/export/starexec/sandbox2/solver/bin/starexec_run_its /export/starexec/sandbox2/benchmark/theBenchmark.koat /export/starexec/sandbox2/output/output_files


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WORST_CASE(?,O(n^3))  

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

#### Computed strongly connected components 
0. recursive  : [lbl101/10]
1. recursive  : [lbl121/15,lbl123/15]
2. recursive  : [lbl101_loop_cont/17,lbl121_loop_cont/17,lbl53/16,lbl71/16]
3. non_recursive  : [exit_location/1]
4. non_recursive  : [stop/17]
5. non_recursive  : [lbl71_loop_cont/18]
6. non_recursive  : [lbl21/17]
7. non_recursive  : [start/17]
8. non_recursive  : [start0/17]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into lbl101/10
1. SCC is partially evaluated into lbl121/15
2. SCC is partially evaluated into lbl71/16
3. SCC is completely evaluated into other SCCs
4. SCC is completely evaluated into other SCCs
5. SCC is partially evaluated into lbl71_loop_cont/18
6. SCC is partially evaluated into lbl21/17
7. SCC is completely evaluated into other SCCs
8. SCC is partially evaluated into start0/17

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

### Specialization of cost equations lbl101/10 
* CE 18 is refined into CE [22] 
* CE 17 is refined into CE [23] 
* CE 16 is refined into CE [24] 


### Cost equations --> "Loop" of lbl101/10 
* CEs [24] --> Loop 22 
* CEs [22] --> Loop 23 
* CEs [23] --> Loop 24 

### Ranking functions of CR lbl101(E,G,I,K,L,M,O,R,S,T) 
* RF of phase [22]: [E,E-G+1]

#### Partial ranking functions of CR lbl101(E,G,I,K,L,M,O,R,S,T) 
* Partial RF of phase [22]:
  - RF of loop [22:1]:
    E
    E-G+1


### Specialization of cost equations lbl121/15 
* CE 19 is refined into CE [25] 
* CE 21 is refined into CE [26] 
* CE 20 is refined into CE [27] 


### Cost equations --> "Loop" of lbl121/15 
* CEs [25] --> Loop 25 
* CEs [26] --> Loop 26 
* CEs [27] --> Loop 27 

### Ranking functions of CR lbl121(A,C,E,G,I,K,L,M,O,R,S,T,U,V,W) 

#### Partial ranking functions of CR lbl121(A,C,E,G,I,K,L,M,O,R,S,T,U,V,W) 


### Specialization of cost equations lbl71/16 
* CE 6 is refined into CE [28,29] 
* CE 7 is refined into CE [30] 
* CE 10 is refined into CE [31,32] 
* CE 8 is refined into CE [33,34] 
* CE 9 is refined into CE [35] 
* CE 13 is refined into CE [36] 
* CE 11 is refined into CE [37,38] 
* CE 12 is refined into CE [39] 
* CE 4 is refined into CE [40,41] 
* CE 5 is refined into CE [42] 


### Cost equations --> "Loop" of lbl71/16 
* CEs [38] --> Loop 28 
* CEs [39] --> Loop 29 
* CEs [37] --> Loop 30 
* CEs [40,42] --> Loop 31 
* CEs [41] --> Loop 32 
* CEs [36] --> Loop 33 
* CEs [31] --> Loop 34 
* CEs [32] --> Loop 35 
* CEs [33,35] --> Loop 36 
* CEs [34] --> Loop 37 
* CEs [28,30] --> Loop 38 
* CEs [29] --> Loop 39 

### Ranking functions of CR lbl71(A,C,E,G,I,K,L,M,O,R,S,T,U,V,W,X) 

#### Partial ranking functions of CR lbl71(A,C,E,G,I,K,L,M,O,R,S,T,U,V,W,X) 
* Partial RF of phase [28,29,30,31,32]:
  - RF of loop [28:1,29:1,30:1]:
    -E+K-1 depends on loops [31:1,32:1] 
    -E+L-1 depends on loops [31:1,32:1] 
    -E+2*O depends on loops [31:1,32:1] 
    -I+K-1 depends on loops [31:1,32:1] 
    -I+L-1 depends on loops [31:1,32:1] 
    -I+2*O depends on loops [31:1,32:1] 
  - RF of loop [31:1]:
    E-2*G+2 depends on loops [28:1,29:1,30:1] 
    E-2*G-K+2*O+2 depends on loops [28:1,29:1,30:1] 
    E-2*G-L+2*O+2 depends on loops [28:1,29:1,30:1] 
    E/3-2/3 depends on loops [28:1,29:1,30:1] 
    E/3-K/3+2/3 depends on loops [28:1,29:1,30:1] 
    E/3-L/3+2/3 depends on loops [28:1,29:1,30:1] 
    E/3-2/3*O+2/3 depends on loops [28:1,29:1,30:1] 
    -2*G+I+2 depends on loops [28:1,29:1,30:1] 
    -2*G+I-K+2*O+2 depends on loops [28:1,29:1,30:1] 
    -2*G+I-L+2*O+2 depends on loops [28:1,29:1,30:1] 
    I/3-2/3 depends on loops [28:1,29:1,30:1] 
    I/3-K/3+2/3 depends on loops [28:1,29:1,30:1] 
    I/3-L/3+2/3 depends on loops [28:1,29:1,30:1] 
    I/3-2/3*O+2/3 depends on loops [28:1,29:1,30:1] 
  - RF of loop [31:1,32:1]:
    G-1
  - RF of loop [32:1]:
    E/2-G+1/2 depends on loops [28:1,29:1,30:1] 
    E/4-3/4 depends on loops [28:1,29:1,30:1] 
    E/4-K/4+1/2 depends on loops [28:1,29:1,30:1] 
    E/4-L/4+1/2 depends on loops [28:1,29:1,30:1] 
    E/4-O/2+1/2 depends on loops [28:1,29:1,30:1] 
    -G+I/2+1/2 depends on loops [28:1,29:1,30:1] 
    I/4-3/4 depends on loops [28:1,29:1,30:1] 
    I/4-K/4+1/2 depends on loops [28:1,29:1,30:1] 
    I/4-L/4+1/2 depends on loops [28:1,29:1,30:1] 
    I/4-O/2+1/2 depends on loops [28:1,29:1,30:1] 


### Specialization of cost equations lbl71_loop_cont/18 
* CE 15 is refined into CE [43] 
* CE 14 is refined into CE [44] 


### Cost equations --> "Loop" of lbl71_loop_cont/18 
* CEs [43] --> Loop 40 
* CEs [44] --> Loop 41 

### Ranking functions of CR lbl71_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) 

#### Partial ranking functions of CR lbl71_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R) 


### Specialization of cost equations lbl21/17 
* CE 3 is refined into CE [45,46,47,48,49] 
* CE 2 is refined into CE [50] 


### Cost equations --> "Loop" of lbl21/17 
* CEs [46,48] --> Loop 42 
* CEs [45,47,49] --> Loop 43 
* CEs [50] --> Loop 44 

### Ranking functions of CR lbl21(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R) 

#### Partial ranking functions of CR lbl21(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R) 


### Specialization of cost equations start0/17 
* CE 1 is refined into CE [51,52,53] 


### Cost equations --> "Loop" of start0/17 
* CEs [53] --> Loop 45 
* CEs [52] --> Loop 46 
* CEs [51] --> Loop 47 

### Ranking functions of CR start0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R) 

#### Partial ranking functions of CR start0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R) 


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

#### Cost of chains of lbl101(E,G,I,K,L,M,O,R,S,T):
* Chain [[22],24]: 1*it(22)+0
  Such that:it(22) =< E-G+1
it(22) =< E-S

  with precondition: [R=2,K=L,I+1=T,G>=1,S>=0,K>=2*O,K>=I+1,2*O+1>=K,I>=E+G,E>=G+S] 

* Chain [[22],23]: 1*it(22)+0
  Such that:it(22) =< E-G+1

  with precondition: [R=3,K=L,G>=1,K>=2*O,E>=G,K>=I+1,2*O+1>=K,I>=E+G] 

* Chain [24]: 0
  with precondition: [R=2,L=K,E=S,I+1=T,E>=0,G>=1,L>=2*O,O>=G,L>=I+1,2*O+1>=L,I>=E+G] 

* Chain [23]: 0
  with precondition: [R=3,L=K,E>=0,G>=1,L>=2*O,O>=G,L>=I+1,2*O+1>=L,I>=E+G] 


#### Cost of chains of lbl121(A,C,E,G,I,K,L,M,O,R,S,T,U,V,W):
* Chain [27]: 0
  with precondition: [A=0,G=1,R=4,S=0,V=0,T=C,I=K,I=L,I=M+1,E=U,I=W,E>=0,O>=1,I>=2*O,I>=E+1,2*O+1>=I] 

* Chain [26]: 0
  with precondition: [R=3,I=K,I=L,I=M+1,E>=0,G>=1,I>=2*O,I>=E+1,O>=G,2*O+1>=I] 

* Chain [25]: 0
  with precondition: [R=5,U=0,W=0,I=K,I=L,I=M+1,A=S,A=V,A>=1,E>=0,G>=2*A,I>=2*O,I>=E+1,O>=G,2*A+1>=G,2*O+1>=I] 


#### Cost of chains of lbl71(A,C,E,G,I,K,L,M,O,R,S,T,U,V,W,X):
* Chain [[28,29,30,31,32],39]: 3*it(28)+2*it(31)+1*s(1)+1*s(6)+1*s(7)+0
  Such that:aux(223) =< G+W
aux(237) =< -E+2*O
aux(238) =< -E+W
aux(239) =< G
aux(240) =< W
s(1) =< aux(240)
it(31) =< aux(239)
aux(94) =< aux(223)
aux(162) =< aux(240)
aux(94) =< aux(240)
aux(126) =< aux(240)
aux(126) =< aux(94)
aux(183) =< aux(240)
aux(167) =< aux(94)
aux(162) =< aux(240)-3
aux(7) =< it(31)*aux(126)
aux(4) =< it(31)*aux(240)
aux(1) =< it(31)*aux(240)
aux(10) =< it(31)*aux(94)
aux(1) =< it(31)*aux(94)
aux(5) =< it(31)*aux(183)
aux(2) =< it(31)*aux(183)
aux(11) =< it(31)*aux(167)
aux(2) =< it(31)*aux(167)
s(7) =< it(31)*aux(162)
aux(13) =< aux(4)
aux(13) =< aux(10)
aux(14) =< aux(5)
aux(14) =< aux(11)
it(28) =< aux(11)+aux(10)+aux(238)
it(28) =< aux(7)+aux(7)+aux(237)
it(28) =< aux(5)+aux(4)+aux(238)
it(28) =< aux(2)+aux(1)+aux(238)
it(28) =< aux(7)+aux(7)+aux(238)
it(28) =< aux(14)+aux(13)+aux(238)
s(6) =< it(28)*aux(240)

  with precondition: [R=4,E=I,K=L,K=W,E>=0,G>=1,K>=2*O,K>=E+1,K>=G+2,O>=G,2*O+1>=K,G+K>=E+3] 

* Chain [[28,29,30,31,32],38]: 3*it(28)+2*it(31)+1*s(6)+1*s(7)+0
  Such that:aux(223) =< G+W
aux(241) =< -E+2*O
aux(242) =< -E+W
aux(243) =< G
aux(244) =< W
it(31) =< aux(243)
aux(94) =< aux(223)
aux(162) =< aux(244)
aux(94) =< aux(244)
aux(126) =< aux(244)
aux(126) =< aux(94)
aux(183) =< aux(244)
aux(167) =< aux(94)
aux(162) =< aux(244)-3
aux(7) =< it(31)*aux(126)
aux(4) =< it(31)*aux(244)
aux(1) =< it(31)*aux(244)
aux(10) =< it(31)*aux(94)
aux(1) =< it(31)*aux(94)
aux(5) =< it(31)*aux(183)
aux(2) =< it(31)*aux(183)
aux(11) =< it(31)*aux(167)
aux(2) =< it(31)*aux(167)
s(7) =< it(31)*aux(162)
aux(13) =< aux(4)
aux(13) =< aux(10)
aux(14) =< aux(5)
aux(14) =< aux(11)
it(28) =< aux(11)+aux(10)+aux(242)
it(28) =< aux(7)+aux(7)+aux(241)
it(28) =< aux(5)+aux(4)+aux(242)
it(28) =< aux(2)+aux(1)+aux(242)
it(28) =< aux(7)+aux(7)+aux(242)
it(28) =< aux(14)+aux(13)+aux(242)
s(6) =< it(28)*aux(244)

  with precondition: [R=4,E=I,K=L,K=W,E>=0,G>=1,K>=2*O,K>=E+1,O>=G,2*O+1>=K,G+K>=E+3] 

* Chain [[28,29,30,31,32],37]: 3*it(28)+2*it(31)+1*s(6)+1*s(7)+1*s(8)+0
  Such that:aux(223) =< G+L
aux(245) =< -E+L
aux(246) =< -E+2*O
aux(247) =< G
aux(248) =< L
s(8) =< aux(248)
it(31) =< aux(247)
aux(94) =< aux(223)
aux(162) =< aux(248)
aux(94) =< aux(248)
aux(126) =< aux(248)
aux(126) =< aux(94)
aux(183) =< aux(248)
aux(167) =< aux(94)
aux(162) =< aux(248)-3
aux(7) =< it(31)*aux(126)
aux(4) =< it(31)*aux(248)
aux(1) =< it(31)*aux(248)
aux(10) =< it(31)*aux(94)
aux(1) =< it(31)*aux(94)
aux(5) =< it(31)*aux(183)
aux(2) =< it(31)*aux(183)
aux(11) =< it(31)*aux(167)
aux(2) =< it(31)*aux(167)
s(7) =< it(31)*aux(162)
aux(13) =< aux(4)
aux(13) =< aux(10)
aux(14) =< aux(5)
aux(14) =< aux(11)
it(28) =< aux(11)+aux(10)+aux(245)
it(28) =< aux(7)+aux(7)+aux(246)
it(28) =< aux(5)+aux(4)+aux(245)
it(28) =< aux(2)+aux(1)+aux(245)
it(28) =< aux(7)+aux(7)+aux(245)
it(28) =< aux(14)+aux(13)+aux(245)
s(6) =< it(28)*aux(248)

  with precondition: [R=3,E=I,K=L,E>=0,G>=1,K>=2*O,K>=E+1,K>=G+2,O>=G,2*O+1>=K,G+K>=E+3] 

* Chain [[28,29,30,31,32],36]: 3*it(28)+2*it(31)+1*s(6)+1*s(7)+0
  Such that:aux(223) =< G+L
aux(249) =< -E+L
aux(250) =< -E+2*O
aux(251) =< G
aux(252) =< L
it(31) =< aux(251)
aux(94) =< aux(223)
aux(162) =< aux(252)
aux(94) =< aux(252)
aux(126) =< aux(252)
aux(126) =< aux(94)
aux(183) =< aux(252)
aux(167) =< aux(94)
aux(162) =< aux(252)-3
aux(7) =< it(31)*aux(126)
aux(4) =< it(31)*aux(252)
aux(1) =< it(31)*aux(252)
aux(10) =< it(31)*aux(94)
aux(1) =< it(31)*aux(94)
aux(5) =< it(31)*aux(183)
aux(2) =< it(31)*aux(183)
aux(11) =< it(31)*aux(167)
aux(2) =< it(31)*aux(167)
s(7) =< it(31)*aux(162)
aux(13) =< aux(4)
aux(13) =< aux(10)
aux(14) =< aux(5)
aux(14) =< aux(11)
it(28) =< aux(11)+aux(10)+aux(249)
it(28) =< aux(7)+aux(7)+aux(250)
it(28) =< aux(5)+aux(4)+aux(249)
it(28) =< aux(2)+aux(1)+aux(249)
it(28) =< aux(7)+aux(7)+aux(249)
it(28) =< aux(14)+aux(13)+aux(249)
s(6) =< it(28)*aux(252)

  with precondition: [R=3,E=I,K=L,E>=0,G>=1,K>=2*O,K>=E+1,O>=G,2*O+1>=K,G+K>=E+3] 

* Chain [[28,29,30,31,32],35]: 3*it(28)+2*it(31)+1*s(6)+1*s(7)+1*s(9)+0
  Such that:aux(223) =< G+K
aux(253) =< -E+K
aux(254) =< G
aux(255) =< -I+K
aux(256) =< -I+2*O
aux(257) =< K
aux(212) =< aux(253)
aux(212) =< aux(255)
s(9) =< aux(257)
it(31) =< aux(254)
aux(94) =< aux(223)
aux(162) =< aux(257)
aux(94) =< aux(257)
aux(126) =< aux(257)
aux(126) =< aux(94)
aux(183) =< aux(257)
aux(167) =< aux(94)
aux(162) =< aux(257)-3
aux(7) =< it(31)*aux(126)
aux(4) =< it(31)*aux(257)
aux(1) =< it(31)*aux(257)
aux(10) =< it(31)*aux(94)
aux(1) =< it(31)*aux(94)
aux(5) =< it(31)*aux(183)
aux(2) =< it(31)*aux(183)
aux(11) =< it(31)*aux(167)
aux(2) =< it(31)*aux(167)
s(7) =< it(31)*aux(162)
aux(13) =< aux(4)
aux(13) =< aux(10)
aux(14) =< aux(5)
aux(14) =< aux(11)
it(28) =< aux(11)+aux(10)+aux(255)
it(28) =< aux(7)+aux(7)+aux(256)
it(28) =< aux(5)+aux(4)+aux(255)
it(28) =< aux(2)+aux(1)+aux(255)
it(28) =< aux(7)+aux(7)+aux(212)
it(28) =< aux(14)+aux(13)+aux(212)
it(28) =< aux(14)+aux(13)+aux(255)
s(6) =< it(28)*aux(257)

  with precondition: [R=3,E=I,K=L,E>=0,G>=1,K>=2*O,K>=E+1,O>=G,2*O+1>=K,G+K>=E+3] 

* Chain [[28,29,30,31,32],34]: 3*it(28)+2*it(31)+1*s(6)+1*s(7)+0
  Such that:aux(223) =< G+K
aux(258) =< -E+K
aux(259) =< G
aux(260) =< -I+K
aux(261) =< -I+L
aux(262) =< -I+2*O
aux(263) =< K
aux(212) =< aux(258)
aux(212) =< aux(261)
it(31) =< aux(259)
aux(94) =< aux(223)
aux(162) =< aux(263)
aux(94) =< aux(263)
aux(126) =< aux(263)
aux(126) =< aux(94)
aux(183) =< aux(263)
aux(167) =< aux(94)
aux(162) =< aux(263)-3
aux(7) =< it(31)*aux(126)
aux(4) =< it(31)*aux(263)
aux(1) =< it(31)*aux(263)
aux(10) =< it(31)*aux(94)
aux(1) =< it(31)*aux(94)
aux(5) =< it(31)*aux(183)
aux(2) =< it(31)*aux(183)
aux(11) =< it(31)*aux(167)
aux(2) =< it(31)*aux(167)
s(7) =< it(31)*aux(162)
aux(13) =< aux(4)
aux(13) =< aux(10)
aux(14) =< aux(5)
aux(14) =< aux(11)
it(28) =< aux(11)+aux(10)+aux(260)
it(28) =< aux(7)+aux(7)+aux(262)
it(28) =< aux(5)+aux(4)+aux(260)
it(28) =< aux(2)+aux(1)+aux(260)
it(28) =< aux(7)+aux(7)+aux(212)
it(28) =< aux(14)+aux(13)+aux(212)
it(28) =< aux(14)+aux(13)+aux(260)
s(6) =< it(28)*aux(263)

  with precondition: [R=3,E=I,K=L,E>=0,G>=1,K>=2*O,K>=E+1,O>=G,2*O+1>=K,G+K>=E+3] 

* Chain [[28,29,30,31,32],33]: 3*it(28)+2*it(31)+1*s(6)+1*s(7)+0
  Such that:aux(223) =< G+K
aux(264) =< -E+K
aux(265) =< -E+2*O
aux(266) =< G
aux(267) =< -I+L
aux(268) =< K
aux(212) =< aux(264)
aux(212) =< aux(267)
it(31) =< aux(266)
aux(94) =< aux(223)
aux(162) =< aux(268)
aux(94) =< aux(268)
aux(126) =< aux(268)
aux(126) =< aux(94)
aux(183) =< aux(268)
aux(167) =< aux(94)
aux(162) =< aux(268)-3
aux(7) =< it(31)*aux(126)
aux(4) =< it(31)*aux(268)
aux(1) =< it(31)*aux(268)
aux(10) =< it(31)*aux(94)
aux(1) =< it(31)*aux(94)
aux(5) =< it(31)*aux(183)
aux(2) =< it(31)*aux(183)
aux(11) =< it(31)*aux(167)
aux(2) =< it(31)*aux(167)
s(7) =< it(31)*aux(162)
aux(13) =< aux(4)
aux(13) =< aux(10)
aux(14) =< aux(5)
aux(14) =< aux(11)
it(28) =< aux(11)+aux(10)+aux(264)
it(28) =< aux(7)+aux(7)+aux(265)
it(28) =< aux(5)+aux(4)+aux(264)
it(28) =< aux(2)+aux(1)+aux(264)
it(28) =< aux(7)+aux(7)+aux(212)
it(28) =< aux(14)+aux(13)+aux(212)
it(28) =< aux(14)+aux(13)+aux(264)
s(6) =< it(28)*aux(268)

  with precondition: [R=3,E=I,K=L,E>=0,G>=1,K>=2*O,K>=E+1,O>=G,2*O+1>=K,G+K>=E+3] 

* Chain [33]: 0
  with precondition: [R=3,E=I,L=K,E>=0,G>=1,L>=2*O,O>=G,2*O+1>=L] 


#### Cost of chains of lbl71_loop_cont(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,Q,R):
* Chain [41]: 0
  with precondition: [A=3,L=K,O>=1,L>=2*O,2*O+1>=L] 

* Chain [40]: 0
  with precondition: [A=4,L=K,O>=1,L>=2*O,2*O+1>=L] 


#### Cost of chains of lbl21(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R):
* Chain [44]: 0
  with precondition: [B=A,D=C,F=E,H=G,J=I,L=K,N=M,0>=O,L>=2*O,2*O+1>=L] 

* Chain [43]: 10*s(122)+4*s(135)+12*s(138)+4*s(139)+1*s(143)+1*s(181)+3*s(184)+1*s(185)+0
  Such that:aux(280) =< K
s(163) =< K+O
aux(277) =< L
aux(278) =< L+O
aux(281) =< O
aux(282) =< 2*O
s(122) =< aux(281)
s(169) =< s(163)
s(170) =< aux(280)
s(169) =< aux(280)
s(171) =< aux(280)
s(171) =< s(169)
s(172) =< aux(280)
s(173) =< s(169)
s(170) =< aux(280)-3
s(174) =< s(122)*s(171)
s(175) =< s(122)*aux(280)
s(176) =< s(122)*aux(280)
s(177) =< s(122)*s(169)
s(176) =< s(122)*s(169)
s(178) =< s(122)*s(172)
s(179) =< s(122)*s(172)
s(180) =< s(122)*s(173)
s(179) =< s(122)*s(173)
s(181) =< s(122)*s(170)
s(182) =< s(175)
s(182) =< s(177)
s(183) =< s(178)
s(183) =< s(180)
s(184) =< s(180)+s(177)+aux(280)
s(184) =< s(174)+s(174)+aux(282)
s(184) =< s(178)+s(175)+aux(280)
s(184) =< s(179)+s(176)+aux(280)
s(184) =< s(174)+s(174)+aux(280)
s(184) =< s(183)+s(182)+aux(280)
s(185) =< s(184)*aux(280)
s(123) =< aux(278)
s(124) =< aux(277)
s(123) =< aux(277)
s(125) =< aux(277)
s(125) =< s(123)
s(126) =< aux(277)
s(127) =< s(123)
s(124) =< aux(277)-3
s(128) =< s(122)*s(125)
s(129) =< s(122)*aux(277)
s(130) =< s(122)*aux(277)
s(131) =< s(122)*s(123)
s(130) =< s(122)*s(123)
s(132) =< s(122)*s(126)
s(133) =< s(122)*s(126)
s(134) =< s(122)*s(127)
s(133) =< s(122)*s(127)
s(135) =< s(122)*s(124)
s(136) =< s(129)
s(136) =< s(131)
s(137) =< s(132)
s(137) =< s(134)
s(138) =< s(134)+s(131)+aux(277)
s(138) =< s(128)+s(128)+aux(282)
s(138) =< s(132)+s(129)+aux(277)
s(138) =< s(133)+s(130)+aux(277)
s(138) =< s(128)+s(128)+aux(277)
s(138) =< s(137)+s(136)+aux(277)
s(139) =< s(138)*aux(277)
s(143) =< aux(277)

  with precondition: [B=A,D=C,F=E,H=G,J=I,L=K,N=M,O>=1,L>=2*O,2*O+1>=L] 

* Chain [42]: 2*s(191)+4*s(192)+2*s(205)+6*s(208)+2*s(209)+0
  Such that:aux(285) =< K
aux(286) =< K+O
aux(287) =< O
aux(288) =< 2*O
s(191) =< aux(285)
s(192) =< aux(287)
s(193) =< aux(286)
s(194) =< aux(285)
s(193) =< aux(285)
s(195) =< aux(285)
s(195) =< s(193)
s(196) =< aux(285)
s(197) =< s(193)
s(194) =< aux(285)-3
s(198) =< s(192)*s(195)
s(199) =< s(192)*aux(285)
s(200) =< s(192)*aux(285)
s(201) =< s(192)*s(193)
s(200) =< s(192)*s(193)
s(202) =< s(192)*s(196)
s(203) =< s(192)*s(196)
s(204) =< s(192)*s(197)
s(203) =< s(192)*s(197)
s(205) =< s(192)*s(194)
s(206) =< s(199)
s(206) =< s(201)
s(207) =< s(202)
s(207) =< s(204)
s(208) =< s(204)+s(201)+aux(285)
s(208) =< s(198)+s(198)+aux(288)
s(208) =< s(202)+s(199)+aux(285)
s(208) =< s(203)+s(200)+aux(285)
s(208) =< s(198)+s(198)+aux(285)
s(208) =< s(207)+s(206)+aux(285)
s(209) =< s(208)*aux(285)

  with precondition: [B=A,D=C,F=E,H=G,J=I,L=K,N=M,L>=2*O,2*O+1>=L,L>=O+2] 


#### Cost of chains of start0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R):
* Chain [47]: 0
  with precondition: [1>=L] 

* Chain [46]: 10*s(240)+5*s(253)+15*s(256)+5*s(257)+1*s(275)+0
  Such that:s(238) =< L/2
aux(289) =< L
aux(290) =< 3/2*L
s(240) =< s(238)
s(241) =< aux(290)
s(242) =< aux(289)
s(241) =< aux(289)
s(243) =< aux(289)
s(243) =< s(241)
s(244) =< aux(289)
s(245) =< s(241)
s(242) =< aux(289)-3
s(246) =< s(240)*s(243)
s(247) =< s(240)*aux(289)
s(248) =< s(240)*aux(289)
s(249) =< s(240)*s(241)
s(248) =< s(240)*s(241)
s(250) =< s(240)*s(244)
s(251) =< s(240)*s(244)
s(252) =< s(240)*s(245)
s(251) =< s(240)*s(245)
s(253) =< s(240)*s(242)
s(254) =< s(247)
s(254) =< s(249)
s(255) =< s(250)
s(255) =< s(252)
s(256) =< s(252)+s(249)+aux(289)
s(256) =< s(246)+s(246)+aux(289)
s(256) =< s(250)+s(247)+aux(289)
s(256) =< s(251)+s(248)+aux(289)
s(256) =< s(255)+s(254)+aux(289)
s(257) =< s(256)*aux(289)
s(275) =< aux(289)

  with precondition: [L>=2] 

* Chain [45]: 2*s(280)+4*s(281)+2*s(294)+6*s(297)+2*s(298)+0
  Such that:s(278) =< L/2
s(277) =< 3/2*L
aux(291) =< L
aux(292) =< 2*L
s(278) =< aux(291)
s(279) =< aux(291)
s(277) =< aux(292)
s(279) =< aux(292)
s(280) =< aux(291)
s(281) =< s(278)
s(282) =< s(277)
s(283) =< aux(291)
s(282) =< aux(291)
s(284) =< aux(291)
s(284) =< s(282)
s(285) =< aux(291)
s(286) =< s(282)
s(283) =< aux(291)-3
s(287) =< s(281)*s(284)
s(288) =< s(281)*aux(291)
s(289) =< s(281)*aux(291)
s(290) =< s(281)*s(282)
s(289) =< s(281)*s(282)
s(291) =< s(281)*s(285)
s(292) =< s(281)*s(285)
s(293) =< s(281)*s(286)
s(292) =< s(281)*s(286)
s(294) =< s(281)*s(283)
s(295) =< s(288)
s(295) =< s(290)
s(296) =< s(291)
s(296) =< s(293)
s(297) =< s(293)+s(290)+aux(291)
s(297) =< s(287)+s(287)+s(279)
s(297) =< s(291)+s(288)+aux(291)
s(297) =< s(292)+s(289)+aux(291)
s(297) =< s(287)+s(287)+aux(291)
s(297) =< s(296)+s(295)+aux(291)
s(298) =< s(297)*aux(291)

  with precondition: [L>=3] 


Closed-form bounds of start0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R): 
-------------------------------------
* Chain [47] with precondition: [1>=L] 
    - Upper bound: 0 
    - Complexity: constant 
* Chain [46] with precondition: [L>=2] 
    - Upper bound: 5*L*L+16*L+L/2*(3/2*L*(10*L))+L/2*(5*L)+L/2*(45*L)+5*L 
    - Complexity: n^3 
* Chain [45] with precondition: [L>=3] 
    - Upper bound: 2*L*L+8*L+L/2*(3/2*L*(4*L))+L/2*(2*L)+L/2*(18*L)+2*L 
    - Complexity: n^3 

### Maximum cost of start0(A,B,C,D,E,F,G,H,I,J,K,L,M,N,O,P,R): nat(L)*3*nat(L)+nat(L)*8+nat(L)*6*nat(3/2*L)*nat(L/2)+nat(L)*3*nat(L/2)+nat(3/2*L)*18*nat(L/2)+nat(L/2)*6+(nat(L)*2*nat(L)+nat(L)*8+nat(L)*4*nat(3/2*L)*nat(L/2)+nat(L)*2*nat(L/2)+nat(3/2*L)*12*nat(L/2)+nat(L/2)*4) 
Asymptotic class: n^3 
* Total analysis performed in 7702 ms.