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+1]
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+1
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+1]
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+1
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+2,A+1=E,B>=1,A>=B] 
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+1
0.03/0.17	
0.03/0.17	  with precondition: [C=3,B>=1,A>=B] 
0.03/0.17	
0.03/0.17	* Chain [9]: 0
0.03/0.17	  with precondition: [C=3,A>=1,B>=1] 
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:it(11) =< A+1
0.03/0.17	aux(1) =< A+2
0.03/0.17	s(3) =< it(11)*aux(1)
0.03/0.17	
0.03/0.17	  with precondition: [C=3,A>=0] 
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(1) =< A+2
0.03/0.17	aux(2) =< A
0.03/0.17	aux(3) =< A+1
0.03/0.17	it(11) =< aux(2)
0.03/0.17	it(11) =< aux(3)
0.03/0.17	s(3) =< it(11)*aux(1)
0.03/0.17	
0.03/0.17	  with precondition: [C=3,A>=1] 
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+1
0.03/0.17	
0.03/0.17	  with precondition: [C=3,A>=0] 
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(11)+1*s(12)+0
0.03/0.17	  Such that:s(10) =< A+1
0.03/0.17	s(9) =< A+2
0.03/0.17	s(11) =< s(10)
0.03/0.17	s(12) =< s(11)*s(9)
0.03/0.17	
0.03/0.17	  with precondition: [A>=0] 
0.03/0.17	
0.03/0.17	* Chain [14]: 2*s(16)+1*s(17)+0
0.03/0.17	  Such that:s(14) =< A
0.03/0.17	s(15) =< A+1
0.03/0.17	s(13) =< A+2
0.03/0.17	s(16) =< s(14)
0.03/0.17	s(16) =< s(15)
0.03/0.17	s(17) =< s(16)*s(13)
0.03/0.17	
0.03/0.17	  with precondition: [A>=1] 
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>=0] 
0.03/0.17	    - Upper bound: 2*A+2+(A+2)*(A+1) 
0.03/0.17	    - Complexity: n^2 
0.03/0.17	* Chain [14] with precondition: [A>=1] 
0.03/0.17	    - Upper bound: (A+2)*A+2*A 
0.03/0.17	    - Complexity: n^2 
0.03/0.17	
0.03/0.17	### Maximum cost of start(A,B,C): max([nat(A+2)*nat(A)+nat(A)*2,nat(A+2)*nat(A+1)+nat(A+1)*2]) 
0.03/0.17	Asymptotic class: n^2 
0.03/0.17	* Total analysis performed in 114 ms.
0.03/0.17	
0.03/0.27	EOF