0.63/0.69	WORST_CASE(?,O(n^2))  
0.63/0.69	
0.63/0.69	Preprocessing Cost Relations
0.63/0.69	=====================================
0.63/0.69	
0.63/0.69	#### Computed strongly connected components 
0.63/0.69	0. recursive  : [f10/7]
0.63/0.69	1. non_recursive  : [exit_location/1]
0.63/0.69	2. recursive  : [f22/10]
0.63/0.69	3. recursive  : [f18/10,f22_loop_cont/11]
0.63/0.69	4. recursive  : [f34/4]
0.63/0.69	5. non_recursive  : [f43/9]
0.63/0.69	6. non_recursive  : [f34_loop_cont/10]
0.63/0.69	7. non_recursive  : [f18_loop_cont/10]
0.63/0.69	8. non_recursive  : [f10_loop_cont/10]
0.63/0.69	9. non_recursive  : [f0/9]
0.63/0.69	
0.63/0.69	#### Obtained direct recursion through partial evaluation 
0.63/0.69	0. SCC is partially evaluated into f10/7
0.63/0.69	1. SCC is completely evaluated into other SCCs
0.63/0.69	2. SCC is partially evaluated into f22/10
0.63/0.69	3. SCC is partially evaluated into f18/10
0.63/0.69	4. SCC is partially evaluated into f34/4
0.63/0.69	5. SCC is completely evaluated into other SCCs
0.63/0.69	6. SCC is partially evaluated into f34_loop_cont/10
0.63/0.69	7. SCC is partially evaluated into f18_loop_cont/10
0.63/0.69	8. SCC is partially evaluated into f10_loop_cont/10
0.63/0.69	9. SCC is partially evaluated into f0/9
0.63/0.69	
0.63/0.69	Control-Flow Refinement of Cost Relations
0.63/0.69	=====================================
0.63/0.69	
0.63/0.69	### Specialization of cost equations f10/7 
0.63/0.69	* CE 4 is refined into CE [22] 
0.63/0.69	* CE 3 is refined into CE [23] 
0.63/0.69	* CE 2 is refined into CE [24] 
0.63/0.69	
0.63/0.69	
0.63/0.69	### Cost equations --> "Loop" of f10/7 
0.63/0.69	* CEs [24] --> Loop 22 
0.63/0.69	* CEs [22] --> Loop 23 
0.63/0.69	* CEs [23] --> Loop 24 
0.63/0.69	
0.63/0.69	### Ranking functions of CR f10(B,C,D,E,J,K,L) 
0.63/0.69	* RF of phase [22]: [-B+C]
0.63/0.69	
0.63/0.69	#### Partial ranking functions of CR f10(B,C,D,E,J,K,L) 
0.63/0.69	* Partial RF of phase [22]:
0.63/0.69	  - RF of loop [22:1]:
0.63/0.69	    -B+C
0.63/0.69	
0.63/0.69	
0.63/0.69	### Specialization of cost equations f22/10 
0.63/0.69	* CE 16 is refined into CE [25] 
0.63/0.69	* CE 15 is refined into CE [26] 
0.63/0.69	* CE 14 is refined into CE [27] 
0.63/0.69	* CE 13 is refined into CE [28] 
0.63/0.69	
0.63/0.69	
0.63/0.69	### Cost equations --> "Loop" of f22/10 
0.63/0.69	* CEs [27] --> Loop 25 
0.63/0.69	* CEs [28] --> Loop 26 
0.63/0.69	* CEs [25] --> Loop 27 
0.63/0.69	* CEs [26] --> Loop 28 
0.63/0.69	
0.63/0.69	### Ranking functions of CR f22(D,E,F,G,H,J,K,L,M,N) 
0.63/0.69	* RF of phase [25,26]: [D-G]
0.63/0.69	
0.63/0.69	#### Partial ranking functions of CR f22(D,E,F,G,H,J,K,L,M,N) 
0.63/0.69	* Partial RF of phase [25,26]:
0.63/0.69	  - RF of loop [25:1]:
0.63/0.69	    D-F-1
0.63/0.69	  - RF of loop [25:1,26:1]:
0.63/0.69	    D-G
0.63/0.69	
0.63/0.69	
0.63/0.69	### Specialization of cost equations f18/10 
0.63/0.69	* CE 9 is refined into CE [29] 
0.63/0.69	* CE 7 is refined into CE [30,31] 
0.63/0.69	* CE 10 is refined into CE [32] 
0.63/0.69	* CE 8 is refined into CE [33] 
0.63/0.69	
0.63/0.69	
0.63/0.69	### Cost equations --> "Loop" of f18/10 
0.63/0.69	* CEs [33] --> Loop 29 
0.63/0.69	* CEs [29] --> Loop 30 
0.63/0.69	* CEs [30,31] --> Loop 31 
0.63/0.69	* CEs [32] --> Loop 32 
0.63/0.69	
0.63/0.69	### Ranking functions of CR f18(D,E,F,G,H,J,K,L,M,N) 
0.63/0.69	* RF of phase [29]: [D-E-1]
0.63/0.69	
0.63/0.69	#### Partial ranking functions of CR f18(D,E,F,G,H,J,K,L,M,N) 
0.63/0.69	* Partial RF of phase [29]:
0.63/0.69	  - RF of loop [29:1]:
0.63/0.69	    D-E-1
0.63/0.69	
0.63/0.69	
0.63/0.69	### Specialization of cost equations f34/4 
0.63/0.69	* CE 18 is refined into CE [34] 
0.63/0.69	* CE 19 is refined into CE [35] 
0.63/0.69	* CE 17 is refined into CE [36] 
0.63/0.69	
0.63/0.69	
0.63/0.69	### Cost equations --> "Loop" of f34/4 
0.63/0.69	* CEs [36] --> Loop 33 
0.63/0.69	* CEs [34] --> Loop 34 
0.63/0.69	* CEs [35] --> Loop 35 
0.63/0.69	
0.63/0.69	### Ranking functions of CR f34(D,E,J,K) 
0.63/0.69	* RF of phase [33]: [D-E-1]
0.63/0.69	
0.63/0.69	#### Partial ranking functions of CR f34(D,E,J,K) 
0.63/0.69	* Partial RF of phase [33]:
0.63/0.69	  - RF of loop [33:1]:
0.63/0.69	    D-E-1
0.63/0.69	
0.63/0.69	
0.63/0.69	### Specialization of cost equations f34_loop_cont/10 
0.63/0.69	* CE 20 is refined into CE [37] 
0.63/0.69	* CE 21 is refined into CE [38] 
0.63/0.69	
0.63/0.69	
0.63/0.69	### Cost equations --> "Loop" of f34_loop_cont/10 
0.63/0.69	* CEs [37] --> Loop 36 
0.63/0.69	* CEs [38] --> Loop 37 
0.63/0.69	
0.63/0.69	### Ranking functions of CR f34_loop_cont(A,B,C,D,E,F,G,H,I,J) 
0.63/0.69	
0.63/0.69	#### Partial ranking functions of CR f34_loop_cont(A,B,C,D,E,F,G,H,I,J) 
0.63/0.69	
0.63/0.69	
0.63/0.69	### Specialization of cost equations f18_loop_cont/10 
0.63/0.69	* CE 12 is refined into CE [39,40,41,42] 
0.63/0.69	* CE 11 is refined into CE [43] 
0.63/0.69	
0.63/0.69	
0.63/0.69	### Cost equations --> "Loop" of f18_loop_cont/10 
0.63/0.69	* CEs [40,41] --> Loop 38 
0.63/0.69	* CEs [42] --> Loop 39 
0.63/0.69	* CEs [39] --> Loop 40 
0.63/0.69	* CEs [43] --> Loop 41 
0.63/0.69	
0.63/0.69	### Ranking functions of CR f18_loop_cont(A,B,C,D,E,F,G,H,I,J) 
0.63/0.69	
0.63/0.69	#### Partial ranking functions of CR f18_loop_cont(A,B,C,D,E,F,G,H,I,J) 
0.63/0.69	
0.63/0.69	
0.63/0.69	### Specialization of cost equations f10_loop_cont/10 
0.63/0.69	* CE 5 is refined into CE [44] 
0.63/0.69	* CE 6 is refined into CE [45,46,47,48,49,50,51,52,53] 
0.63/0.69	
0.63/0.69	
0.63/0.69	### Cost equations --> "Loop" of f10_loop_cont/10 
0.63/0.69	* CEs [44] --> Loop 42 
0.63/0.69	* CEs [47] --> Loop 43 
0.63/0.69	* CEs [46,51] --> Loop 44 
0.63/0.69	* CEs [48] --> Loop 45 
0.63/0.69	* CEs [53] --> Loop 46 
0.63/0.69	* CEs [50] --> Loop 47 
0.63/0.69	* CEs [52] --> Loop 48 
0.63/0.69	* CEs [49] --> Loop 49 
0.63/0.69	* CEs [45] --> Loop 50 
0.63/0.69	
0.63/0.69	### Ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H,I,J) 
0.63/0.69	
0.63/0.69	#### Partial ranking functions of CR f10_loop_cont(A,B,C,D,E,F,G,H,I,J) 
0.63/0.69	
0.63/0.69	
0.63/0.69	### Specialization of cost equations f0/9 
0.63/0.69	* CE 1 is refined into CE [54,55,56,57,58,59,60,61,62,63,64] 
0.63/0.69	
0.63/0.69	
0.63/0.69	### Cost equations --> "Loop" of f0/9 
0.63/0.69	* CEs [62] --> Loop 51 
0.63/0.69	* CEs [59,61] --> Loop 52 
0.63/0.69	* CEs [57,64] --> Loop 53 
0.63/0.69	* CEs [54,55,56] --> Loop 54 
0.63/0.69	* CEs [58,60] --> Loop 55 
0.63/0.69	* CEs [63] --> Loop 56 
0.63/0.69	
0.63/0.69	### Ranking functions of CR f0(A,B,C,D,E,F,G,H,J) 
0.63/0.69	
0.63/0.69	#### Partial ranking functions of CR f0(A,B,C,D,E,F,G,H,J) 
0.63/0.69	
0.63/0.69	
0.63/0.69	Computing Bounds
0.63/0.69	=====================================
0.63/0.69	
0.63/0.69	#### Cost of chains of f10(B,C,D,E,J,K,L):
0.63/0.69	* Chain [[22],24]: 1*it(22)+0
0.63/0.69	  Such that:it(22) =< -B+C
0.63/0.69	
0.63/0.69	  with precondition: [J=2,L=0,C=K,B>=0,C>=B+1] 
0.63/0.69	
0.63/0.69	* Chain [[22],23]: 1*it(22)+0
0.63/0.69	  Such that:it(22) =< -B+C
0.63/0.69	
0.63/0.69	  with precondition: [J=3,B>=0,C>=B+1] 
0.63/0.69	
0.63/0.69	* Chain [24]: 0
0.63/0.69	  with precondition: [J=2,L=0,B=K,B>=0,B>=C] 
0.63/0.69	
0.63/0.69	* Chain [23]: 0
0.63/0.69	  with precondition: [J=3,B>=0] 
0.63/0.69	
0.63/0.69	
0.63/0.69	#### Cost of chains of f22(D,E,F,G,H,J,K,L,M,N):
0.63/0.69	* Chain [[25,26],28]: 1*it(25)+1*it(26)+0
0.63/0.69	  Such that:it(25) =< -F+L
0.63/0.69	aux(3) =< D-G
0.63/0.69	it(25) =< aux(3)
0.63/0.69	it(26) =< aux(3)
0.63/0.69	
0.63/0.69	  with precondition: [J=2,E+1=K,D=M,F>=E,G>=F+1,L>=F,D>=G+1,D>=L+1] 
0.63/0.69	
0.63/0.69	* Chain [[25,26],27]: 1*it(25)+1*it(26)+0
0.63/0.69	  Such that:it(25) =< D-F
0.63/0.69	aux(4) =< D-G
0.63/0.69	it(25) =< aux(4)
0.63/0.69	it(26) =< aux(4)
0.63/0.69	
0.63/0.69	  with precondition: [J=3,F>=E,G>=F+1,D>=G+1] 
0.63/0.69	
0.63/0.69	* Chain [27]: 0
0.63/0.69	  with precondition: [J=3,D>=E+2,F>=E,G>=F+1] 
0.63/0.69	
0.63/0.69	
0.63/0.69	#### Cost of chains of f18(D,E,F,G,H,J,K,L,M,N):
0.63/0.69	* Chain [[29],32]: 1*it(29)+1*s(7)+1*s(8)+0
0.63/0.69	  Such that:aux(8) =< D-E
0.63/0.69	it(29) =< aux(8)
0.63/0.69	aux(6) =< aux(8)-1
0.63/0.69	s(9) =< it(29)*aux(8)
0.63/0.69	s(7) =< it(29)*aux(6)
0.63/0.69	s(7) =< s(9)
0.63/0.69	s(8) =< s(9)
0.63/0.69	
0.63/0.69	  with precondition: [J=3,D>=E+2] 
0.63/0.69	
0.63/0.69	* Chain [[29],31]: 3*it(29)+1*s(7)+1*s(8)+0
0.63/0.69	  Such that:aux(10) =< D-E
0.63/0.69	it(29) =< aux(10)
0.63/0.69	aux(6) =< aux(10)-1
0.63/0.69	s(9) =< it(29)*aux(10)
0.63/0.69	s(7) =< it(29)*aux(6)
0.63/0.69	s(7) =< s(9)
0.63/0.69	s(8) =< s(9)
0.63/0.69	
0.63/0.69	  with precondition: [J=3,D>=E+3] 
0.63/0.69	
0.63/0.69	* Chain [[29],30]: 1*it(29)+1*s(7)+1*s(8)+0
0.63/0.69	  Such that:aux(11) =< D-E
0.63/0.69	it(29) =< aux(11)
0.63/0.69	aux(6) =< aux(11)-1
0.63/0.69	s(9) =< it(29)*aux(11)
0.63/0.69	s(7) =< it(29)*aux(6)
0.63/0.69	s(7) =< s(9)
0.63/0.69	s(8) =< s(9)
0.63/0.69	
0.63/0.69	  with precondition: [J=5,K=0,D=M,L+2>=D,D>=E+2,D>=L+1] 
0.63/0.69	
0.63/0.69	* Chain [32]: 0
0.63/0.69	  with precondition: [J=3] 
0.63/0.69	
0.63/0.69	* Chain [31]: 2*s(10)+0
0.63/0.69	  Such that:aux(9) =< D-E
0.63/0.69	s(10) =< aux(9)
0.63/0.69	
0.63/0.69	  with precondition: [J=3,D>=E+2] 
0.63/0.69	
0.63/0.69	* Chain [30]: 0
0.63/0.69	  with precondition: [J=5,K=0,L=F,M=G,N=H,E+1>=D] 
0.63/0.69	
0.63/0.69	
0.63/0.69	#### Cost of chains of f34(D,E,J,K):
0.63/0.69	* Chain [[33],35]: 1*it(33)+0
0.63/0.69	  Such that:it(33) =< D-E
0.63/0.69	
0.63/0.69	  with precondition: [J=3,D>=E+2] 
0.63/0.69	
0.63/0.69	* Chain [[33],34]: 1*it(33)+0
0.63/0.69	  Such that:it(33) =< D-E
0.63/0.69	
0.63/0.69	  with precondition: [J=4,D=K+1,D>=E+2] 
0.63/0.69	
0.63/0.69	* Chain [35]: 0
0.63/0.69	  with precondition: [J=3] 
0.63/0.69	
0.63/0.69	* Chain [34]: 0
0.63/0.69	  with precondition: [J=4,E=K,E+1>=D] 
0.63/0.69	
0.63/0.69	
0.63/0.69	#### Cost of chains of f34_loop_cont(A,B,C,D,E,F,G,H,I,J):
0.63/0.69	* Chain [37]: 0
0.63/0.69	  with precondition: [A=3,E=D] 
0.63/0.69	
0.63/0.69	* Chain [36]: 0
0.63/0.69	  with precondition: [A=4,E=D] 
0.63/0.69	
0.63/0.69	
0.63/0.69	#### Cost of chains of f18_loop_cont(A,B,C,D,E,F,G,H,I,J):
0.63/0.69	* Chain [41]: 0
0.63/0.69	  with precondition: [A=3,E=D] 
0.63/0.69	
0.63/0.69	* Chain [40]: 0
0.63/0.69	  with precondition: [A=5,E=D] 
0.63/0.69	
0.63/0.69	* Chain [39]: 0
0.63/0.69	  with precondition: [A=5,E=D,F+1>=E] 
0.63/0.69	
0.63/0.69	* Chain [38]: 2*s(21)+0
0.63/0.69	  Such that:aux(13) =< D-F
0.63/0.69	s(21) =< aux(13)
0.63/0.69	
0.63/0.69	  with precondition: [A=5,E=D,E>=F+2] 
0.63/0.69	
0.63/0.69	
0.63/0.69	#### Cost of chains of f10_loop_cont(A,B,C,D,E,F,G,H,I,J):
0.63/0.69	* Chain [50]: 0
0.63/0.69	  with precondition: [A=2,E=D] 
0.63/0.69	
0.63/0.69	* Chain [49]: 0
0.63/0.69	  with precondition: [A=2,E=D,1>=E,F+1>=E] 
0.63/0.69	
0.63/0.69	* Chain [48]: 1*s(24)+1*s(27)+1*s(28)+0
0.63/0.69	  Such that:s(23) =< D-F
0.63/0.69	s(24) =< s(23)
0.63/0.69	s(25) =< s(23)-1
0.63/0.69	s(26) =< s(24)*s(23)
0.63/0.69	s(27) =< s(24)*s(25)
0.63/0.69	s(27) =< s(26)
0.63/0.69	s(28) =< s(26)
0.63/0.69	
0.63/0.69	  with precondition: [A=2,E=D,1>=E,E>=F+2] 
0.63/0.69	
0.63/0.69	* Chain [47]: 2*s(30)+0
0.63/0.69	  Such that:s(29) =< D
0.63/0.69	s(30) =< s(29)
0.63/0.69	
0.63/0.69	  with precondition: [A=2,E=D,E>=2,F+1>=E] 
0.63/0.69	
0.63/0.69	* Chain [46]: 1*s(32)+1*s(35)+1*s(36)+2*s(38)+0
0.63/0.69	  Such that:s(37) =< D
0.63/0.69	s(31) =< D-F
0.63/0.69	s(38) =< s(37)
0.63/0.69	s(32) =< s(31)
0.63/0.69	s(33) =< s(31)-1
0.63/0.69	s(34) =< s(32)*s(31)
0.63/0.69	s(35) =< s(32)*s(33)
0.63/0.69	s(35) =< s(34)
0.63/0.69	s(36) =< s(34)
0.63/0.69	
0.63/0.69	  with precondition: [A=2,E=D,E>=2,E>=F+2] 
0.63/0.69	
0.63/0.69	* Chain [45]: 0
0.63/0.69	  with precondition: [A=2,E=D,F+1>=E] 
0.63/0.69	
0.63/0.69	* Chain [44]: 4*s(40)+2*s(43)+2*s(44)+0
0.63/0.69	  Such that:aux(14) =< D-F
0.63/0.69	s(40) =< aux(14)
0.63/0.69	s(41) =< aux(14)-1
0.63/0.69	s(42) =< s(40)*aux(14)
0.63/0.69	s(43) =< s(40)*s(41)
0.63/0.69	s(43) =< s(42)
0.63/0.69	s(44) =< s(42)
0.63/0.69	
0.63/0.69	  with precondition: [A=2,E=D,E>=F+2] 
0.63/0.69	
0.63/0.69	* Chain [43]: 3*s(52)+1*s(55)+1*s(56)+0
0.63/0.69	  Such that:s(51) =< D-F
0.63/0.69	s(52) =< s(51)
0.63/0.69	s(53) =< s(51)-1
0.63/0.69	s(54) =< s(52)*s(51)
0.63/0.69	s(55) =< s(52)*s(53)
0.63/0.69	s(55) =< s(54)
0.63/0.69	s(56) =< s(54)
0.63/0.69	
0.63/0.69	  with precondition: [A=2,E=D,E>=F+3] 
0.63/0.69	
0.63/0.69	* Chain [42]: 0
0.63/0.69	  with precondition: [A=3,E=D] 
0.63/0.69	
0.63/0.69	
0.63/0.69	#### Cost of chains of f0(A,B,C,D,E,F,G,H,J):
0.63/0.69	* Chain [56]: 0
0.63/0.69	  with precondition: [] 
0.63/0.69	
0.63/0.69	* Chain [55]: 2
0.63/0.69	  with precondition: [C=1] 
0.63/0.69	
0.63/0.69	* Chain [54]: 0
0.63/0.69	  with precondition: [0>=C] 
0.63/0.69	
0.63/0.69	* Chain [53]: 2*s(59)+0
0.63/0.69	  Such that:aux(16) =< C
0.63/0.69	s(59) =< aux(16)
0.63/0.69	
0.63/0.69	  with precondition: [C>=1] 
0.63/0.69	
0.63/0.69	* Chain [52]: 9*s(61)+3*s(68)+3*s(69)+0
0.63/0.69	  Such that:aux(19) =< C
0.63/0.69	s(61) =< aux(19)
0.63/0.69	s(66) =< aux(19)-1
0.63/0.69	s(67) =< s(61)*aux(19)
0.63/0.69	s(68) =< s(61)*s(66)
0.63/0.69	s(68) =< s(67)
0.63/0.69	s(69) =< s(67)
0.63/0.69	
0.63/0.69	  with precondition: [C>=2] 
0.63/0.69	
0.63/0.69	* Chain [51]: 4*s(77)+1*s(82)+1*s(83)+0
0.63/0.69	  Such that:aux(20) =< C
0.63/0.69	s(77) =< aux(20)
0.63/0.69	s(80) =< aux(20)-1
0.63/0.69	s(81) =< s(77)*aux(20)
0.63/0.69	s(82) =< s(77)*s(80)
0.63/0.69	s(82) =< s(81)
0.63/0.69	s(83) =< s(81)
0.63/0.69	
0.63/0.69	  with precondition: [C>=3] 
0.63/0.69	
0.63/0.69	
0.63/0.69	Closed-form bounds of f0(A,B,C,D,E,F,G,H,J): 
0.63/0.69	-------------------------------------
0.63/0.69	* Chain [56] with precondition: [] 
0.63/0.69	    - Upper bound: 0 
0.63/0.69	    - Complexity: constant 
0.63/0.69	* Chain [55] with precondition: [C=1] 
0.63/0.69	    - Upper bound: 2 
0.63/0.69	    - Complexity: constant 
0.63/0.69	* Chain [54] with precondition: [0>=C] 
0.63/0.69	    - Upper bound: 0 
0.63/0.69	    - Complexity: constant 
0.63/0.69	* Chain [53] with precondition: [C>=1] 
0.63/0.69	    - Upper bound: 2*C 
0.63/0.69	    - Complexity: n 
0.63/0.69	* Chain [52] with precondition: [C>=2] 
0.63/0.69	    - Upper bound: 3*C*C+9*C+(C-1)*(3*C) 
0.63/0.69	    - Complexity: n^2 
0.63/0.69	* Chain [51] with precondition: [C>=3] 
0.63/0.69	    - Upper bound: 4*C+C*C+(C-1)*C 
0.63/0.69	    - Complexity: n^2 
0.63/0.69	
0.63/0.69	### Maximum cost of f0(A,B,C,D,E,F,G,H,J): max([2,nat(C)*2*nat(C)+nat(C)*5+nat(C)*2*nat(nat(C)+ -1)+(nat(C)*nat(C)+nat(C)*2+nat(nat(C)+ -1)*nat(C))+nat(C)*2]) 
0.63/0.69	Asymptotic class: n^2 
0.63/0.69	* Total analysis performed in 597 ms.
0.63/0.69	
0.70/0.79	EOF