] 
0.04/0.42	
0.04/0.42	
0.04/0.42	### Cost equations --> "Loop" of evalrealbubbleentryin/5 
0.04/0.42	* CEs [29,32] --> Loop 26 
0.04/0.42	* CEs [28,30,31] --> Loop 27 
0.04/0.42	* CEs [33] --> Loop 28 
0.04/0.42	* CEs [27] --> Loop 29 
0.04/0.42	
0.04/0.42	### Ranking functions of CR evalrealbubbleentryin(A,B,C,D,G) 
0.04/0.42	
0.04/0.42	#### Partial ranking functions of CR evalrealbubbleentryin(A,B,C,D,G) 
0.04/0.42	
0.04/0.42	
0.04/0.42	### Specialization of cost equations evalrealbubblestart/5 
0.04/0.42	* CE 1 is refined into CE [34,35,36,37] 
0.04/0.42	
0.04/0.42	
0.04/0.42	### Cost equations --> "Loop" of evalrealbubblestart/5 
0.04/0.42	* CEs [37] --> Loop 30 
0.04/0.42	* CEs [36] --> Loop 31 
0.04/0.42	* CEs [35] --> Loop 32 
0.04/0.42	* CEs [34] --> Loop 33 
0.04/0.42	
0.04/0.42	### Ranking functions of CR evalrealbubblestart(A,B,C,D,G) 
0.04/0.42	
0.04/0.42	#### Partial ranking functions of CR evalrealbubblestart(A,B,C,D,G) 
0.04/0.42	
0.04/0.42	
0.04/0.42	Computing Bounds
0.04/0.42	=====================================
0.04/0.42	
0.04/0.42	#### Cost of chains of evalrealbubblebb4in(A,B,C,D,G,H,I,J):
0.04/0.42	* Chain [[15,16],18]: 2*it(15)+0
0.04/0.42	  Such that:aux(3) =< -B+H
0.04/0.42	it(15) =< aux(3)
0.04/0.42	
0.04/0.42	  with precondition: [G=2,A=H,I=J,C>=0,I>=0,A>=B+1,B>=C,A+C>=B+I] 
0.04/0.42	
0.04/0.42	* Chain [[15,16],17]: 2*it(15)+0
0.04/0.42	  Such that:aux(4) =< A-B
0.04/0.42	it(15) =< aux(4)
0.04/0.42	
0.04/0.42	  with precondition: [G=3,C>=0,A>=B+1,B>=C] 
0.04/0.42	
0.04/0.42	* Chain [17]: 0
0.04/0.42	  with precondition: [G=3,A>=1,C>=0,B>=C] 
0.04/0.42	
0.04/0.42	
0.04/0.42	#### Cost of chains of evalrealbubblebb7in(A,B,C,D,G,H,I,J,K):
0.04/0.42	* Chain [[19],23]: 1*it(19)+2*s(5)+0
0.04/0.42	  Such that:aux(7) =< A
0.04/0.42	it(19) =< aux(7)
0.04/0.42	s(6) =< it(19)*aux(7)
0.04/0.42	s(5) =< s(6)
0.04/0.42	
0.04/0.42	  with precondition: [G=3,A>=1] 
0.04/0.42	
0.04/0.42	* Chain [[19],22]: 3*it(19)+2*s(5)+0
0.04/0.42	  Such that:aux(8) =< A
0.04/0.42	it(19) =< aux(8)
0.04/0.42	s(6) =< it(19)*aux(8)
0.04/0.42	s(5) =< s(6)
0.04/0.42	
0.04/0.42	  with precondition: [G=3,A>=2] 
0.04/0.42	
0.04/0.42	* Chain [[19],21]: 1*it(19)+2*s(5)+2*s(10)+0
0.04/0.42	  Such that:aux(6) =< A
0.04/0.42	it(19) =< A-H
0.04/0.42	s(9) =< H
0.04/0.42	s(10) =< s(9)
0.04/0.42	it(19) =< aux(6)
0.04/0.42	s(6) =< it(19)*aux(6)
0.04/0.42	s(5) =< s(6)
0.04/0.42	
0.04/0.42	  with precondition: [G=4,J=0,K=0,H=I,H>=1,A>=H+1] 
0.04/0.42	
0.04/0.42	* Chain [[19],20]: 1*it(19)+2*s(5)+0
0.04/0.42	  Such that:aux(9) =< A
0.04/0.42	it(19) =< aux(9)
0.04/0.42	s(6) =< it(19)*aux(9)
0.04/0.42	s(5) =< s(6)
0.04/0.42	
0.04/0.42	  with precondition: [G=4,H=0,I=1,J=1,K=1,A>=1] 
0.04/0.42	
0.04/0.42	* Chain [23]: 0
0.04/0.42	  with precondition: [G=3] 
0.04/0.42	
0.04/0.42	* Chain [22]: 2*s(8)+0
0.04/0.42	  Such that:s(7) =< A
0.04/0.42	s(8) =< s(7)
0.04/0.42	
0.04/0.42	  with precondition: [G=3,A>=1] 
0.04/0.42	
0.04/0.42	* Chain [21]: 2*s(10)+0
0.04/0.42	  Such that:s(9) =< A
0.04/0.42	s(10) =< s(9)
0.04/0.42	
0.04/0.42	  with precondition: [G=4,J=0,K=0,A=H,A=I,A>=1] 
0.04/0.42	
0.04/0.42	* Chain [20]: 0
0.04/0.42	  with precondition: [G=4,I=B,J=C,K=D,A=H,0>=A] 
0.04/0.42	
0.04/0.42	
0.04/0.42	#### Cost of chains of evalrealbubblebb7in_loop_cont(A,B,C,D,E,F):
0.04/0.42	* Chain [25]: 0
0.04/0.42	  with precondition: [A=3] 
0.04/0.42	
0.04/0.42	* Chain [24]: 0
0.04/0.42	  with precondition: [A=4] 
0.04/0.42	
0.04/0.42	
0.04/0.42	#### Cost of chains of evalrealbubbleentryin(A,B,C,D,G):
0.04/0.42	* Chain [29]: 0
0.04/0.42	  with precondition: [] 
0.04/0.42	
0.04/0.42	* Chain [28]: 0
0.04/0.42	  with precondition: [1>=A] 
0.04/0.42	
0.04/0.42	* Chain [27]: 6*s(18)+4*s(20)+0
0.04/0.42	  Such that:aux(11) =< A
0.04/0.42	s(18) =< aux(11)
0.04/0.42	s(19) =< s(18)*aux(11)
0.04/0.42	s(20) =< s(19)
0.04/0.42	
0.04/0.42	  with precondition: [A>=2] 
0.04/0.42	
0.04/0.42	* Chain [26]: 6*s(28)+4*s(30)+0
0.04/0.42	  Such that:aux(13) =< A
0.04/0.42	s(28) =< aux(13)
0.04/0.42	s(29) =< s(28)*aux(13)
0.04/0.42	s(30) =< s(29)
0.04/0.42	
0.04/0.42	  with precondition: [A>=3] 
0.04/0.42	
0.04/0.42	
0.04/0.42	#### Cost of chains of evalrealbubblestart(A,B,C,D,G):
0.04/0.42	* Chain [33]: 0
0.04/0.42	  with precondition: [] 
0.04/0.42	
0.04/0.42	* Chain [32]: 0
0.04/0.42	  with precondition: [1>=A] 
0.04/0.42	
0.04/0.42	* Chain [31]: 6*s(38)+4*s(40)+0
0.04/0.42	  Such that:s(37) =< A
0.04/0.42	s(38) =< s(37)
0.04/0.42	s(39) =< s(38)*s(37)
0.04/0.42	s(40) =< s(39)
0.04/0.42	
0.04/0.42	  with precondition: [A>=2] 
0.04/0.42	
0.04/0.42	* Chain [30]: 6*s(42)+4*s(44)+0
0.04/0.42	  Such that:s(41) =< A
0.04/0.42	s(42) =< s(41)
0.04/0.42	s(43) =< s(42)*s(41)
0.04/0.42	s(44) =< s(43)
0.04/0.42	
0.04/0.42	  with precondition: [A>=3] 
0.04/0.42	
0.04/0.42	
0.04/0.42	Closed-form bounds of evalrealbubblestart(A,B,C,D,G): 
0.04/0.42	-------------------------------------
0.04/0.42	* Chain [33] with precondition: [] 
0.04/0.42	    - Upper bound: 0 
0.04/0.42	    - Complexity: constant 
0.04/0.42	* Chain [32] with precondition: [1>=A] 
0.04/0.42	    - Upper bound: 0 
0.04/0.42	    - Complexity: constant 
0.04/0.42	* Chain [31] with precondition: [A>=2] 
0.04/0.42	    - Upper bound: 4*A*A+6*A 
0.04/0.42	    - Complexity: n^2 
0.04/0.42	* Chain [30] with precondition: [A>=3] 
0.04/0.42	    - Upper bound: 4*A*A+6*A 
0.04/0.42	    - Complexity: n^2 
0.04/0.42	
0.04/0.42	### Maximum cost of evalrealbubblestart(A,B,C,D,G): nat(A)*4*nat(A)+nat(A)*6 
0.04/0.42	Asymptotic class: n^2 
0.04/0.42	* Total analysis performed in 344 ms.
0.04/0.42	
0.04/0.52	EOF