0.03/0.17	WORST_CASE(?,O(n^2))  
0.03/0.17	
0.03/0.17	Preprocessing Cost Relations
0.03/0.17	=====================================
0.03/0.17	
0.03/0.17	#### Computed strongly connected components 
0.03/0.17	0. recursive  : [eval2/5]
0.03/0.17	1. recursive  : [eval1/3,eval2_loop_cont/4]
0.03/0.17	2. non_recursive  : [exit_location/1]
0.03/0.17	3. non_recursive  : [eval1_loop_cont/2]
0.03/0.17	4. non_recursive  : [start/3]
0.03/0.17	
0.03/0.17	#### Obtained direct recursion through partial evaluation 
0.03/0.17	0. SCC is partially evaluated into eval2/5
0.03/0.17	1. SCC is partially evaluated into eval1/3
0.03/0.17	2. SCC is completely evaluated into other SCCs
0.03/0.17	3. SCC is completely evaluated into other SCCs
0.03/0.17	4. SCC is partially evaluated into start/3
0.03/0.17	
0.03/0.17	Control-Flow Refinement of Cost Relations
0.03/0.17	=====================================
0.03/0.17	
0.03/0.17	### Specialization of cost equations eval2/5 
0.03/0.17	* CE 7 is refined into CE [8] 
0.03/0.17	* CE 6 is refined into CE [9] 
0.03/0.17	* CE 5 is refined into CE [10] 
0.03/0.17	
0.03/0.17	
0.03/0.17	### Cost equations --> "Loop" of eval2/5 
0.03/0.17	* CEs [10] --> Loop 8 
0.03/0.17	* CEs [8] --> Loop 9 
0.03/0.17	* CEs [9] --> Loop 10 
0.03/0.17	
0.03/0.17	### Ranking functions of CR eval2(A,B,C,D,E) 
0.03/0.17	* RF of phase [8]: [A-B]
0.03/0.17	
0.03/0.17	#### Partial ranking functions of CR eval2(A,B,C,D,E) 
0.03/0.17	* Partial RF of phase [8]:
0.03/0.17	  - RF of loop [8:1]:
0.03/0.17	    A-B
0.03/0.17	
0.03/0.17	
0.03/0.17	### Specialization of cost equations eval1/3 
0.03/0.17	* CE 2 is refined into CE [11,12] 
0.03/0.17	* CE 4 is refined into CE [13] 
0.03/0.17	* CE 3 is refined into CE [14] 
0.03/0.17	
0.03/0.17	
0.03/0.17	### Cost equations --> "Loop" of eval1/3 
0.03/0.17	* CEs [14] --> Loop 11 
0.03/0.17	* CEs [11,12] --> Loop 12 
0.03/0.17	* CEs [13] --> Loop 13 
0.03/0.17	
0.03/0.17	### Ranking functions of CR eval1(A,B,C) 
0.03/0.17	* RF of phase [11]: [A]
0.03/0.17	
0.03/0.17	#### Partial ranking functions of CR eval1(A,B,C) 
0.03/0.17	* Partial RF of phase [11]:
0.03/0.17	  - RF of loop [11:1]:
0.03/0.17	    A
0.03/0.17	
0.03/0.17	
0.03/0.17	### Specialization of cost equations start/3 
0.03/0.17	* CE 1 is refined into CE [15,16,17] 
0.03/0.17	
0.03/0.17	
0.03/0.17	### Cost equations --> "Loop" of start/3 
0.03/0.17	* CEs [17] --> Loop 14 
0.03/0.17	* CEs [16] --> Loop 15 
0.03/0.17	* CEs [15] --> Loop 16 
0.03/0.17	
0.03/0.17	### Ranking functions of CR start(A,B,C) 
0.03/0.17	
0.03/0.17	#### Partial ranking functions of CR start(A,B,C) 
0.03/0.17	
0.03/0.17	
0.03/0.17	Computing Bounds
0.03/0.17	=====================================
0.03/0.17	
0.03/0.17	#### Cost of chains of eval2(A,B,C,D,E):
0.03/0.17	* Chain [[8],10]: 1*it(8)+0
0.03/0.17	  Such that:it(8) =< -B+E
0.03/0.17	
0.03/0.17	  with precondition: [C=2,A=D+1,A=E,B>=0,A>=B+1] 
0.03/0.17	
0.03/0.17	* Chain [[8],9]: 1*it(8)+0
0.03/0.17	  Such that:it(8) =< A-B
0.03/0.17	
0.03/0.17	  with precondition: [C=3,B>=0,A>=B+1] 
0.03/0.17	
0.03/0.17	* Chain [9]: 0
0.03/0.17	  with precondition: [C=3,A>=1,B>=0] 
0.03/0.17	
0.03/0.17	
0.03/0.17	#### Cost of chains of eval1(A,B,C):
0.03/0.17	* Chain [[11],13]: 1*it(11)+1*s(3)+0
0.03/0.17	  Such that:aux(3) =< A
0.03/0.17	it(11) =< aux(3)
0.03/0.17	s(3) =< it(11)*aux(3)
0.03/0.17	
0.03/0.17	  with precondition: [C=3,A>=1] 
0.03/0.17	
0.03/0.17	* Chain [[11],12]: 2*it(11)+1*s(3)+0
0.03/0.17	  Such that:aux(4) =< A
0.03/0.17	it(11) =< aux(4)
0.03/0.17	s(3) =< it(11)*aux(4)
0.03/0.17	
0.03/0.17	  with precondition: [C=3,A>=2] 
0.03/0.17	
0.03/0.17	* Chain [13]: 0
0.03/0.17	  with precondition: [C=3] 
0.03/0.17	
0.03/0.17	* Chain [12]: 1*s(4)+0
0.03/0.17	  Such that:s(4) =< A
0.03/0.17	
0.03/0.17	  with precondition: [C=3,A>=1] 
0.03/0.17	
0.03/0.17	
0.03/0.17	#### Cost of chains of start(A,B,C):
0.03/0.17	* Chain [16]: 0
0.03/0.17	  with precondition: [] 
0.03/0.17	
0.03/0.17	* Chain [15]: 2*s(10)+1*s(11)+0
0.03/0.17	  Such that:s(9) =< A
0.03/0.17	s(10) =< s(9)
0.03/0.17	s(11) =< s(10)*s(9)
0.03/0.17	
0.03/0.17	  with precondition: [A>=1] 
0.03/0.17	
0.03/0.17	* Chain [14]: 2*s(13)+1*s(14)+0
0.03/0.17	  Such that:s(12) =< A
0.03/0.17	s(13) =< s(12)
0.03/0.17	s(14) =< s(13)*s(12)
0.03/0.17	
0.03/0.17	  with precondition: [A>=2] 
0.03/0.17	
0.03/0.17	
0.03/0.17	Closed-form bounds of start(A,B,C): 
0.03/0.17	-------------------------------------
0.03/0.17	* Chain [16] with precondition: [] 
0.03/0.17	    - Upper bound: 0 
0.03/0.17	    - Complexity: constant 
0.03/0.17	* Chain [15] with precondition: [A>=1] 
0.03/0.17	    - Upper bound: 2*A+A*A 
0.03/0.17	    - Complexity: n^2 
0.03/0.17	* Chain [14] with precondition: [A>=2] 
0.03/0.17	    - Upper bound: 2*A+A*A 
0.03/0.17	    - Complexity: n^2 
0.03/0.17	
0.03/0.17	### Maximum cost of start(A,B,C): nat(A)*nat(A)+nat(A)*2 
0.03/0.17	Asymptotic class: n^2 
0.03/0.17	* Total analysis performed in 109 ms.
0.03/0.17	
0.03/0.27	EOF