0.03/0.11	WORST_CASE(?,O(n^1))  
0.03/0.11	
0.03/0.11	Preprocessing Cost Relations
0.03/0.11	=====================================
0.03/0.11	
0.03/0.11	#### Computed strongly connected components 
0.03/0.11	0. recursive  : [sumto/4]
0.03/0.11	1. non_recursive  : [end/3]
0.03/0.11	2. non_recursive  : [exit_location/1]
0.03/0.11	3. non_recursive  : [sumto_loop_cont/4]
0.03/0.11	4. non_recursive  : [start/3]
0.03/0.11	
0.03/0.11	#### Obtained direct recursion through partial evaluation 
0.03/0.11	0. SCC is partially evaluated into sumto/4
0.03/0.11	1. SCC is completely evaluated into other SCCs
0.03/0.11	2. SCC is completely evaluated into other SCCs
0.03/0.11	3. SCC is partially evaluated into sumto_loop_cont/4
0.03/0.11	4. SCC is partially evaluated into start/3
0.03/0.11	
0.03/0.11	Control-Flow Refinement of Cost Relations
0.03/0.11	=====================================
0.03/0.11	
0.03/0.11	### Specialization of cost equations sumto/4 
0.03/0.11	* CE 4 is refined into CE [7] 
0.03/0.11	* CE 2 is refined into CE [8] 
0.03/0.11	* CE 3 is refined into CE [9] 
0.03/0.11	
0.03/0.11	
0.03/0.11	### Cost equations --> "Loop" of sumto/4 
0.03/0.11	* CEs [9] --> Loop 7 
0.03/0.11	* CEs [7] --> Loop 8 
0.03/0.11	* CEs [8] --> Loop 9 
0.03/0.11	
0.03/0.11	### Ranking functions of CR sumto(A,B,C,D) 
0.03/0.11	* RF of phase [7]: [-A+B+1]
0.03/0.11	
0.03/0.11	#### Partial ranking functions of CR sumto(A,B,C,D) 
0.03/0.11	* Partial RF of phase [7]:
0.03/0.11	  - RF of loop [7:1]:
0.03/0.11	    -A+B+1
0.03/0.11	
0.03/0.11	
0.03/0.11	### Specialization of cost equations sumto_loop_cont/4 
0.03/0.11	* CE 6 is refined into CE [10] 
0.03/0.11	* CE 5 is refined into CE [11] 
0.03/0.11	
0.03/0.11	
0.03/0.11	### Cost equations --> "Loop" of sumto_loop_cont/4 
0.03/0.11	* CEs [10] --> Loop 10 
0.03/0.11	* CEs [11] --> Loop 11 
0.03/0.11	
0.03/0.11	### Ranking functions of CR sumto_loop_cont(A,B,C,D) 
0.03/0.11	
0.03/0.11	#### Partial ranking functions of CR sumto_loop_cont(A,B,C,D) 
0.03/0.11	
0.03/0.11	
0.03/0.11	### Specialization of cost equations start/3 
0.03/0.11	* CE 1 is refined into CE [12,13,14,15] 
0.03/0.11	
0.03/0.11	
0.03/0.11	### Cost equations --> "Loop" of start/3 
0.03/0.11	* CEs [12] --> Loop 12 
0.03/0.11	* CEs [13,15] --> Loop 13 
0.03/0.11	* CEs [14] --> Loop 14 
0.03/0.11	
0.03/0.11	### Ranking functions of CR start(A,B,C) 
0.03/0.11	
0.03/0.11	#### Partial ranking functions of CR start(A,B,C) 
0.03/0.11	
0.03/0.11	
0.03/0.11	Computing Bounds
0.03/0.11	=====================================
0.03/0.11	
0.03/0.11	#### Cost of chains of sumto(A,B,C,D):
0.03/0.11	* Chain [[7],9]: 1*it(7)+0
0.03/0.11	  Such that:it(7) =< -A+B+1
0.03/0.11	
0.03/0.11	  with precondition: [C=2,B+1=D,B>=A] 
0.03/0.11	
0.03/0.11	* Chain [[7],8]: 1*it(7)+0
0.03/0.11	  Such that:it(7) =< -A+B+1
0.03/0.11	
0.03/0.11	  with precondition: [C=3,B>=A] 
0.03/0.11	
0.03/0.11	* Chain [9]: 0
0.03/0.11	  with precondition: [C=2,A=D,A>=B+1] 
0.03/0.11	
0.03/0.11	* Chain [8]: 0
0.03/0.11	  with precondition: [C=3] 
0.03/0.11	
0.03/0.11	
0.03/0.11	#### Cost of chains of sumto_loop_cont(A,B,C,D):
0.03/0.11	* Chain [11]: 0
0.03/0.11	  with precondition: [A=2] 
0.03/0.11	
0.03/0.11	* Chain [10]: 0
0.03/0.11	  with precondition: [A=3] 
0.03/0.11	
0.03/0.11	
0.03/0.11	#### Cost of chains of start(A,B,C):
0.03/0.11	* Chain [14]: 0
0.03/0.11	  with precondition: [] 
0.03/0.11	
0.03/0.11	* Chain [13]: 2*s(1)+0
0.03/0.11	  Such that:aux(1) =< -A+B+1
0.03/0.11	s(1) =< aux(1)
0.03/0.11	
0.03/0.11	  with precondition: [B>=A] 
0.03/0.11	
0.03/0.11	* Chain [12]: 0
0.03/0.11	  with precondition: [A>=B+1] 
0.03/0.11	
0.03/0.11	
0.03/0.11	Closed-form bounds of start(A,B,C): 
0.03/0.11	-------------------------------------
0.03/0.11	* Chain [14] with precondition: [] 
0.03/0.11	    - Upper bound: 0 
0.03/0.11	    - Complexity: constant 
0.03/0.11	* Chain [13] with precondition: [B>=A] 
0.03/0.11	    - Upper bound: -2*A+2*B+2 
0.03/0.11	    - Complexity: n 
0.03/0.11	* Chain [12] with precondition: [A>=B+1] 
0.03/0.11	    - Upper bound: 0 
0.03/0.11	    - Complexity: constant 
0.03/0.11	
0.03/0.11	### Maximum cost of start(A,B,C): nat(-A+B+1)*2 
0.03/0.11	Asymptotic class: n 
0.03/0.11	* Total analysis performed in 57 ms.
0.03/0.11	
0.03/0.21	EOF