1.02/1.04	WORST_CASE(?,O(n^1))  
1.02/1.04	
1.02/1.04	Preprocessing Cost Relations
1.02/1.04	=====================================
1.02/1.04	
1.02/1.04	#### Computed strongly connected components 
1.02/1.04	0. recursive  : [f1/40]
1.02/1.04	1. non_recursive  : [exit_location/1]
1.02/1.04	2. recursive  : [f10/29]
1.02/1.04	3. non_recursive  : [f4/25]
1.02/1.04	4. non_recursive  : [f10_loop_cont/26]
1.02/1.04	5. non_recursive  : [f1_loop_cont/26]
1.02/1.04	6. non_recursive  : [f3/25]
1.02/1.04	
1.02/1.04	#### Obtained direct recursion through partial evaluation 
1.02/1.04	0. SCC is partially evaluated into f1/40
1.02/1.04	1. SCC is completely evaluated into other SCCs
1.02/1.04	2. SCC is partially evaluated into f10/29
1.02/1.04	3. SCC is completely evaluated into other SCCs
1.02/1.04	4. SCC is partially evaluated into f10_loop_cont/26
1.02/1.04	5. SCC is partially evaluated into f1_loop_cont/26
1.02/1.04	6. SCC is partially evaluated into f3/25
1.02/1.04	
1.02/1.04	Control-Flow Refinement of Cost Relations
1.02/1.04	=====================================
1.02/1.04	
1.02/1.04	### Specialization of cost equations f1/40 
1.02/1.04	* CE 4 is refined into CE [14] 
1.02/1.04	* CE 5 is refined into CE [15] 
1.02/1.04	* CE 6 is refined into CE [16] 
1.02/1.04	* CE 3 is refined into CE [17] 
1.02/1.04	
1.02/1.04	
1.02/1.04	### Cost equations --> "Loop" of f1/40 
1.02/1.04	* CEs [17] --> Loop 14 
1.02/1.04	* CEs [14] --> Loop 15 
1.02/1.04	* CEs [15] --> Loop 16 
1.02/1.04	* CEs [16] --> Loop 17 
1.02/1.04	
1.02/1.04	### Ranking functions of CR f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2) 
1.02/1.04	* RF of phase [14]: [A-B]
1.02/1.04	
1.02/1.04	#### Partial ranking functions of CR f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2) 
1.02/1.04	* Partial RF of phase [14]:
1.02/1.04	  - RF of loop [14:1]:
1.02/1.04	    A-B
1.02/1.04	
1.02/1.04	
1.02/1.04	### Specialization of cost equations f10/29 
1.02/1.04	* CE 11 is refined into CE [18] 
1.02/1.04	* CE 10 is refined into CE [19] 
1.02/1.04	* CE 9 is refined into CE [20] 
1.02/1.04	
1.02/1.04	
1.02/1.04	### Cost equations --> "Loop" of f10/29 
1.02/1.04	* CEs [20] --> Loop 18 
1.02/1.04	* CEs [18] --> Loop 19 
1.02/1.04	* CEs [19] --> Loop 20 
1.02/1.04	
1.02/1.04	### Ranking functions of CR f10(A,B,C,I,K,N,P,Q,R,S,T,U,V,W,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1) 
1.02/1.04	* RF of phase [18]: [U+1]
1.02/1.04	
1.02/1.04	#### Partial ranking functions of CR f10(A,B,C,I,K,N,P,Q,R,S,T,U,V,W,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1) 
1.02/1.04	* Partial RF of phase [18]:
1.02/1.04	  - RF of loop [18:1]:
1.02/1.04	    U+1
1.02/1.04	
1.02/1.04	
1.02/1.04	### Specialization of cost equations f10_loop_cont/26 
1.02/1.04	* CE 13 is refined into CE [21] 
1.02/1.04	* CE 12 is refined into CE [22] 
1.02/1.04	
1.02/1.04	
1.02/1.04	### Cost equations --> "Loop" of f10_loop_cont/26 
1.02/1.04	* CEs [21] --> Loop 21 
1.02/1.04	* CEs [22] --> Loop 22 
1.02/1.04	
1.02/1.04	### Ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z) 
1.02/1.04	
1.02/1.04	#### Partial ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z) 
1.02/1.04	
1.02/1.04	
1.02/1.04	### Specialization of cost equations f1_loop_cont/26 
1.02/1.04	* CE 8 is refined into CE [23,24,25,26] 
1.02/1.04	* CE 7 is refined into CE [27] 
1.02/1.04	
1.02/1.04	
1.02/1.04	### Cost equations --> "Loop" of f1_loop_cont/26 
1.02/1.04	* CEs [26] --> Loop 23 
1.02/1.04	* CEs [25] --> Loop 24 
1.02/1.04	* CEs [24] --> Loop 25 
1.02/1.04	* CEs [23] --> Loop 26 
1.02/1.04	* CEs [27] --> Loop 27 
1.02/1.04	
1.02/1.04	### Ranking functions of CR f1_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z) 
1.02/1.04	
1.02/1.04	#### Partial ranking functions of CR f1_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z) 
1.02/1.04	
1.02/1.04	
1.02/1.04	### Specialization of cost equations f3/25 
1.02/1.04	* CE 2 is refined into CE [28,29,30,31,32,33,34,35,36,37] 
1.02/1.04	* CE 1 is refined into CE [38] 
1.02/1.04	
1.02/1.04	
1.02/1.04	### Cost equations --> "Loop" of f3/25 
1.02/1.04	* CEs [34,36] --> Loop 28 
1.02/1.04	* CEs [29,35,37] --> Loop 29 
1.02/1.04	* CEs [28] --> Loop 30 
1.02/1.04	* CEs [38] --> Loop 31 
1.02/1.04	* CEs [30,32] --> Loop 32 
1.02/1.04	* CEs [31,33] --> Loop 33 
1.02/1.04	
1.02/1.04	### Ranking functions of CR f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,I1) 
1.02/1.04	
1.02/1.04	#### Partial ranking functions of CR f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,I1) 
1.02/1.04	
1.02/1.04	
1.02/1.04	Computing Bounds
1.02/1.04	=====================================
1.02/1.04	
1.02/1.04	#### Cost of chains of f1(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1,X1,Y1,Z1,A2,B2):
1.02/1.04	* Chain [[14],17]: 1*it(14)+0
1.02/1.04	  Such that:it(14) =< A-B
1.02/1.04	
1.02/1.04	  with precondition: [I1=3,C=K,B>=2,A>=B+1] 
1.02/1.04	
1.02/1.04	* Chain [[14],16]: 1*it(14)+0
1.02/1.04	  Such that:it(14) =< A-B
1.02/1.04	
1.02/1.04	  with precondition: [I1=4,X1=0,Z1=0,C=K,L1=T1,A=V1+1,L1=W1,L1=Y1,L1=A2,L1=B2,0>=L1+1,B>=2,J1>=2,A>=B+1] 
1.02/1.04	
1.02/1.04	* Chain [[14],15]: 1*it(14)+0
1.02/1.04	  Such that:it(14) =< A-B
1.02/1.04	
1.02/1.04	  with precondition: [I1=4,X1=0,Z1=0,C=K,L1=T1,A=V1+1,L1=W1,L1=Y1,L1=A2,L1=B2,B>=2,J1>=2,L1>=1,A>=B+1] 
1.02/1.04	
1.02/1.04	* Chain [17]: 0
1.02/1.04	  with precondition: [I1=3,K=C,B>=2,A>=B] 
1.02/1.04	
1.02/1.04	* Chain [16]: 0
1.02/1.04	  with precondition: [I1=4,X1=0,Z1=0,B=A,K=C,M1=D,N1=E,O1=F,P1=G,Q1=H,R1=I,S1=J,U1=L,V1=M,K=L1,K=T1,K=W1,K=Y1,K=A2,K=B2,0>=K+1,B>=2,J1>=2] 
1.02/1.04	
1.02/1.04	* Chain [15]: 0
1.02/1.04	  with precondition: [I1=4,X1=0,Z1=0,B=A,K=C,M1=D,N1=E,O1=F,P1=G,Q1=H,R1=I,S1=J,U1=L,V1=M,K=L1,K=T1,K=W1,K=Y1,K=A2,K=B2,B>=2,K>=1,J1>=2] 
1.02/1.04	
1.02/1.04	
1.02/1.04	#### Cost of chains of f10(A,B,C,I,K,N,P,Q,R,S,T,U,V,W,I1,J1,K1,L1,M1,N1,O1,P1,Q1,R1,S1,T1,U1,V1,W1):
1.02/1.04	* Chain [[18],20]: 1*it(18)+0
1.02/1.04	  Such that:it(18) =< U-U1
1.02/1.04	
1.02/1.04	  with precondition: [N=0,P=0,I1=2,L1=N1,U1=W1,J1>=2,K1>=2,U1>=0,U>=U1+1] 
1.02/1.04	
1.02/1.04	* Chain [[18],19]: 1*it(18)+0
1.02/1.04	  Such that:it(18) =< U+1
1.02/1.04	
1.02/1.04	  with precondition: [P=0,I1=3,U>=0] 
1.02/1.04	
1.02/1.04	* Chain [20]: 0
1.02/1.04	  with precondition: [I1=2,K1=B,L1=C,N1=K,P=N,V1=V,W1=W,U=U1,U>=0,J1>=2] 
1.02/1.04	
1.02/1.04	* Chain [19]: 0
1.02/1.04	  with precondition: [I1=3] 
1.02/1.04	
1.02/1.04	
1.02/1.04	#### Cost of chains of f10_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z):
1.02/1.04	* Chain [22]: 0
1.02/1.04	  with precondition: [A=2] 
1.02/1.04	
1.02/1.04	* Chain [21]: 0
1.02/1.04	  with precondition: [A=3] 
1.02/1.04	
1.02/1.04	
1.02/1.04	#### Cost of chains of f1_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,Y,Z):
1.02/1.04	* Chain [27]: 0
1.02/1.04	  with precondition: [A=3,V=P] 
1.02/1.04	
1.02/1.04	* Chain [26]: 1*s(1)+0
1.02/1.04	  Such that:s(1) =< V
1.02/1.04	
1.02/1.04	  with precondition: [A=4,O=0,Q=0,V=P,V>=1] 
1.02/1.04	
1.02/1.04	* Chain [25]: 1*s(2)+0
1.02/1.04	  Such that:s(2) =< P+1
1.02/1.04	
1.02/1.04	  with precondition: [A=4,Q=0,V=P,V>=0] 
1.02/1.04	
1.02/1.04	* Chain [24]: 0
1.02/1.04	  with precondition: [A=4,Q=O,V=P,V>=0] 
1.02/1.04	
1.02/1.04	* Chain [23]: 0
1.02/1.04	  with precondition: [A=4,V=P] 
1.02/1.04	
1.02/1.04	
1.02/1.04	#### Cost of chains of f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,I1):
1.02/1.04	* Chain [33]: 0
1.02/1.04	  with precondition: [A=2] 
1.02/1.04	
1.02/1.04	* Chain [32]: 2*s(3)+0
1.02/1.04	  Such that:aux(1) =< U+1
1.02/1.04	s(3) =< aux(1)
1.02/1.04	
1.02/1.04	  with precondition: [A=2,U>=0] 
1.02/1.04	
1.02/1.04	* Chain [31]: 0
1.02/1.04	  with precondition: [0>=A] 
1.02/1.04	
1.02/1.04	* Chain [30]: 0
1.02/1.04	  with precondition: [A>=2] 
1.02/1.04	
1.02/1.04	* Chain [29]: 3*s(5)+0
1.02/1.04	  Such that:aux(2) =< A
1.02/1.04	s(5) =< aux(2)
1.02/1.04	
1.02/1.04	  with precondition: [A>=3] 
1.02/1.04	
1.02/1.04	* Chain [28]: 2*s(8)+2*s(9)+0
1.02/1.04	  Such that:aux(3) =< A
1.02/1.04	aux(4) =< U+1
1.02/1.04	s(8) =< aux(3)
1.02/1.04	s(9) =< aux(4)
1.02/1.04	
1.02/1.04	  with precondition: [A>=3,U>=0] 
1.02/1.04	
1.02/1.04	
1.02/1.04	Closed-form bounds of f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,I1): 
1.02/1.04	-------------------------------------
1.02/1.04	* Chain [33] with precondition: [A=2] 
1.02/1.04	    - Upper bound: 0 
1.02/1.04	    - Complexity: constant 
1.02/1.04	* Chain [32] with precondition: [A=2,U>=0] 
1.02/1.04	    - Upper bound: 2*U+2 
1.02/1.04	    - Complexity: n 
1.02/1.04	* Chain [31] with precondition: [0>=A] 
1.02/1.04	    - Upper bound: 0 
1.02/1.04	    - Complexity: constant 
1.02/1.04	* Chain [30] with precondition: [A>=2] 
1.02/1.04	    - Upper bound: 0 
1.02/1.04	    - Complexity: constant 
1.02/1.04	* Chain [29] with precondition: [A>=3] 
1.02/1.04	    - Upper bound: 3*A 
1.02/1.04	    - Complexity: n 
1.02/1.04	* Chain [28] with precondition: [A>=3,U>=0] 
1.02/1.04	    - Upper bound: 2*A+2*U+2 
1.02/1.04	    - Complexity: n 
1.02/1.04	
1.02/1.04	### Maximum cost of f3(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R,S,T,U,V,W,X,I1): max([nat(U+1)*2,nat(A)*2+max([nat(A),nat(U+1)*2])]) 
1.02/1.04	Asymptotic class: n 
1.02/1.04	* Total analysis performed in 898 ms.
1.02/1.04	
1.05/1.14	EOF