0.03/0.28	WORST_CASE(?,O(n^1))  
0.03/0.28	
0.03/0.28	Preprocessing Cost Relations
0.03/0.28	=====================================
0.03/0.28	
0.03/0.28	#### Computed strongly connected components 
0.03/0.28	0. recursive  : [eval/6]
0.03/0.28	1. non_recursive  : [exit_location/1]
0.03/0.28	2. non_recursive  : [eval_loop_cont/2]
0.03/0.28	3. non_recursive  : [start/6]
0.03/0.28	
0.03/0.28	#### Obtained direct recursion through partial evaluation 
0.03/0.28	0. SCC is partially evaluated into eval/6
0.03/0.28	1. SCC is completely evaluated into other SCCs
0.03/0.28	2. SCC is completely evaluated into other SCCs
0.03/0.28	3. SCC is partially evaluated into start/6
0.03/0.28	
0.03/0.28	Control-Flow Refinement of Cost Relations
0.03/0.28	=====================================
0.03/0.28	
0.03/0.28	### Specialization of cost equations eval/6 
0.03/0.28	* CE 6 is refined into CE [7] 
0.03/0.28	* CE 3 is refined into CE [8] 
0.03/0.28	* CE 4 is refined into CE [9] 
0.03/0.28	* CE 2 is refined into CE [10] 
0.03/0.28	* CE 5 is refined into CE [11] 
0.03/0.28	
0.03/0.28	
0.03/0.28	### Cost equations --> "Loop" of eval/6 
0.03/0.28	* CEs [8] --> Loop 7 
0.03/0.28	* CEs [9] --> Loop 8 
0.03/0.28	* CEs [10] --> Loop 9 
0.03/0.28	* CEs [11] --> Loop 10 
0.03/0.28	* CEs [7] --> Loop 11 
0.03/0.28	
0.03/0.28	### Ranking functions of CR eval(A,B,C,D,E,F) 
0.03/0.28	* RF of phase [7,9]: [A-B+C-D-1]
0.03/0.28	* RF of phase [8]: [C-D]
0.03/0.28	* RF of phase [10]: [A-B]
0.03/0.28	
0.03/0.28	#### Partial ranking functions of CR eval(A,B,C,D,E,F) 
0.03/0.28	* Partial RF of phase [7,9]:
0.03/0.28	  - RF of loop [7:1]:
0.03/0.28	    C-D
0.03/0.28	  - RF of loop [9:1]:
0.03/0.28	    A-B
0.03/0.28	* Partial RF of phase [8]:
0.03/0.28	  - RF of loop [8:1]:
0.03/0.28	    C-D
0.03/0.28	* Partial RF of phase [10]:
0.03/0.28	  - RF of loop [10:1]:
0.03/0.28	    A-B
0.03/0.28	
0.03/0.28	
0.03/0.28	### Specialization of cost equations start/6 
0.03/0.28	* CE 1 is refined into CE [12,13,14,15] 
0.03/0.28	
0.03/0.28	
0.03/0.28	### Cost equations --> "Loop" of start/6 
0.03/0.28	* CEs [15] --> Loop 12 
0.03/0.28	* CEs [14] --> Loop 13 
0.03/0.28	* CEs [13] --> Loop 14 
0.03/0.28	* CEs [12] --> Loop 15 
0.03/0.28	
0.03/0.28	### Ranking functions of CR start(A,B,C,D,E,F) 
0.03/0.28	
0.03/0.28	#### Partial ranking functions of CR start(A,B,C,D,E,F) 
0.03/0.28	
0.03/0.28	
0.03/0.28	Computing Bounds
0.03/0.28	=====================================
0.03/0.28	
0.03/0.28	#### Cost of chains of eval(A,B,C,D,E,F):
0.03/0.28	* Chain [[10],11]: 1*it(10)+0
0.03/0.28	  Such that:it(10) =< A-B
0.03/0.28	
0.03/0.28	  with precondition: [F=2,A>=B+1,D>=C] 
0.03/0.28	
0.03/0.28	* Chain [[8],11]: 1*it(8)+0
0.03/0.28	  Such that:it(8) =< C-D
0.03/0.28	
0.03/0.28	  with precondition: [F=2,B>=A,C>=D+1] 
0.03/0.28	
0.03/0.28	* Chain [[7,9],[10],11]: 1*it(7)+2*it(9)+0
0.03/0.28	  Such that:it(7) =< C-D
0.03/0.28	aux(3) =< A-B
0.03/0.28	aux(4) =< A-B+C-D
0.03/0.28	it(9) =< aux(3)
0.03/0.28	it(9) =< aux(4)
0.03/0.28	it(7) =< aux(4)
0.03/0.28	
0.03/0.28	  with precondition: [F=2,A>=B+1,C>=D+1] 
0.03/0.28	
0.03/0.28	* Chain [[7,9],[8],11]: 2*it(7)+1*it(9)+0
0.03/0.28	  Such that:it(9) =< A-B
0.03/0.28	aux(5) =< A-B+C-D
0.03/0.28	aux(6) =< C-D
0.03/0.28	it(7) =< aux(5)
0.03/0.28	it(7) =< aux(6)
0.03/0.28	it(9) =< aux(5)
0.03/0.28	
0.03/0.28	  with precondition: [F=2,A>=B+1,C>=D+1] 
0.03/0.28	
0.03/0.28	* Chain [[7,9],11]: 1*it(7)+1*it(9)+0
0.03/0.28	  Such that:it(9) =< A-B
0.03/0.28	it(7) =< C-D
0.03/0.28	aux(7) =< A-B+C-D
0.03/0.28	it(7) =< aux(7)
0.03/0.28	it(9) =< aux(7)
0.03/0.28	
0.03/0.28	  with precondition: [F=2,A>=B+1,C>=D+1] 
0.03/0.28	
0.03/0.28	* Chain [11]: 0
0.03/0.28	  with precondition: [F=2] 
0.03/0.28	
0.03/0.28	
0.03/0.28	#### Cost of chains of start(A,B,C,D,E,F):
0.03/0.28	* Chain [15]: 0
0.03/0.28	  with precondition: [] 
0.03/0.28	
0.03/0.28	* Chain [14]: 1*s(12)+0
0.03/0.28	  Such that:s(12) =< C-D
0.03/0.28	
0.03/0.28	  with precondition: [B>=A,C>=D+1] 
0.03/0.28	
0.03/0.28	* Chain [13]: 1*s(13)+0
0.03/0.28	  Such that:s(13) =< A-B
0.03/0.28	
0.03/0.28	  with precondition: [A>=B+1,D>=C] 
0.03/0.28	
0.03/0.28	* Chain [12]: 4*s(17)+4*s(18)+0
0.03/0.28	  Such that:s(14) =< A-B
0.03/0.28	s(15) =< A-B+C-D
0.03/0.28	s(16) =< C-D
0.03/0.28	s(17) =< s(14)
0.03/0.28	s(18) =< s(16)
0.03/0.28	s(18) =< s(15)
0.03/0.28	s(17) =< s(15)
0.03/0.28	
0.03/0.28	  with precondition: [A>=B+1,C>=D+1] 
0.03/0.28	
0.03/0.28	
0.03/0.28	Closed-form bounds of start(A,B,C,D,E,F): 
0.03/0.28	-------------------------------------
0.03/0.28	* Chain [15] with precondition: [] 
0.03/0.28	    - Upper bound: 0 
0.03/0.28	    - Complexity: constant 
0.03/0.28	* Chain [14] with precondition: [B>=A,C>=D+1] 
0.03/0.28	    - Upper bound: C-D 
0.03/0.28	    - Complexity: n 
0.03/0.28	* Chain [13] with precondition: [A>=B+1,D>=C] 
0.03/0.28	    - Upper bound: A-B 
0.03/0.28	    - Complexity: n 
0.03/0.28	* Chain [12] with precondition: [A>=B+1,C>=D+1] 
0.03/0.28	    - Upper bound: 4*A-4*B+4*C-4*D 
0.03/0.28	    - Complexity: n 
0.03/0.28	
0.03/0.28	### Maximum cost of start(A,B,C,D,E,F): max([nat(C-D),nat(C-D)*4+nat(A-B)*3+nat(A-B)]) 
0.03/0.28	Asymptotic class: n 
0.03/0.28	* Total analysis performed in 213 ms.
0.03/0.28	
0.03/0.38	EOF