0.03/0.21	WORST_CASE(?,O(n^2))  
0.03/0.21	
0.03/0.21	Preprocessing Cost Relations
0.03/0.21	=====================================
0.03/0.21	
0.03/0.21	#### Computed strongly connected components 
0.03/0.21	0. recursive  : [l2/9]
0.03/0.21	1. recursive  : [l1/5,l2_loop_cont/6]
0.03/0.21	2. non_recursive  : [exit_location/1]
0.03/0.21	3. non_recursive  : [l1_loop_cont/2]
0.03/0.21	4. non_recursive  : [l0/5]
0.03/0.21	
0.03/0.21	#### Obtained direct recursion through partial evaluation 
0.03/0.21	0. SCC is partially evaluated into l2/9
0.03/0.21	1. SCC is partially evaluated into l1/5
0.03/0.21	2. SCC is completely evaluated into other SCCs
0.03/0.21	3. SCC is completely evaluated into other SCCs
0.03/0.21	4. SCC is partially evaluated into l0/5
0.03/0.21	
0.03/0.21	Control-Flow Refinement of Cost Relations
0.03/0.21	=====================================
0.03/0.21	
0.03/0.21	### Specialization of cost equations l2/9 
0.03/0.21	* CE 7 is refined into CE [8] 
0.03/0.21	* CE 6 is refined into CE [9] 
0.03/0.21	* CE 5 is refined into CE [10] 
0.03/0.21	
0.03/0.21	
0.03/0.21	### Cost equations --> "Loop" of l2/9 
0.03/0.21	* CEs [10] --> Loop 8 
0.03/0.21	* CEs [8] --> Loop 9 
0.03/0.21	* CEs [9] --> Loop 10 
0.03/0.21	
0.03/0.21	### Ranking functions of CR l2(A,B,C,D,E,F,G,H,I) 
0.03/0.21	* RF of phase [8]: [B-C]
0.03/0.21	
0.03/0.21	#### Partial ranking functions of CR l2(A,B,C,D,E,F,G,H,I) 
0.03/0.21	* Partial RF of phase [8]:
0.03/0.21	  - RF of loop [8:1]:
0.03/0.21	    B-C
0.03/0.21	
0.03/0.21	
0.03/0.21	### Specialization of cost equations l1/5 
0.03/0.21	* CE 2 is refined into CE [11,12] 
0.03/0.21	* CE 4 is refined into CE [13] 
0.03/0.21	* CE 3 is refined into CE [14] 
0.03/0.21	
0.03/0.21	
0.03/0.21	### Cost equations --> "Loop" of l1/5 
0.03/0.21	* CEs [14] --> Loop 11 
0.03/0.21	* CEs [11,12] --> Loop 12 
0.03/0.21	* CEs [13] --> Loop 13 
0.03/0.21	
0.03/0.21	### Ranking functions of CR l1(A,B,C,D,E) 
0.03/0.21	* RF of phase [11]: [B]
0.03/0.21	
0.03/0.21	#### Partial ranking functions of CR l1(A,B,C,D,E) 
0.03/0.21	* Partial RF of phase [11]:
0.03/0.21	  - RF of loop [11:1]:
0.03/0.21	    B
0.03/0.21	
0.03/0.21	
0.03/0.21	### Specialization of cost equations l0/5 
0.03/0.21	* CE 1 is refined into CE [15,16,17] 
0.03/0.21	
0.03/0.21	
0.03/0.21	### Cost equations --> "Loop" of l0/5 
0.03/0.21	* CEs [17] --> Loop 14 
0.03/0.21	* CEs [16] --> Loop 15 
0.03/0.21	* CEs [15] --> Loop 16 
0.03/0.21	
0.03/0.21	### Ranking functions of CR l0(A,B,C,D,E) 
0.03/0.21	
0.03/0.21	#### Partial ranking functions of CR l0(A,B,C,D,E) 
0.03/0.21	
0.03/0.21	
0.03/0.21	Computing Bounds
0.03/0.21	=====================================
0.03/0.21	
0.03/0.21	#### Cost of chains of l2(A,B,C,D,E,F,G,H,I):
0.03/0.21	* Chain [[8],10]: 1*it(8)+0
0.03/0.21	  Such that:it(8) =< B-C
0.03/0.21	
0.03/0.21	  with precondition: [E=2,B=G+1,B=H,A+I=F,B>=C+1] 
0.03/0.21	
0.03/0.21	* Chain [[8],9]: 1*it(8)+0
0.03/0.21	  Such that:it(8) =< B-C
0.03/0.21	
0.03/0.21	  with precondition: [E=3,B>=C+1] 
0.03/0.21	
0.03/0.21	* Chain [9]: 0
0.03/0.21	  with precondition: [E=3,B>=C] 
0.03/0.21	
0.03/0.21	
0.03/0.21	#### Cost of chains of l1(A,B,C,D,E):
0.03/0.21	* Chain [[11],13]: 1*it(11)+1*s(3)+0
0.03/0.21	  Such that:aux(3) =< B
0.03/0.21	it(11) =< aux(3)
0.03/0.21	s(3) =< it(11)*aux(3)
0.03/0.21	
0.03/0.21	  with precondition: [E=3,B>=1] 
0.03/0.21	
0.03/0.21	* Chain [[11],12]: 2*it(11)+1*s(3)+0
0.03/0.21	  Such that:aux(4) =< B
0.03/0.21	it(11) =< aux(4)
0.03/0.21	s(3) =< it(11)*aux(4)
0.03/0.21	
0.03/0.21	  with precondition: [E=3,B>=2] 
0.03/0.21	
0.03/0.21	* Chain [13]: 0
0.03/0.21	  with precondition: [E=3] 
0.03/0.21	
0.03/0.21	* Chain [12]: 1*s(4)+0
0.03/0.21	  Such that:s(4) =< B
0.03/0.21	
0.03/0.21	  with precondition: [E=3,B>=1] 
0.03/0.21	
0.03/0.21	
0.03/0.21	#### Cost of chains of l0(A,B,C,D,E):
0.03/0.21	* Chain [16]: 0
0.03/0.21	  with precondition: [] 
0.03/0.21	
0.03/0.21	* Chain [15]: 2*s(10)+1*s(11)+0
0.03/0.21	  Such that:s(9) =< B
0.03/0.21	s(10) =< s(9)
0.03/0.21	s(11) =< s(10)*s(9)
0.03/0.21	
0.03/0.21	  with precondition: [B>=1] 
0.03/0.21	
0.03/0.21	* Chain [14]: 2*s(13)+1*s(14)+0
0.03/0.21	  Such that:s(12) =< B
0.03/0.21	s(13) =< s(12)
0.03/0.21	s(14) =< s(13)*s(12)
0.03/0.21	
0.03/0.21	  with precondition: [B>=2] 
0.03/0.21	
0.03/0.21	
0.03/0.21	Closed-form bounds of l0(A,B,C,D,E): 
0.03/0.21	-------------------------------------
0.03/0.21	* Chain [16] with precondition: [] 
0.03/0.21	    - Upper bound: 0 
0.03/0.21	    - Complexity: constant 
0.03/0.21	* Chain [15] with precondition: [B>=1] 
0.03/0.21	    - Upper bound: 2*B+B*B 
0.03/0.21	    - Complexity: n^2 
0.03/0.21	* Chain [14] with precondition: [B>=2] 
0.03/0.21	    - Upper bound: 2*B+B*B 
0.03/0.21	    - Complexity: n^2 
0.03/0.21	
0.03/0.21	### Maximum cost of l0(A,B,C,D,E): nat(B)*nat(B)+nat(B)*2 
0.03/0.21	Asymptotic class: n^2 
0.03/0.21	* Total analysis performed in 148 ms.
0.03/0.21	
0.03/0.31	EOF