1.01/1.04	WORST_CASE(?,O(n^1))  
1.01/1.04	
1.01/1.04	Preprocessing Cost Relations
1.01/1.04	=====================================
1.01/1.04	
1.01/1.04	#### Computed strongly connected components 
1.01/1.04	0. recursive  : [lbl111/17]
1.01/1.04	1. non_recursive  : [exit_location/1]
1.01/1.04	2. recursive  : [lbl221/17]
1.01/1.04	3. recursive  : [lbl161/17,lbl221_loop_cont/18]
1.01/1.04	4. non_recursive  : [stop/9]
1.01/1.04	5. non_recursive  : [lbl161_loop_cont/10]
1.01/1.04	6. non_recursive  : [lbl111_loop_cont/10]
1.01/1.04	7. non_recursive  : [start/9]
1.01/1.04	8. non_recursive  : [start0/9]
1.01/1.04	
1.01/1.04	#### Obtained direct recursion through partial evaluation 
1.01/1.04	0. SCC is partially evaluated into lbl111/17
1.01/1.04	1. SCC is completely evaluated into other SCCs
1.01/1.04	2. SCC is partially evaluated into lbl221/17
1.01/1.04	3. SCC is partially evaluated into lbl161/17
1.01/1.04	4. SCC is completely evaluated into other SCCs
1.01/1.04	5. SCC is partially evaluated into lbl161_loop_cont/10
1.01/1.04	6. SCC is partially evaluated into lbl111_loop_cont/10
1.01/1.04	7. SCC is partially evaluated into start/9
1.01/1.04	8. SCC is partially evaluated into start0/9
1.01/1.04	
1.01/1.04	Control-Flow Refinement of Cost Relations
1.01/1.04	=====================================
1.01/1.04	
1.01/1.04	### Specialization of cost equations lbl111/17 
1.01/1.04	* CE 6 is refined into CE [21] 
1.01/1.04	* CE 8 is refined into CE [22] 
1.01/1.04	* CE 7 is refined into CE [23] 
1.01/1.04	* CE 5 is refined into CE [24] 
1.01/1.04	* CE 4 is refined into CE [25] 
1.01/1.04	
1.01/1.04	
1.01/1.04	### Cost equations --> "Loop" of lbl111/17 
1.01/1.04	* CEs [25] --> Loop 20 
1.01/1.04	* CEs [21] --> Loop 21 
1.01/1.04	* CEs [22] --> Loop 22 
1.01/1.04	* CEs [23] --> Loop 23 
1.01/1.04	* CEs [24] --> Loop 24 
1.01/1.04	
1.01/1.04	### Ranking functions of CR lbl111(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
1.01/1.04	* RF of phase [20]: [-A/11-D+112/11,-D-H/11+112/11,-F/11+101/11]
1.01/1.04	
1.01/1.04	#### Partial ranking functions of CR lbl111(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
1.01/1.04	* Partial RF of phase [20]:
1.01/1.04	  - RF of loop [20:1]:
1.01/1.04	    -A/11-D+112/11
1.01/1.04	    -D-H/11+112/11
1.01/1.04	    -F/11+101/11
1.01/1.04	
1.01/1.04	
1.01/1.04	### Specialization of cost equations lbl221/17 
1.01/1.04	* CE 16 is refined into CE [26] 
1.01/1.04	* CE 13 is refined into CE [27] 
1.01/1.04	* CE 14 is refined into CE [28] 
1.01/1.04	* CE 15 is refined into CE [29] 
1.01/1.04	
1.01/1.04	
1.01/1.04	### Cost equations --> "Loop" of lbl221/17 
1.01/1.04	* CEs [28] --> Loop 25 
1.01/1.04	* CEs [29] --> Loop 26 
1.01/1.04	* CEs [26] --> Loop 27 
1.01/1.04	* CEs [27] --> Loop 28 
1.01/1.04	
1.01/1.04	### Ranking functions of CR lbl221(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
1.01/1.04	* RF of phase [25,26]: [10*D-F+91]
1.01/1.04	
1.01/1.04	#### Partial ranking functions of CR lbl221(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
1.01/1.04	* Partial RF of phase [25,26]:
1.01/1.04	  - RF of loop [25:1]:
1.01/1.04	    -F+111 depends on loops [26:1] 
1.01/1.04	  - RF of loop [26:1]:
1.01/1.04	    D-2
1.01/1.04	    F/9-110/9 depends on loops [25:1] 
1.01/1.04	
1.01/1.04	
1.01/1.04	### Specialization of cost equations lbl161/17 
1.01/1.04	* CE 20 is refined into CE [30] 
1.01/1.04	* CE 19 is refined into CE [31] 
1.01/1.04	
1.01/1.04	
1.01/1.04	### Cost equations --> "Loop" of lbl161/17 
1.01/1.04	* CEs [30] --> Loop 29 
1.01/1.04	* CEs [31] --> Loop 30 
1.01/1.04	
1.01/1.04	### Ranking functions of CR lbl161(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
1.01/1.04	
1.01/1.04	#### Partial ranking functions of CR lbl161(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
1.01/1.04	
1.01/1.04	
1.01/1.04	### Specialization of cost equations lbl161_loop_cont/10 
1.01/1.04	* CE 18 is refined into CE [32] 
1.01/1.04	* CE 17 is refined into CE [33] 
1.01/1.04	
1.01/1.04	
1.01/1.04	### Cost equations --> "Loop" of lbl161_loop_cont/10 
1.01/1.04	* CEs [32] --> Loop 31 
1.01/1.04	* CEs [33] --> Loop 32 
1.01/1.04	
1.01/1.04	### Ranking functions of CR lbl161_loop_cont(A,B,C,D,E,F,G,H,I,J) 
1.01/1.04	
1.01/1.04	#### Partial ranking functions of CR lbl161_loop_cont(A,B,C,D,E,F,G,H,I,J) 
1.01/1.04	
1.01/1.04	
1.01/1.04	### Specialization of cost equations lbl111_loop_cont/10 
1.01/1.04	* CE 9 is refined into CE [34,35] 
1.01/1.04	* CE 10 is refined into CE [36,37,38,39] 
1.01/1.04	* CE 12 is refined into CE [40] 
1.01/1.04	* CE 11 is refined into CE [41,42] 
1.01/1.04	
1.01/1.04	
1.01/1.04	### Cost equations --> "Loop" of lbl111_loop_cont/10 
1.01/1.04	* CEs [38,39] --> Loop 33 
1.01/1.04	* CEs [35] --> Loop 34 
1.01/1.04	* CEs [36,37] --> Loop 35 
1.01/1.04	* CEs [34] --> Loop 36 
1.01/1.04	* CEs [40] --> Loop 37 
1.01/1.04	* CEs [41] --> Loop 38 
1.01/1.04	* CEs [42] --> Loop 39 
1.01/1.04	
1.01/1.04	### Ranking functions of CR lbl111_loop_cont(A,B,C,D,E,F,G,H,I,J) 
1.01/1.04	
1.01/1.04	#### Partial ranking functions of CR lbl111_loop_cont(A,B,C,D,E,F,G,H,I,J) 
1.01/1.04	
1.01/1.04	
1.01/1.04	### Specialization of cost equations start/9 
1.01/1.04	* CE 2 is refined into CE [43] 
1.01/1.04	* CE 3 is refined into CE [44,45,46,47,48,49,50,51,52,53] 
1.01/1.04	
1.01/1.04	
1.01/1.04	### Cost equations --> "Loop" of start/9 
1.01/1.04	* CEs [43] --> Loop 40 
1.01/1.04	* CEs [51,52,53] --> Loop 41 
1.01/1.04	* CEs [46,47,48,49] --> Loop 42 
1.01/1.04	* CEs [50] --> Loop 43 
1.01/1.04	* CEs [45] --> Loop 44 
1.01/1.04	* CEs [44] --> Loop 45 
1.01/1.04	
1.01/1.04	### Ranking functions of CR start(A,B,C,D,E,F,G,H,I) 
1.01/1.04	
1.01/1.04	#### Partial ranking functions of CR start(A,B,C,D,E,F,G,H,I) 
1.01/1.04	
1.01/1.04	
1.01/1.04	### Specialization of cost equations start0/9 
1.01/1.04	* CE 1 is refined into CE [54,55,56,57,58,59] 
1.01/1.04	
1.01/1.04	
1.01/1.04	### Cost equations --> "Loop" of start0/9 
1.01/1.04	* CEs [59] --> Loop 46 
1.01/1.04	* CEs [58] --> Loop 47 
1.01/1.04	* CEs [57] --> Loop 48 
1.01/1.04	* CEs [56] --> Loop 49 
1.01/1.04	* CEs [55] --> Loop 50 
1.01/1.04	* CEs [54] --> Loop 51 
1.01/1.04	
1.01/1.04	### Ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 
1.01/1.04	
1.01/1.04	#### Partial ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 
1.01/1.04	
1.01/1.04	
1.01/1.04	Computing Bounds
1.01/1.04	=====================================
1.01/1.04	
1.01/1.04	#### Cost of chains of lbl111(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q):
1.01/1.04	* Chain [[20],23]: 1*it(20)+0
1.01/1.04	  Such that:it(20) =< -A/11-D+112/11
1.01/1.04	
1.01/1.04	  with precondition: [I=5,O=102,B=C,A=H,A=J,B=K,B=L,E=N,G=P,A=Q,A+11*M=111,A+11*D=F+11,100>=F,F>=A+11] 
1.01/1.04	
1.01/1.04	* Chain [[20],22]: 1*it(20)+0
1.01/1.04	  Such that:it(20) =< -F/11+101/11
1.01/1.04	
1.01/1.04	  with precondition: [I=4,B=C,A=H,A+11*D=F+11,100>=F,F>=A+11] 
1.01/1.04	
1.01/1.04	* Chain [[20],21]: 1*it(20)+0
1.01/1.04	  Such that:it(20) =< -A/11-D+112/11
1.01/1.04	
1.01/1.04	  with precondition: [I=5,B=C,A=H,A=J,B=K,B=L,E=N,G=P,A=Q,A+11*D=F+11,A+11*M=O+10,121>=11*M+A,F>=A+11,A+11*M>=112,A+11*M>=F+22] 
1.01/1.04	
1.01/1.04	* Chain [24]: 0
1.01/1.04	  with precondition: [A=100,D=2,F=111,H=100,I=3,J=100,K=91,M=1,O=101,Q=100,C=B,N=E,P=G,C=L] 
1.01/1.04	
1.01/1.04	* Chain [22]: 0
1.01/1.04	  with precondition: [I=4,C=B,A=H,A+11*D=F+11,111>=F,F>=A+11] 
1.01/1.04	
1.01/1.04	* Chain [21]: 0
1.01/1.04	  with precondition: [I=5,C=B,N=E,P=G,A=H,A=J,C=K,C=L,D=M,A=Q,A+11*D=F+11,A+11*D=O+10,D>=2,121>=11*D+A,A+11*D>=112] 
1.01/1.04	
1.01/1.04	
1.01/1.04	#### Cost of chains of lbl221(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q):
1.01/1.04	* Chain [[25,26],28]: 1*it(25)+1*it(26)+0
1.01/1.04	  Such that:it(26) =< D
1.01/1.04	aux(7) =< 10*D-F+91
1.01/1.04	it(25) =< aux(7)
1.01/1.04	it(26) =< aux(7)
1.01/1.04	
1.01/1.04	  with precondition: [I=3,K=91,M=1,O=101,B=C,A=H,A=J,B=L,E=N,G=P,A=Q,111>=F,D>=2,F>=102,91>=A+D,D+108>=F,F+10>=11*D+A] 
1.01/1.04	
1.01/1.04	* Chain [[25,26],27]: 1*it(25)+1*it(26)+0
1.01/1.04	  Such that:aux(5) =< 10*D-F+91
1.01/1.04	aux(6) =< -F-10*H+1001
1.01/1.04	it(26) =< F/10-H/10
1.01/1.04	it(26) =< -H+89
1.01/1.04	aux(6) =< -H+98
1.01/1.04	it(25) =< aux(5)
1.01/1.04	it(26) =< aux(5)
1.01/1.04	it(25) =< aux(6)
1.01/1.04	it(26) =< aux(6)
1.01/1.04	
1.01/1.04	  with precondition: [I=4,B=C,A=H,89>=A,111>=F,D>=2,F>=102,199>=A+F,D+108>=F,F+10>=11*D+A] 
1.01/1.04	
1.01/1.04	* Chain [28]: 0
1.01/1.04	  with precondition: [D=2,F=111,I=3,K=91,M=1,O=101,B=C,N=E,P=G,A=H,A=J,B=L,A=Q,89>=A] 
1.01/1.04	
1.01/1.04	* Chain [27]: 0
1.01/1.04	  with precondition: [I=4] 
1.01/1.04	
1.01/1.04	
1.01/1.04	#### Cost of chains of lbl161(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q):
1.01/1.04	* Chain [30]: 0
1.01/1.04	  with precondition: [B=91,D=1,F=101,I=2,K=91,M=1,O=101,L=C,N=E,P=G,A=H,A=J,A=Q,89>=A] 
1.01/1.04	
1.01/1.04	* Chain [29]: 0
1.01/1.04	  with precondition: [I=4] 
1.01/1.04	
1.01/1.04	
1.01/1.04	#### Cost of chains of lbl161_loop_cont(A,B,C,D,E,F,G,H,I,J):
1.01/1.04	* Chain [32]: 0
1.01/1.04	  with precondition: [A=2] 
1.01/1.04	
1.01/1.04	* Chain [31]: 0
1.01/1.04	  with precondition: [A=4] 
1.01/1.04	
1.01/1.04	
1.01/1.04	#### Cost of chains of lbl111_loop_cont(A,B,C,D,E,F,G,H,I,J):
1.01/1.04	* Chain [39]: 0
1.01/1.04	  with precondition: [A=3] 
1.01/1.04	
1.01/1.04	* Chain [38]: 0
1.01/1.04	  with precondition: [A=3,C=91,E=1,G=101,B=I,89>=B] 
1.01/1.04	
1.01/1.04	* Chain [37]: 0
1.01/1.04	  with precondition: [A=4] 
1.01/1.04	
1.01/1.04	* Chain [36]: 0
1.01/1.04	  with precondition: [A=5] 
1.01/1.04	
1.01/1.04	* Chain [35]: 1
1.01/1.04	  with precondition: [A=5,E=2,G=111,D=C,B=I,89>=B] 
1.01/1.04	
1.01/1.04	* Chain [34]: 1*s(3)+1*s(4)+0
1.01/1.04	  Such that:s(1) =< 10*E-G+91
1.01/1.04	s(2) =< -G-10*I+1001
1.01/1.04	s(3) =< G/10-I/10
1.01/1.04	s(3) =< -I+89
1.01/1.04	s(2) =< -I+98
1.01/1.04	s(4) =< s(1)
1.01/1.04	s(3) =< s(1)
1.01/1.04	s(4) =< s(2)
1.01/1.04	s(3) =< s(2)
1.01/1.04	
1.01/1.04	  with precondition: [A=5,D=C,B=I,89>=B,111>=G,E>=2,G>=102,199>=B+G,E+108>=G,G+10>=11*E+B] 
1.01/1.04	
1.01/1.04	* Chain [33]: 2*s(5)+2*s(7)+1
1.01/1.04	  Such that:aux(8) =< E
1.01/1.04	aux(9) =< 10*E-G+91
1.01/1.04	s(5) =< aux(8)
1.01/1.04	s(7) =< aux(9)
1.01/1.04	s(5) =< aux(9)
1.01/1.04	
1.01/1.04	  with precondition: [A=5,D=C,B=I,111>=G,E>=2,G>=102,91>=B+E,E+108>=G,G+10>=11*E+B] 
1.01/1.04	
1.01/1.04	
1.01/1.04	#### Cost of chains of start(A,B,C,D,E,F,G,H,I):
1.01/1.04	* Chain [45]: 0
1.01/1.04	  with precondition: [A=100,H=100,C=B,E=D,G=F] 
1.01/1.04	
1.01/1.04	* Chain [44]: 0
1.01/1.04	  with precondition: [H=A,C=B,E=D,G=F,100>=H] 
1.01/1.04	
1.01/1.04	* Chain [43]: 0
1.01/1.04	  with precondition: [H=A,C=B,E=D,G=F,99>=H,H>=90] 
1.01/1.04	
1.01/1.04	* Chain [42]: 4*s(11)+1*s(16)+1*s(17)+2*s(21)+2*s(22)+1
1.01/1.04	  Such that:s(16) =< -A+89
1.01/1.04	s(15) =< -A+98
1.01/1.04	s(16) =< -A/10+51/5
1.01/1.04	s(19) =< -A/11+111/11
1.01/1.04	aux(10) =< -10/11*A+989/11
1.01/1.04	aux(11) =< -A/11+90/11
1.01/1.04	s(11) =< aux(11)
1.01/1.04	s(17) =< aux(10)
1.01/1.04	s(16) =< aux(10)
1.01/1.04	s(17) =< s(15)
1.01/1.04	s(16) =< s(15)
1.01/1.04	s(21) =< s(19)
1.01/1.04	s(22) =< aux(10)
1.01/1.04	s(21) =< aux(10)
1.01/1.04	
1.01/1.04	  with precondition: [H=A,C=B,E=D,G=F,89>=H] 
1.01/1.04	
1.01/1.04	* Chain [41]: 3*s(23)+1*s(27)+1*s(28)+2*s(32)+2*s(33)+1
1.01/1.04	  Such that:aux(12) =< -11*A+1101
1.01/1.04	s(27) =< -A+89
1.01/1.04	aux(13) =< -A+98
1.01/1.04	aux(14) =< -A+101
1.01/1.04	s(31) =< -10/11*A+999/11
1.01/1.04	s(30) =< -A/11+11
1.01/1.04	aux(15) =< -A/11+90/11
1.01/1.04	s(23) =< aux(15)
1.01/1.04	s(25) =< aux(12)
1.01/1.04	s(27) =< aux(12)
1.01/1.04	s(25) =< aux(13)
1.01/1.04	s(28) =< s(25)
1.01/1.04	s(27) =< s(25)
1.01/1.04	s(28) =< aux(13)
1.01/1.04	s(27) =< aux(13)
1.01/1.04	s(30) =< aux(14)
1.01/1.04	s(31) =< aux(14)
1.01/1.04	s(32) =< s(30)
1.01/1.04	s(33) =< s(31)
1.01/1.04	s(32) =< s(31)
1.01/1.04	
1.01/1.04	  with precondition: [H=A,C=B,E=D,G=F,88>=H] 
1.01/1.04	
1.01/1.04	* Chain [40]: 0
1.01/1.04	  with precondition: [H=A,C=B,E=D,G=F,H>=101] 
1.01/1.04	
1.01/1.04	
1.01/1.04	#### Cost of chains of start0(A,B,C,D,E,F,G,H,I):
1.01/1.04	* Chain [51]: 0
1.01/1.04	  with precondition: [A=100] 
1.01/1.04	
1.01/1.04	* Chain [50]: 0
1.01/1.04	  with precondition: [100>=A] 
1.01/1.04	
1.01/1.04	* Chain [49]: 0
1.01/1.04	  with precondition: [99>=A,A>=90] 
1.01/1.04	
1.01/1.04	* Chain [48]: 1*s(34)+4*s(39)+1*s(40)+2*s(41)+2*s(42)+1
1.01/1.04	  Such that:s(34) =< -A+89
1.01/1.04	s(35) =< -A+98
1.01/1.04	s(37) =< -10/11*A+989/11
1.01/1.04	s(34) =< -A/10+51/5
1.01/1.04	s(38) =< -A/11+90/11
1.01/1.04	s(36) =< -A/11+111/11
1.01/1.04	s(39) =< s(38)
1.01/1.04	s(40) =< s(37)
1.01/1.04	s(34) =< s(37)
1.01/1.04	s(40) =< s(35)
1.01/1.04	s(34) =< s(35)
1.01/1.04	s(41) =< s(36)
1.01/1.04	s(42) =< s(37)
1.01/1.04	s(41) =< s(37)
1.01/1.04	
1.01/1.04	  with precondition: [89>=A] 
1.01/1.04	
1.01/1.04	* Chain [47]: 1*s(44)+3*s(50)+1*s(52)+2*s(53)+2*s(54)+1
1.01/1.04	  Such that:s(43) =< -11*A+1101
1.01/1.04	s(44) =< -A+89
1.01/1.04	s(45) =< -A+98
1.01/1.04	s(46) =< -A+101
1.01/1.04	s(47) =< -10/11*A+999/11
1.01/1.04	s(48) =< -A/11+11
1.01/1.04	s(49) =< -A/11+90/11
1.01/1.04	s(50) =< s(49)
1.01/1.04	s(51) =< s(43)
1.01/1.04	s(44) =< s(43)
1.01/1.04	s(51) =< s(45)
1.01/1.04	s(52) =< s(51)
1.01/1.04	s(44) =< s(51)
1.01/1.04	s(52) =< s(45)
1.01/1.04	s(44) =< s(45)
1.01/1.04	s(48) =< s(46)
1.01/1.04	s(47) =< s(46)
1.01/1.04	s(53) =< s(48)
1.01/1.04	s(54) =< s(47)
1.01/1.04	s(53) =< s(47)
1.01/1.04	
1.01/1.04	  with precondition: [88>=A] 
1.01/1.04	
1.01/1.04	* Chain [46]: 0
1.01/1.04	  with precondition: [A>=101] 
1.01/1.04	
1.01/1.04	
1.01/1.04	Closed-form bounds of start0(A,B,C,D,E,F,G,H,I): 
1.01/1.04	-------------------------------------
1.01/1.04	* Chain [51] with precondition: [A=100] 
1.01/1.04	    - Upper bound: 0 
1.01/1.04	    - Complexity: constant 
1.01/1.04	* Chain [50] with precondition: [100>=A] 
1.01/1.04	    - Upper bound: 0 
1.01/1.04	    - Complexity: constant 
1.01/1.04	* Chain [49] with precondition: [99>=A,A>=90] 
1.01/1.04	    - Upper bound: 0 
1.01/1.04	    - Complexity: constant 
1.01/1.04	* Chain [48] with precondition: [89>=A] 
1.01/1.04	    - Upper bound: -47/11*A+4539/11 
1.01/1.04	    - Complexity: n 
1.01/1.04	* Chain [47] with precondition: [88>=A] 
1.01/1.04	    - Upper bound: -157/11*A+15611/11 
1.01/1.04	    - Complexity: n 
1.01/1.04	* Chain [46] with precondition: [A>=101] 
1.01/1.04	    - Upper bound: 0 
1.01/1.04	    - Complexity: constant 
1.01/1.04	
1.01/1.04	### Maximum cost of start0(A,B,C,D,E,F,G,H,I): nat(-A+89)+1+nat(-A/11+90/11)*3+max([nat(-10/11*A+989/11)*3+nat(-A/11+90/11)+nat(-A/11+111/11)*2,nat(-10/11*A+999/11)*2+nat(-11*A+1101)+nat(-A/11+11)*2]) 
1.01/1.04	Asymptotic class: n 
1.01/1.04	* Total analysis performed in 929 ms.
1.01/1.04	
1.04/1.14	EOF