0.03/0.18	WORST_CASE(?,O(n^1))  
0.03/0.18	
0.03/0.18	Preprocessing Cost Relations
0.03/0.18	=====================================
0.03/0.18	
0.03/0.18	#### Computed strongly connected components 
0.03/0.18	0. recursive  : [eval1/4,eval2/4]
0.03/0.18	1. non_recursive  : [exit_location/1]
0.03/0.18	2. non_recursive  : [eval1_loop_cont/2]
0.03/0.18	3. non_recursive  : [start/4]
0.03/0.18	
0.03/0.18	#### Obtained direct recursion through partial evaluation 
0.03/0.18	0. SCC is partially evaluated into eval1/4
0.03/0.18	1. SCC is completely evaluated into other SCCs
0.03/0.18	2. SCC is completely evaluated into other SCCs
0.03/0.18	3. SCC is partially evaluated into start/4
0.03/0.18	
0.03/0.18	Control-Flow Refinement of Cost Relations
0.03/0.18	=====================================
0.03/0.18	
0.03/0.18	### Specialization of cost equations eval1/4 
0.03/0.18	* CE 5 is refined into CE [6] 
0.03/0.18	* CE 2 is refined into CE [7] 
0.03/0.18	* CE 3 is refined into CE [8] 
0.03/0.18	* CE 4 is refined into CE [9] 
0.03/0.18	
0.03/0.18	
0.03/0.18	### Cost equations --> "Loop" of eval1/4 
0.03/0.18	* CEs [7] --> Loop 6 
0.03/0.18	* CEs [8] --> Loop 7 
0.03/0.18	* CEs [9] --> Loop 8 
0.03/0.18	* CEs [6] --> Loop 9 
0.03/0.18	
0.03/0.18	### Ranking functions of CR eval1(A,B,C,D) 
0.03/0.18	* RF of phase [6]: [A-B]
0.03/0.18	* RF of phase [7,8]: [2*A-B-C-1]
0.03/0.18	
0.03/0.18	#### Partial ranking functions of CR eval1(A,B,C,D) 
0.03/0.18	* Partial RF of phase [6]:
0.03/0.18	  - RF of loop [6:1]:
0.03/0.18	    A-B
0.03/0.18	* Partial RF of phase [7,8]:
0.03/0.18	  - RF of loop [7:1]:
0.03/0.18	    A-C
0.03/0.18	  - RF of loop [8:1]:
0.03/0.18	    A-B
0.03/0.18	
0.03/0.18	
0.03/0.18	### Specialization of cost equations start/4 
0.03/0.18	* CE 1 is refined into CE [10,11,12] 
0.03/0.18	
0.03/0.18	
0.03/0.18	### Cost equations --> "Loop" of start/4 
0.03/0.18	* CEs [12] --> Loop 10 
0.03/0.18	* CEs [11] --> Loop 11 
0.03/0.18	* CEs [10] --> Loop 12 
0.03/0.18	
0.03/0.18	### Ranking functions of CR start(A,B,C,D) 
0.03/0.18	
0.03/0.18	#### Partial ranking functions of CR start(A,B,C,D) 
0.03/0.18	
0.03/0.18	
0.03/0.18	Computing Bounds
0.03/0.18	=====================================
0.03/0.18	
0.03/0.18	#### Cost of chains of eval1(A,B,C,D):
0.03/0.18	* Chain [[7,8],[6],9]: 2*it(6)+1*it(7)+0
0.03/0.18	  Such that:it(7) =< A-C
0.03/0.18	aux(3) =< A-B
0.03/0.18	aux(4) =< 2*A-B-C
0.03/0.18	it(6) =< aux(3)
0.03/0.18	it(6) =< aux(4)
0.03/0.18	it(7) =< aux(4)
0.03/0.18	
0.03/0.18	  with precondition: [D=2,A>=B+1,A>=C+1] 
0.03/0.18	
0.03/0.18	* Chain [[7,8],9]: 1*it(7)+1*it(8)+0
0.03/0.18	  Such that:it(8) =< A-B
0.03/0.18	it(7) =< A-C
0.03/0.18	aux(5) =< 2*A-B-C
0.03/0.18	it(7) =< aux(5)
0.03/0.18	it(8) =< aux(5)
0.03/0.18	
0.03/0.18	  with precondition: [D=2,A>=B+1,A>=C+1] 
0.03/0.18	
0.03/0.18	* Chain [[6],9]: 1*it(6)+0
0.03/0.18	  Such that:it(6) =< A-B
0.03/0.18	
0.03/0.18	  with precondition: [D=2,C>=A,A>=B+1] 
0.03/0.18	
0.03/0.18	* Chain [9]: 0
0.03/0.18	  with precondition: [D=2] 
0.03/0.18	
0.03/0.18	
0.03/0.18	#### Cost of chains of start(A,B,C,D):
0.03/0.18	* Chain [12]: 0
0.03/0.18	  with precondition: [] 
0.03/0.18	
0.03/0.18	* Chain [11]: 1*s(8)+0
0.03/0.18	  Such that:s(8) =< A-B
0.03/0.18	
0.03/0.18	  with precondition: [C>=A,A>=B+1] 
0.03/0.18	
0.03/0.18	* Chain [10]: 3*s(12)+2*s(13)+0
0.03/0.18	  Such that:s(9) =< A-B
0.03/0.18	s(10) =< A-C
0.03/0.18	s(11) =< 2*A-B-C
0.03/0.18	s(12) =< s(9)
0.03/0.18	s(13) =< s(10)
0.03/0.18	s(13) =< s(11)
0.03/0.18	s(12) =< s(11)
0.03/0.18	
0.03/0.18	  with precondition: [A>=B+1,A>=C+1] 
0.03/0.18	
0.03/0.18	
0.03/0.18	Closed-form bounds of start(A,B,C,D): 
0.03/0.18	-------------------------------------
0.03/0.18	* Chain [12] with precondition: [] 
0.03/0.18	    - Upper bound: 0 
0.03/0.18	    - Complexity: constant 
0.03/0.18	* Chain [11] with precondition: [C>=A,A>=B+1] 
0.03/0.18	    - Upper bound: A-B 
0.03/0.18	    - Complexity: n 
0.03/0.18	* Chain [10] with precondition: [A>=B+1,A>=C+1] 
0.03/0.18	    - Upper bound: 5*A-3*B-2*C 
0.03/0.18	    - Complexity: n 
0.03/0.18	
0.03/0.18	### Maximum cost of start(A,B,C,D): nat(A-C)*2+nat(A-B)*2+nat(A-B) 
0.03/0.18	Asymptotic class: n 
0.03/0.18	* Total analysis performed in 118 ms.
0.03/0.18	
0.03/0.28	EOF