/export/starexec/sandbox/solver/bin/starexec_run_its /export/starexec/sandbox/benchmark/theBenchmark.koat /export/starexec/sandbox/output/output_files


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WORST_CASE(?,O(n^1))  

Preprocessing Cost Relations
=====================================

#### Computed strongly connected components 
0. recursive  : [lbl111/17]
1. non_recursive  : [exit_location/1]
2. recursive  : [lbl221/17]
3. recursive  : [lbl161/17,lbl221_loop_cont/18]
4. non_recursive  : [stop/9]
5. non_recursive  : [lbl161_loop_cont/10]
6. non_recursive  : [lbl111_loop_cont/10]
7. non_recursive  : [start/9]
8. non_recursive  : [start0/9]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into lbl111/17
1. SCC is completely evaluated into other SCCs
2. SCC is partially evaluated into lbl221/17
3. SCC is partially evaluated into lbl161/17
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into lbl161_loop_cont/10
6. SCC is partially evaluated into lbl111_loop_cont/10
7. SCC is partially evaluated into start/9
8. SCC is partially evaluated into start0/9

Control-Flow Refinement of Cost Relations
=====================================

### Specialization of cost equations lbl111/17 
* CE 6 is refined into CE [21] 
* CE 8 is refined into CE [22] 
* CE 7 is refined into CE [23] 
* CE 5 is refined into CE [24] 
* CE 4 is refined into CE [25] 


### Cost equations --> "Loop" of lbl111/17 
* CEs [25] --> Loop 20 
* CEs [21] --> Loop 21 
* CEs [22] --> Loop 22 
* CEs [23] --> Loop 23 
* CEs [24] --> Loop 24 

### Ranking functions of CR lbl111(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
* RF of phase [20]: [-A/11-D+112/11,-D-H/11+112/11,-F/11+101/11]

#### Partial ranking functions of CR lbl111(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
* Partial RF of phase [20]:
  - RF of loop [20:1]:
    -A/11-D+112/11
    -D-H/11+112/11
    -F/11+101/11


### Specialization of cost equations lbl221/17 
* CE 16 is refined into CE [26] 
* CE 13 is refined into CE [27] 
* CE 14 is refined into CE [28] 
* CE 15 is refined into CE [29] 


### Cost equations --> "Loop" of lbl221/17 
* CEs [28] --> Loop 25 
* CEs [29] --> Loop 26 
* CEs [26] --> Loop 27 
* CEs [27] --> Loop 28 

### Ranking functions of CR lbl221(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
* RF of phase [25,26]: [10*D-F+91]

#### Partial ranking functions of CR lbl221(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 
* Partial RF of phase [25,26]:
  - RF of loop [25:1]:
    -F+111 depends on loops [26:1] 
  - RF of loop [26:1]:
    D-2
    F/9-110/9 depends on loops [25:1] 


### Specialization of cost equations lbl161/17 
* CE 20 is refined into CE [30] 
* CE 19 is refined into CE [31] 


### Cost equations --> "Loop" of lbl161/17 
* CEs [30] --> Loop 29 
* CEs [31] --> Loop 30 

### Ranking functions of CR lbl161(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 

#### Partial ranking functions of CR lbl161(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q) 


### Specialization of cost equations lbl161_loop_cont/10 
* CE 18 is refined into CE [32] 
* CE 17 is refined into CE [33] 


### Cost equations --> "Loop" of lbl161_loop_cont/10 
* CEs [32] --> Loop 31 
* CEs [33] --> Loop 32 

### Ranking functions of CR lbl161_loop_cont(A,B,C,D,E,F,G,H,I,J) 

#### Partial ranking functions of CR lbl161_loop_cont(A,B,C,D,E,F,G,H,I,J) 


### Specialization of cost equations lbl111_loop_cont/10 
* CE 9 is refined into CE [34,35] 
* CE 10 is refined into CE [36,37,38,39] 
* CE 12 is refined into CE [40] 
* CE 11 is refined into CE [41,42] 


### Cost equations --> "Loop" of lbl111_loop_cont/10 
* CEs [38,39] --> Loop 33 
* CEs [35] --> Loop 34 
* CEs [36,37] --> Loop 35 
* CEs [34] --> Loop 36 
* CEs [40] --> Loop 37 
* CEs [41] --> Loop 38 
* CEs [42] --> Loop 39 

### Ranking functions of CR lbl111_loop_cont(A,B,C,D,E,F,G,H,I,J) 

#### Partial ranking functions of CR lbl111_loop_cont(A,B,C,D,E,F,G,H,I,J) 


### Specialization of cost equations start/9 
* CE 2 is refined into CE [43] 
* CE 3 is refined into CE [44,45,46,47,48,49,50,51,52,53] 


### Cost equations --> "Loop" of start/9 
* CEs [43] --> Loop 40 
* CEs [51,52,53] --> Loop 41 
* CEs [46,47,48,49] --> Loop 42 
* CEs [50] --> Loop 43 
* CEs [45] --> Loop 44 
* CEs [44] --> Loop 45 

### Ranking functions of CR start(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR start(A,B,C,D,E,F,G,H,I) 


### Specialization of cost equations start0/9 
* CE 1 is refined into CE [54,55,56,57,58,59] 


### Cost equations --> "Loop" of start0/9 
* CEs [59] --> Loop 46 
* CEs [58] --> Loop 47 
* CEs [57] --> Loop 48 
* CEs [56] --> Loop 49 
* CEs [55] --> Loop 50 
* CEs [54] --> Loop 51 

### Ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 

#### Partial ranking functions of CR start0(A,B,C,D,E,F,G,H,I) 


Computing Bounds
=====================================

#### Cost of chains of lbl111(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q):
* Chain [[20],23]: 1*it(20)+0
  Such that:it(20) =< -A/11-D+112/11

  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] 

* Chain [[20],22]: 1*it(20)+0
  Such that:it(20) =< -F/11+101/11

  with precondition: [I=4,B=C,A=H,A+11*D=F+11,100>=F,F>=A+11] 

* Chain [[20],21]: 1*it(20)+0
  Such that:it(20) =< -A/11-D+112/11

  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] 

* Chain [24]: 0
  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] 

* Chain [22]: 0
  with precondition: [I=4,C=B,A=H,A+11*D=F+11,111>=F,F>=A+11] 

* Chain [21]: 0
  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] 


#### Cost of chains of lbl221(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q):
* Chain [[25,26],28]: 1*it(25)+1*it(26)+0
  Such that:it(26) =< D
aux(7) =< 10*D-F+91
it(25) =< aux(7)
it(26) =< aux(7)

  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] 

* Chain [[25,26],27]: 1*it(25)+1*it(26)+0
  Such that:aux(5) =< 10*D-F+91
aux(6) =< -F-10*H+1001
it(26) =< F/10-H/10
it(26) =< -H+89
aux(6) =< -H+98
it(25) =< aux(5)
it(26) =< aux(5)
it(25) =< aux(6)
it(26) =< aux(6)

  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] 

* Chain [28]: 0
  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] 

* Chain [27]: 0
  with precondition: [I=4] 


#### Cost of chains of lbl161(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q):
* Chain [30]: 0
  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] 

* Chain [29]: 0
  with precondition: [I=4] 


#### Cost of chains of lbl161_loop_cont(A,B,C,D,E,F,G,H,I,J):
* Chain [32]: 0
  with precondition: [A=2] 

* Chain [31]: 0
  with precondition: [A=4] 


#### Cost of chains of lbl111_loop_cont(A,B,C,D,E,F,G,H,I,J):
* Chain [39]: 0
  with precondition: [A=3] 

* Chain [38]: 0
  with precondition: [A=3,C=91,E=1,G=101,B=I,89>=B] 

* Chain [37]: 0
  with precondition: [A=4] 

* Chain [36]: 0
  with precondition: [A=5] 

* Chain [35]: 1
  with precondition: [A=5,E=2,G=111,D=C,B=I,89>=B] 

* Chain [34]: 1*s(3)+1*s(4)+0
  Such that:s(1) =< 10*E-G+91
s(2) =< -G-10*I+1001
s(3) =< G/10-I/10
s(3) =< -I+89
s(2) =< -I+98
s(4) =< s(1)
s(3) =< s(1)
s(4) =< s(2)
s(3) =< s(2)

  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] 

* Chain [33]: 2*s(5)+2*s(7)+1
  Such that:aux(8) =< E
aux(9) =< 10*E-G+91
s(5) =< aux(8)
s(7) =< aux(9)
s(5) =< aux(9)

  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] 


#### Cost of chains of start(A,B,C,D,E,F,G,H,I):
* Chain [45]: 0
  with precondition: [A=100,H=100,C=B,E=D,G=F] 

* Chain [44]: 0
  with precondition: [H=A,C=B,E=D,G=F,100>=H] 

* Chain [43]: 0
  with precondition: [H=A,C=B,E=D,G=F,99>=H,H>=90] 

* Chain [42]: 4*s(11)+1*s(16)+1*s(17)+2*s(21)+2*s(22)+1
  Such that:s(16) =< -A+89
s(15) =< -A+98
s(16) =< -A/10+51/5
s(19) =< -A/11+111/11
aux(10) =< -10/11*A+989/11
aux(11) =< -A/11+90/11
s(11) =< aux(11)
s(17) =< aux(10)
s(16) =< aux(10)
s(17) =< s(15)
s(16) =< s(15)
s(21) =< s(19)
s(22) =< aux(10)
s(21) =< aux(10)

  with precondition: [H=A,C=B,E=D,G=F,89>=H] 

* Chain [41]: 3*s(23)+1*s(27)+1*s(28)+2*s(32)+2*s(33)+1
  Such that:aux(12) =< -11*A+1101
s(27) =< -A+89
aux(13) =< -A+98
aux(14) =< -A+101
s(31) =< -10/11*A+999/11
s(30) =< -A/11+11
aux(15) =< -A/11+90/11
s(23) =< aux(15)
s(25) =< aux(12)
s(27) =< aux(12)
s(25) =< aux(13)
s(28) =< s(25)
s(27) =< s(25)
s(28) =< aux(13)
s(27) =< aux(13)
s(30) =< aux(14)
s(31) =< aux(14)
s(32) =< s(30)
s(33) =< s(31)
s(32) =< s(31)

  with precondition: [H=A,C=B,E=D,G=F,88>=H] 

* Chain [40]: 0
  with precondition: [H=A,C=B,E=D,G=F,H>=101] 


#### Cost of chains of start0(A,B,C,D,E,F,G,H,I):
* Chain [51]: 0
  with precondition: [A=100] 

* Chain [50]: 0
  with precondition: [100>=A] 

* Chain [49]: 0
  with precondition: [99>=A,A>=90] 

* Chain [48]: 1*s(34)+4*s(39)+1*s(40)+2*s(41)+2*s(42)+1
  Such that:s(34) =< -A+89
s(35) =< -A+98
s(37) =< -10/11*A+989/11
s(34) =< -A/10+51/5
s(38) =< -A/11+90/11
s(36) =< -A/11+111/11
s(39) =< s(38)
s(40) =< s(37)
s(34) =< s(37)
s(40) =< s(35)
s(34) =< s(35)
s(41) =< s(36)
s(42) =< s(37)
s(41) =< s(37)

  with precondition: [89>=A] 

* Chain [47]: 1*s(44)+3*s(50)+1*s(52)+2*s(53)+2*s(54)+1
  Such that:s(43) =< -11*A+1101
s(44) =< -A+89
s(45) =< -A+98
s(46) =< -A+101
s(47) =< -10/11*A+999/11
s(48) =< -A/11+11
s(49) =< -A/11+90/11
s(50) =< s(49)
s(51) =< s(43)
s(44) =< s(43)
s(51) =< s(45)
s(52) =< s(51)
s(44) =< s(51)
s(52) =< s(45)
s(44) =< s(45)
s(48) =< s(46)
s(47) =< s(46)
s(53) =< s(48)
s(54) =< s(47)
s(53) =< s(47)

  with precondition: [88>=A] 

* Chain [46]: 0
  with precondition: [A>=101] 


Closed-form bounds of start0(A,B,C,D,E,F,G,H,I): 
-------------------------------------
* Chain [51] with precondition: [A=100] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [50] with precondition: [100>=A] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [49] with precondition: [99>=A,A>=90] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [48] with precondition: [89>=A] 
    - Upper bound: -47/11*A+4539/11 
    - Complexity: n 
* Chain [47] with precondition: [88>=A] 
    - Upper bound: -157/11*A+15611/11 
    - Complexity: n 
* Chain [46] with precondition: [A>=101] 
    - Upper bound: 0 
    - Complexity: constant 

### 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]) 
Asymptotic class: n 
* Total analysis performed in 926 ms.