1.52/1.68	WORST_CASE(?,O(n^1))  
1.52/1.68	
1.52/1.68	Preprocessing Cost Relations
1.52/1.68	=====================================
1.52/1.68	
1.52/1.68	#### Computed strongly connected components 
1.52/1.68	0. recursive  : [lbl121/11,lbl141/11,lbl171/11,lbl191/11,lbl21/11,lbl81/11]
1.52/1.68	1. non_recursive  : [exit_location/1]
1.52/1.68	2. non_recursive  : [stop/11]
1.52/1.68	3. non_recursive  : [lbl81_loop_cont/12]
1.52/1.68	4. non_recursive  : [start/11]
1.52/1.68	5. non_recursive  : [start0/11]
1.52/1.68	
1.52/1.68	#### Obtained direct recursion through partial evaluation 
1.52/1.68	0. SCC is partially evaluated into lbl81/11
1.52/1.68	1. SCC is completely evaluated into other SCCs
1.52/1.68	2. SCC is completely evaluated into other SCCs
1.52/1.68	3. SCC is partially evaluated into lbl81_loop_cont/12
1.52/1.68	4. SCC is partially evaluated into start/11
1.52/1.68	5. SCC is partially evaluated into start0/11
1.52/1.68	
1.52/1.68	Control-Flow Refinement of Cost Relations
1.52/1.68	=====================================
1.52/1.68	
1.52/1.68	### Specialization of cost equations lbl81/11 
1.52/1.68	* CE 16 is refined into CE [19] 
1.52/1.68	* CE 14 is refined into CE [20] 
1.52/1.68	* CE 15 is refined into CE [21] 
1.52/1.68	* CE 11 is refined into CE [22] 
1.52/1.68	* CE 9 is refined into CE [23] 
1.52/1.68	* CE 7 is refined into CE [24] 
1.52/1.68	* CE 5 is refined into CE [25] 
1.52/1.68	* CE 12 is refined into CE [26] 
1.52/1.68	* CE 13 is refined into CE [27] 
1.52/1.68	* CE 10 is refined into CE [28] 
1.52/1.68	* CE 8 is refined into CE [29] 
1.52/1.68	* CE 6 is refined into CE [30] 
1.52/1.68	* CE 4 is refined into CE [31] 
1.52/1.68	
1.52/1.68	
1.52/1.68	### Cost equations --> "Loop" of lbl81/11 
1.52/1.68	* CEs [26] --> Loop 19 
1.52/1.68	* CEs [27] --> Loop 20 
1.52/1.68	* CEs [28] --> Loop 21 
1.52/1.68	* CEs [29] --> Loop 22 
1.52/1.68	* CEs [30] --> Loop 23 
1.52/1.68	* CEs [31] --> Loop 24 
1.52/1.68	* CEs [19] --> Loop 25 
1.52/1.68	* CEs [20] --> Loop 26 
1.52/1.68	* CEs [21] --> Loop 27 
1.52/1.68	* CEs [22] --> Loop 28 
1.52/1.68	* CEs [23] --> Loop 29 
1.52/1.68	* CEs [24] --> Loop 30 
1.52/1.68	* CEs [25] --> Loop 31 
1.52/1.68	
1.52/1.68	### Ranking functions of CR lbl81(A,B,D,F,H,J,L,M,N,O,P) 
1.52/1.68	* RF of phase [19,20,21,22,23,24]: [A-H,-H+J]
1.52/1.68	
1.52/1.68	#### Partial ranking functions of CR lbl81(A,B,D,F,H,J,L,M,N,O,P) 
1.52/1.68	* Partial RF of phase [19,20,21,22,23,24]:
1.52/1.68	  - RF of loop [19:1,20:1,21:1,22:1,23:1,24:1]:
1.52/1.68	    A-H
1.52/1.68	    -H+J
1.52/1.68	  - RF of loop [21:1]:
1.52/1.68	    A+B-1 depends on loops [22:1] 
1.52/1.68	    B+J-1 depends on loops [22:1] 
1.52/1.68	  - RF of loop [21:1,23:1]:
1.52/1.68	    A+B+D-1 depends on loops [22:1,24:1] 
1.52/1.68	    B+D+J-1 depends on loops [22:1,24:1] 
1.52/1.68	  - RF of loop [21:1,24:1]:
1.52/1.68	    A+B-D-1 depends on loops [22:1,23:1] 
1.52/1.68	    B-D+J-1 depends on loops [22:1,23:1] 
1.52/1.68	  - RF of loop [22:1]:
1.52/1.68	    A-B-1 depends on loops [21:1] 
1.52/1.68	    -B+J-1 depends on loops [21:1] 
1.52/1.68	  - RF of loop [22:1,23:1]:
1.52/1.68	    A-B+D-1 depends on loops [21:1,24:1] 
1.52/1.68	    -B+D+J-1 depends on loops [21:1,24:1] 
1.52/1.68	  - RF of loop [22:1,24:1]:
1.52/1.68	    A-B-D-1 depends on loops [21:1,23:1] 
1.52/1.68	    -B-D+J-1 depends on loops [21:1,23:1] 
1.52/1.68	  - RF of loop [23:1]:
1.52/1.68	    A+D-1 depends on loops [24:1] 
1.52/1.68	    D+J-1 depends on loops [24:1] 
1.52/1.68	  - RF of loop [24:1]:
1.52/1.68	    A-D-1 depends on loops [23:1] 
1.52/1.68	    -D+J-1 depends on loops [23:1] 
1.52/1.68	
1.52/1.68	
1.52/1.68	### Specialization of cost equations lbl81_loop_cont/12 
1.52/1.68	* CE 18 is refined into CE [32] 
1.52/1.68	* CE 17 is refined into CE [33] 
1.52/1.68	
1.52/1.68	
1.52/1.68	### Cost equations --> "Loop" of lbl81_loop_cont/12 
1.52/1.68	* CEs [32] --> Loop 32 
1.52/1.68	* CEs [33] --> Loop 33 
1.52/1.68	
1.52/1.68	### Ranking functions of CR lbl81_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L) 
1.52/1.68	
1.52/1.68	#### Partial ranking functions of CR lbl81_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L) 
1.52/1.68	
1.52/1.68	
1.52/1.68	### Specialization of cost equations start/11 
1.52/1.68	* CE 3 is refined into CE [34,35,36,37,38,39,40,41,42,43,44,45,46,47] 
1.52/1.68	* CE 2 is refined into CE [48] 
1.52/1.68	
1.52/1.68	
1.52/1.68	### Cost equations --> "Loop" of start/11 
1.52/1.68	* CEs [38,39,40,41,44,45,47] --> Loop 34 
1.52/1.68	* CEs [46] --> Loop 35 
1.52/1.68	* CEs [48] --> Loop 36 
1.52/1.68	* CEs [34,35,36,37,42,43] --> Loop 37 
1.52/1.68	
1.52/1.68	### Ranking functions of CR start(A,B,C,D,E,F,G,H,I,J,L) 
1.52/1.68	
1.52/1.68	#### Partial ranking functions of CR start(A,B,C,D,E,F,G,H,I,J,L) 
1.52/1.68	
1.52/1.68	
1.52/1.68	### Specialization of cost equations start0/11 
1.52/1.68	* CE 1 is refined into CE [49,50,51,52] 
1.52/1.68	
1.52/1.68	
1.52/1.68	### Cost equations --> "Loop" of start0/11 
1.52/1.68	* CEs [52] --> Loop 38 
1.52/1.68	* CEs [51] --> Loop 39 
1.52/1.68	* CEs [50] --> Loop 40 
1.52/1.68	* CEs [49] --> Loop 41 
1.52/1.68	
1.52/1.68	### Ranking functions of CR start0(A,B,C,D,E,F,G,H,I,J,L) 
1.52/1.68	
1.52/1.68	#### Partial ranking functions of CR start0(A,B,C,D,E,F,G,H,I,J,L) 
1.52/1.68	
1.52/1.68	
1.52/1.68	Computing Bounds
1.52/1.68	=====================================
1.52/1.68	
1.52/1.68	#### Cost of chains of lbl81(A,B,D,F,H,J,L,M,N,O,P):
1.52/1.68	* Chain [[19,20,21,22,23,24],31]: 6*it(19)+0
1.52/1.68	  Such that:aux(69) =< -H+P
1.52/1.68	it(19) =< aux(69)
1.52/1.68	
1.52/1.68	  with precondition: [L=2,O=0,A=J,A=P,A>=H+1,H>=B+D+1,D+H>=B+1,B+H>=D+1,B+D+H>=1,A+M+N>=B+D+H+1,A+D+M+1>=B+H+N,A+B+N>=D+H+M+1,A+B+D+1>=H+M+N] 
1.52/1.68	
1.52/1.68	* Chain [[19,20,21,22,23,24],30]: 6*it(19)+0
1.52/1.68	  Such that:aux(70) =< -H+P
1.52/1.68	it(19) =< aux(70)
1.52/1.68	
1.52/1.68	  with precondition: [L=2,O=1,A=J,A=P,A>=H+1,H>=B+D+1,D+H>=B+1,B+H>=D+1,B+D+H>=1,A+M+N+1>=B+D+H,A+D+M>=B+H+N+1,A+B+N+1>=D+H+M,A+B+D>=H+M+N+1] 
1.52/1.68	
1.52/1.68	* Chain [[19,20,21,22,23,24],29]: 6*it(19)+0
1.52/1.68	  Such that:aux(71) =< -H+P
1.52/1.68	it(19) =< aux(71)
1.52/1.68	
1.52/1.68	  with precondition: [L=2,O=2,A=J,A=P,A>=H+1,H>=B+D+1,D+H>=B+1,B+H>=D+1,B+D+H>=1,A+M+N>=B+D+H+1,A+D+M>=B+H+N+1,A+B+N+1>=D+H+M,A+B+D+1>=H+M+N] 
1.52/1.68	
1.52/1.68	* Chain [[19,20,21,22,23,24],28]: 6*it(19)+0
1.52/1.68	  Such that:aux(72) =< -H+P
1.52/1.68	it(19) =< aux(72)
1.52/1.68	
1.52/1.68	  with precondition: [L=2,O=3,A=J,A=P,A>=H+1,H>=B+D+1,D+H>=B+1,B+H>=D+1,B+D+H>=1,A+M+N+1>=B+D+H,A+D+M+1>=B+H+N,A+B+N>=D+H+M+1,A+B+D>=H+M+N+1] 
1.52/1.68	
1.52/1.68	* Chain [[19,20,21,22,23,24],27]: 6*it(19)+0
1.52/1.68	  Such that:aux(73) =< -H+J
1.52/1.68	it(19) =< aux(73)
1.52/1.68	
1.52/1.68	  with precondition: [L=2,A=J,A=P,0>=O+1,A>=H+1,H>=B+D+1,D+H>=B+1,B+H>=D+1,B+D+H>=1,A+M+N>=B+D+H,A+D+M>=B+H+N,A+B+N>=D+H+M,A+B+D>=H+M+N] 
1.52/1.68	
1.52/1.68	* Chain [[19,20,21,22,23,24],26]: 6*it(19)+0
1.52/1.68	  Such that:aux(74) =< -H+J
1.52/1.68	it(19) =< aux(74)
1.52/1.68	
1.52/1.68	  with precondition: [L=2,A=J,A=P,O>=4,A>=H+1,H>=B+D+1,D+H>=B+1,B+H>=D+1,B+D+H>=1,A+M+N>=B+D+H,A+D+M>=B+H+N,A+B+N>=D+H+M,A+B+D>=H+M+N] 
1.52/1.68	
1.52/1.68	* Chain [[19,20,21,22,23,24],25]: 6*it(19)+0
1.52/1.68	  Such that:aux(75) =< -H+J
1.52/1.68	it(19) =< aux(75)
1.52/1.68	
1.52/1.68	  with precondition: [L=3,A=J,A>=H+1,H>=B+D+1,D+H>=B+1,B+H>=D+1,B+D+H>=1] 
1.52/1.68	
1.52/1.68	* Chain [31]: 0
1.52/1.68	  with precondition: [F=0,L=2,O=0,A=H,A=J,B=M,D+1=N,A=P,A>=B+D+1,A+D>=B+1,A+B>=D+1,A+B+D>=1] 
1.52/1.68	
1.52/1.68	* Chain [30]: 0
1.52/1.68	  with precondition: [F=1,L=2,O=1,A=H,A=J,B=M,D=N+1,A=P,A>=B+D+1,A+D>=B+1,A+B>=D+1,A+B+D>=1] 
1.52/1.68	
1.52/1.68	* Chain [29]: 0
1.52/1.68	  with precondition: [F=2,L=2,O=2,A=H,A=J,B+1=M,D=N,A=P,A>=B+D+1,A+D>=B+1,A+B>=D+1,A+B+D>=1] 
1.52/1.68	
1.52/1.68	* Chain [28]: 0
1.52/1.68	  with precondition: [F=3,L=2,O=3,A=H,A=J,B=M+1,D=N,A=P,A>=B+D+1,A+D>=B+1,A+B>=D+1,A+B+D>=1] 
1.52/1.68	
1.52/1.68	* Chain [27]: 0
1.52/1.68	  with precondition: [L=2,A=H,A=J,B=M,D=N,F=O,A=P,0>=F+1,A>=B+D+1,A+D>=B+1,A+B>=D+1,A+B+D>=1] 
1.52/1.68	
1.52/1.68	* Chain [26]: 0
1.52/1.68	  with precondition: [L=2,A=H,A=J,B=M,D=N,F=O,A=P,F>=4,A>=B+D+1,A+D>=B+1,A+B>=D+1,A+B+D>=1] 
1.52/1.68	
1.52/1.68	* Chain [25]: 0
1.52/1.68	  with precondition: [L=3,J=A,J>=H,H>=B+D+1,D+H>=B+1,B+H>=D+1,B+D+H>=1] 
1.52/1.68	
1.52/1.68	
1.52/1.68	#### Cost of chains of lbl81_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L):
1.52/1.68	* Chain [33]: 0
1.52/1.68	  with precondition: [A=2,K=B,K>=1] 
1.52/1.68	
1.52/1.68	* Chain [32]: 0
1.52/1.68	  with precondition: [A=3,K=B,K>=1] 
1.52/1.68	
1.52/1.68	
1.52/1.68	#### Cost of chains of start(A,B,C,D,E,F,G,H,I,J,L):
1.52/1.68	* Chain [37]: 0
1.52/1.68	  with precondition: [A=1,J=1,C=B,E=D,G=F,I=H] 
1.52/1.68	
1.52/1.68	* Chain [36]: 0
1.52/1.68	  with precondition: [J=A,C=B,E=D,G=F,I=H,0>=J] 
1.52/1.68	
1.52/1.68	* Chain [35]: 0
1.52/1.68	  with precondition: [J=A,C=B,E=D,G=F,I=H,J>=1] 
1.52/1.68	
1.52/1.68	* Chain [34]: 42*s(2)+0
1.52/1.68	  Such that:aux(76) =< A
1.52/1.68	s(2) =< aux(76)
1.52/1.68	
1.52/1.68	  with precondition: [J=A,C=B,E=D,G=F,I=H,J>=2] 
1.52/1.68	
1.52/1.68	
1.52/1.68	#### Cost of chains of start0(A,B,C,D,E,F,G,H,I,J,L):
1.52/1.68	* Chain [41]: 0
1.52/1.68	  with precondition: [A=1] 
1.52/1.68	
1.52/1.68	* Chain [40]: 0
1.52/1.68	  with precondition: [0>=A] 
1.52/1.68	
1.52/1.68	* Chain [39]: 0
1.52/1.68	  with precondition: [A>=1] 
1.52/1.68	
1.52/1.68	* Chain [38]: 42*s(16)+0
1.52/1.68	  Such that:s(15) =< A
1.52/1.68	s(16) =< s(15)
1.52/1.68	
1.52/1.68	  with precondition: [A>=2] 
1.52/1.68	
1.52/1.68	
1.52/1.68	Closed-form bounds of start0(A,B,C,D,E,F,G,H,I,J,L): 
1.52/1.68	-------------------------------------
1.52/1.68	* Chain [41] with precondition: [A=1] 
1.52/1.68	    - Upper bound: 0 
1.52/1.68	    - Complexity: constant 
1.52/1.68	* Chain [40] with precondition: [0>=A] 
1.52/1.68	    - Upper bound: 0 
1.52/1.68	    - Complexity: constant 
1.52/1.68	* Chain [39] with precondition: [A>=1] 
1.52/1.68	    - Upper bound: 0 
1.52/1.68	    - Complexity: constant 
1.52/1.68	* Chain [38] with precondition: [A>=2] 
1.52/1.68	    - Upper bound: 42*A 
1.52/1.68	    - Complexity: n 
1.52/1.68	
1.52/1.68	### Maximum cost of start0(A,B,C,D,E,F,G,H,I,J,L): nat(A)*42 
1.52/1.68	Asymptotic class: n 
1.52/1.68	* Total analysis performed in 1529 ms.
1.52/1.68	
1.68/1.78	EOF