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


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MAYBE

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

#### Computed strongly connected components 
0. recursive  : [f1/31]
1. non_recursive  : [f10/38]
2. non_recursive  : [exit_location/1]
3. recursive  : [f16/34]
4. recursive  : [f8/27]
5. non_recursive  : [f8_loop_cont/39]
6. non_recursive  : [f16_loop_cont/39]
7. non_recursive  : [f1_loop_cont/39]
8. non_recursive  : [f9/38]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into f1/31
1. SCC is completely evaluated into other SCCs
2. SCC is completely evaluated into other SCCs
3. SCC is partially evaluated into f16/34
4. SCC is partially evaluated into f8/27
5. SCC is partially evaluated into f8_loop_cont/39
6. SCC is partially evaluated into f16_loop_cont/39
7. SCC is partially evaluated into f1_loop_cont/39
8. SCC is partially evaluated into f9/38

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

### Specialization of cost equations f1/31 
* CE 6 is refined into CE [24] 
* CE 5 is refined into CE [25] 
* CE 4 is refined into CE [26] 
* CE 3 is refined into CE [27] 


### Cost equations --> "Loop" of f1/31 
* CEs [27] --> Loop 23 
* CEs [24] --> Loop 24 
* CEs [25] --> Loop 25 
* CEs [26] --> Loop 26 

### Ranking functions of CR f1(A,B,C,D,E,H,Q,R,S,T,U,V,W,X,Y,Z,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2) 
* RF of phase [23]: [-A+D,-A+Q]

#### Partial ranking functions of CR f1(A,B,C,D,E,H,Q,R,S,T,U,V,W,X,Y,Z,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2) 
* Partial RF of phase [23]:
  - RF of loop [23:1]:
    -A+D
    -A+Q


### Specialization of cost equations f16/34 
* CE 15 is refined into CE [28] 
* CE 13 is refined into CE [29] 
* CE 14 is refined into CE [30] 
* CE 12 is refined into CE [31] 
* CE 11 is refined into CE [32] 
* CE 10 is refined into CE [33] 
* CE 9 is refined into CE [34] 


### Cost equations --> "Loop" of f16/34 
* CEs [31] --> Loop 27 
* CEs [32] --> Loop 28 
* CEs [33] --> Loop 29 
* CEs [34] --> Loop 30 
* CEs [28] --> Loop 31 
* CEs [29] --> Loop 32 
* CEs [30] --> Loop 33 

### Ranking functions of CR f16(B,C,D,E,F,H,M,N,O,P,A1,B1,C1,D1,E1,F1,G1,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2,T2,U2) 
* RF of phase [27,28,29,30]: [H+1]

#### Partial ranking functions of CR f16(B,C,D,E,F,H,M,N,O,P,A1,B1,C1,D1,E1,F1,G1,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2,T2,U2) 
* Partial RF of phase [27,28,29,30]:
  - RF of loop [27:1,28:1,29:1,30:1]:
    H+1


### Specialization of cost equations f8/27 
* CE 21 is refined into CE [35] 
* CE 20 is refined into CE [36] 
* CE 19 is refined into CE [37] 
* CE 18 is refined into CE [38] 


### Cost equations --> "Loop" of f8/27 
* CEs [37] --> Loop 34 
* CEs [38] --> Loop 35 
* CEs [35] --> Loop 36 
* CEs [36] --> Loop 37 

### Ranking functions of CR f8(B,D,E,F,Y,A1,C1,D1,E1,F1,G1,H1,I1,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2) 
* RF of phase [34,35]: [H1+1]

#### Partial ranking functions of CR f8(B,D,E,F,Y,A1,C1,D1,E1,F1,G1,H1,I1,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2) 
* Partial RF of phase [34,35]:
  - RF of loop [34:1,35:1]:
    H1+1


### Specialization of cost equations f8_loop_cont/39 
* CE 23 is refined into CE [39] 
* CE 22 is refined into CE [40] 


### Cost equations --> "Loop" of f8_loop_cont/39 
* CEs [39] --> Loop 38 
* CEs [40] --> Loop 39 

### Ranking functions of CR f8_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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1) 

#### Partial ranking functions of CR f8_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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1) 


### Specialization of cost equations f16_loop_cont/39 
* CE 17 is refined into CE [41,42,43,44] 
* CE 16 is refined into CE [45] 


### Cost equations --> "Loop" of f16_loop_cont/39 
* CEs [44] --> Loop 40 
* CEs [43] --> Loop 41 
* CEs [42] --> Loop 42 
* CEs [41] --> Loop 43 
* CEs [45] --> Loop 44 

### Ranking functions of CR f16_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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1) 

#### Partial ranking functions of CR f16_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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1) 


### Specialization of cost equations f1_loop_cont/39 
* CE 8 is refined into CE [46,47,48,49,50,51,52,53,54,55] 
* CE 7 is refined into CE [56] 


### Cost equations --> "Loop" of f1_loop_cont/39 
* CEs [55] --> Loop 45 
* CEs [54] --> Loop 46 
* CEs [46,48] --> Loop 47 
* CEs [47,49] --> Loop 48 
* CEs [52] --> Loop 49 
* CEs [53] --> Loop 50 
* CEs [50] --> Loop 51 
* CEs [51] --> Loop 52 
* CEs [56] --> Loop 53 

### 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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1) 

#### 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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1) 


### Specialization of cost equations f9/38 
* CE 1 is refined into CE [57] 
* CE 2 is refined into CE [58,59,60,61,62,63,64,65,66,67] 


### Cost equations --> "Loop" of f9/38 
* CEs [58,59,60,61,62,63,64,65] --> Loop 54 
* CEs [57,66,67] --> Loop 55 

### Ranking functions of CR f9(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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,E2) 

#### Partial ranking functions of CR f9(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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,E2) 


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

#### Cost of chains of f1(A,B,C,D,E,H,Q,R,S,T,U,V,W,X,Y,Z,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2):
* Chain [[23],26]: 1*it(23)+0
  Such that:it(23) =< -A+O2+1

  with precondition: [C=0,E2=5,G2=0,D=Q,R=T,F2=I2,D=O2+1,0>=F2+1,A>=2,H2>=2,D>=A+1,H>=H2,S2>=H2] 

* Chain [[23],25]: 1*it(23)+0
  Such that:it(23) =< -A+O2+1

  with precondition: [C=0,E2=5,G2=0,D=Q,R=T,F2=I2,D=O2+1,A>=2,F2>=1,H2>=2,D>=A+1,H>=H2,S2>=H2] 

* Chain [[23],24]: 1*it(23)+0
  Such that:it(23) =< -A+Q

  with precondition: [E2=3,D=Q,R=T,A>=2,D>=A+1] 

* Chain [26]: 0
  with precondition: [C=0,E2=5,G2=0,D=A,D=Q,T=R,N2=U,O2=V,T=F2,T=I2,0>=T+1,D>=2,H2>=2,H>=H2,S2>=H2] 

* Chain [25]: 0
  with precondition: [C=0,E2=5,G2=0,D=A,D=Q,T=R,N2=U,O2=V,T=F2,T=I2,D>=2,T>=1,H2>=2,H>=H2,S2>=H2] 

* Chain [24]: 0
  with precondition: [E2=3,Q=D,T=R,A>=2,Q>=A] 


#### Cost of chains of f16(B,C,D,E,F,H,M,N,O,P,A1,B1,C1,D1,E1,F1,G1,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2,S2,T2,U2):
* Chain [[27,28,29,30],33]: 4*it(27)+0
  Such that:aux(2) =< -C+N2
aux(1) =< H+1
it(27) =< aux(1)
it(27) =< aux(2)

  with precondition: [B=0,E2=4,F2=0,L2=0,Q2=0,S2=0,K2=O2,I2=P2,I2=R2,I2=T2,I2=U2,K2+N2=C+H,0>=I2+1,C>=0,H2>=2,K2>=0,H>=K2+1] 

* Chain [[27,28,29,30],32]: 4*it(27)+0
  Such that:aux(2) =< -C+N2
aux(1) =< H+1
it(27) =< aux(1)
it(27) =< aux(2)

  with precondition: [B=0,E2=4,F2=0,L2=0,Q2=0,S2=0,K2=O2,I2=P2,I2=R2,I2=T2,I2=U2,K2+N2=C+H,C>=0,H2>=2,I2>=1,K2>=0,H>=K2+1] 

* Chain [[27,28,29,30],31]: 4*it(27)+0
  Such that:aux(3) =< H+1
it(27) =< aux(3)

  with precondition: [E2=3,C>=0,H>=0] 

* Chain [33]: 0
  with precondition: [B=0,E2=4,F2=0,Q2=0,S2=0,J2=F,L2=M,M2=N,N2=O,O2=P,E=I2,H=K2,E=P2,E=R2,E=T2,E=U2,0>=E+1,C>=0,H>=0,H2>=2] 

* Chain [32]: 0
  with precondition: [B=0,E2=4,F2=0,Q2=0,S2=0,J2=F,L2=M,M2=N,N2=O,O2=P,E=I2,H=K2,E=P2,E=R2,E=T2,E=U2,C>=0,E>=1,H>=0,H2>=2] 

* Chain [31]: 0
  with precondition: [E2=3] 


#### Cost of chains of f8(B,D,E,F,Y,A1,C1,D1,E1,F1,G1,H1,I1,E2,F2,G2,H2,I2,J2,K2,L2,M2,N2,O2,P2,Q2,R2):
* Chain [[34,35],37]: 2*it(34)+0
  Such that:aux(4) =< H1+1
aux(5) =< H1-R2
it(34) =< aux(4)
it(34) =< aux(5)

  with precondition: [A1=0,C1=0,E2=2,F2=0,Q2=R2,G2>=2,Q2>=0,H1>=Q2+1] 

* Chain [[34,35],36]: 2*it(34)+0
  Such that:aux(6) =< H1+1
it(34) =< aux(6)

  with precondition: [C1=0,E2=3,H1>=0] 

* Chain [37]: 0
  with precondition: [E2=2,F2=B,H2=E,I2=F,C1=A1,R2=I1,H1=Q2,H1>=0,G2>=2] 

* Chain [36]: 0
  with precondition: [E2=3] 


#### Cost of chains of f8_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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1):
* Chain [39]: 0
  with precondition: [A=2] 

* Chain [38]: 0
  with precondition: [A=3] 


#### Cost of chains of f16_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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1):
* Chain [44]: 0
  with precondition: [A=3,I1=C1] 

* Chain [43]: 2*s(3)+0
  Such that:s(2) =< C1
s(1) =< C1+1
s(3) =< s(1)
s(3) =< s(2)

  with precondition: [A=4,B1=0,D1=0,I1=C1,I1>=1] 

* Chain [42]: 2*s(5)+0
  Such that:s(4) =< I1+1
s(5) =< s(4)

  with precondition: [A=4,D1=0,I1=C1,I1>=0] 

* Chain [41]: 0
  with precondition: [A=4,D1=B1,I1=C1,I1>=0] 

* Chain [40]: 0
  with precondition: [A=4,I1=C1] 


#### 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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,L1,M1):
* Chain [53]: 0
  with precondition: [A=3,I=B] 

* Chain [52]: 0
  with precondition: [A=5,C=0,I=B,0>=F+1,D>=0,I>=0] 

* Chain [51]: 2*s(7)+0
  Such that:s(6) =< I1+1
s(7) =< s(6)

  with precondition: [A=5,C=0,I=B,0>=F+1,D>=0,I>=0,I1>=0] 

* Chain [50]: 0
  with precondition: [A=5,C=0,I=B,D>=0,F>=1,I>=0] 

* Chain [49]: 2*s(9)+0
  Such that:s(8) =< I1+1
s(9) =< s(8)

  with precondition: [A=5,C=0,I=B,D>=0,F>=1,I>=0,I1>=0] 

* Chain [48]: 8*s(12)+0
  Such that:aux(7) =< I
aux(8) =< I+1
s(12) =< aux(8)
s(12) =< aux(7)

  with precondition: [A=5,C=0,I=B,D>=0,I>=1] 

* Chain [47]: 8*s(18)+4*s(20)+0
  Such that:aux(9) =< B
aux(10) =< B+1
aux(11) =< I1+1
s(20) =< aux(11)
s(18) =< aux(10)
s(18) =< aux(9)

  with precondition: [A=5,C=0,I=B,D>=0,I>=1,I1>=0] 

* Chain [46]: 0
  with precondition: [A=5,I=B] 

* Chain [45]: 4*s(27)+0
  Such that:s(26) =< I+1
s(27) =< s(26)

  with precondition: [A=5,I=B,D>=0,I>=0] 


#### Cost of chains of f9(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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,E2):
* Chain [55]: 1*aux(12)+0
  with precondition: [] 

* Chain [54]: 16*s(30)+4*s(33)+0
  Such that:aux(13) =< H+1
s(30) =< aux(13)

  with precondition: [C=0,H>=2] 


Closed-form bounds of f9(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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,E2): 
-------------------------------------
* Chain [55] with precondition: [] 
    - Upper bound: inf 
    - Complexity: infinity 
* Chain [54] with precondition: [C=0,H>=2] 
    - Upper bound: inf 
    - Complexity: infinity 

### Maximum cost of f9(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,A1,B1,C1,D1,E1,F1,G1,H1,I1,J1,K1,E2): inf 
Asymptotic class: infinity 
* Total analysis performed in 2221 ms.