/export/starexec/sandbox2/solver/bin/starexec_run_rcdcRelativeAlsoLower /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


WORST_CASE(?, O(n^2))
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty


The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^2).

(0) DCpxTrs
(1) DerivationalComplexityToRuntimeComplexityProof [BOTH BOUNDS(ID, ID), 0 ms]
(2) CpxRelTRS
(3) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 159 ms]
(4) CpxRelTRS
(5) NonCtorToCtorProof [UPPER BOUND(ID), 0 ms]
(6) CpxRelTRS
(7) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms]
(8) CpxWeightedTrs
(9) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms]
(10) CpxTypedWeightedTrs
(11) CompletionProof [UPPER BOUND(ID), 0 ms]
(12) CpxTypedWeightedCompleteTrs
(13) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms]
(14) CpxRNTS
(15) CompleteCoflocoProof [FINISHED, 462 ms]
(16) BOUNDS(1, n^2)


----------------------------------------

(0)
Obligation:
The Derivational Complexity (innermost) of the given DCpxTrs could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   f(g(x), x, y) -> f(y, y, g(y))
   g(g(x)) -> g(x)

S is empty.
Rewrite Strategy: INNERMOST
----------------------------------------

(1) DerivationalComplexityToRuntimeComplexityProof (BOTH BOUNDS(ID, ID))
The following rules have been added to S to convert the given derivational complexity problem to a runtime complexity problem:

   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_g(x_1) -> g(encArg(x_1))


----------------------------------------

(2)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   f(g(x), x, y) -> f(y, y, g(y))
   g(g(x)) -> g(x)

The (relative) TRS S consists of the following rules:

   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_g(x_1) -> g(encArg(x_1))

Rewrite Strategy: INNERMOST
----------------------------------------

(3) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID))
proved innermost termination of relative rules
----------------------------------------

(4)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   f(g(x), x, y) -> f(y, y, g(y))
   g(g(x)) -> g(x)

The (relative) TRS S consists of the following rules:

   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_g(x_1) -> g(encArg(x_1))

Rewrite Strategy: INNERMOST
----------------------------------------

(5) NonCtorToCtorProof (UPPER BOUND(ID))
transformed non-ctor to ctor-system
----------------------------------------

(6)
Obligation:
The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   f(c_g(x), x, y) -> f(y, y, g(y))
   g(c_g(x)) -> g(x)

The (relative) TRS S consists of the following rules:

   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encArg(cons_g(x_1)) -> g(encArg(x_1))
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3))
   encode_g(x_1) -> g(encArg(x_1))
   g(x0) -> c_g(x0)

Rewrite Strategy: INNERMOST
----------------------------------------

(7) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID))
Transformed relative TRS to weighted TRS
----------------------------------------

(8)
Obligation:
The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2).


The TRS R consists of the following rules:

   f(c_g(x), x, y) -> f(y, y, g(y)) [1]
   g(c_g(x)) -> g(x) [1]
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   g(x0) -> c_g(x0) [0]

Rewrite Strategy: INNERMOST
----------------------------------------

(9) TypeInferenceProof (BOTH BOUNDS(ID, ID))
Infered types.
----------------------------------------

(10)
Obligation:
Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   f(c_g(x), x, y) -> f(y, y, g(y)) [1]
   g(c_g(x)) -> g(x) [1]
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   g(x0) -> c_g(x0) [0]

The TRS has the following type information:
f :: c_g -> c_g -> c_g -> c_g
c_g :: c_g -> c_g
g :: c_g -> c_g
encArg :: cons_f:cons_g -> c_g
cons_f :: cons_f:cons_g -> cons_f:cons_g -> cons_f:cons_g -> cons_f:cons_g
cons_g :: cons_f:cons_g -> cons_f:cons_g
encode_f :: cons_f:cons_g -> cons_f:cons_g -> cons_f:cons_g -> c_g
encode_g :: cons_f:cons_g -> c_g

Rewrite Strategy: INNERMOST
----------------------------------------

(11) CompletionProof (UPPER BOUND(ID))
The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added:

   encArg(v0) -> null_encArg [0]
   encode_f(v0, v1, v2) -> null_encode_f [0]
   encode_g(v0) -> null_encode_g [0]
   g(v0) -> null_g [0]
   f(v0, v1, v2) -> null_f [0]

And the following fresh constants:    null_encArg, null_encode_f, null_encode_g, null_g, null_f, const

----------------------------------------

(12)
Obligation:
Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is:

Runtime Complexity Weighted TRS with Types.
The TRS R consists of the following rules:

   f(c_g(x), x, y) -> f(y, y, g(y)) [1]
   g(c_g(x)) -> g(x) [1]
   encArg(cons_f(x_1, x_2, x_3)) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encArg(cons_g(x_1)) -> g(encArg(x_1)) [0]
   encode_f(x_1, x_2, x_3) -> f(encArg(x_1), encArg(x_2), encArg(x_3)) [0]
   encode_g(x_1) -> g(encArg(x_1)) [0]
   g(x0) -> c_g(x0) [0]
   encArg(v0) -> null_encArg [0]
   encode_f(v0, v1, v2) -> null_encode_f [0]
   encode_g(v0) -> null_encode_g [0]
   g(v0) -> null_g [0]
   f(v0, v1, v2) -> null_f [0]

The TRS has the following type information:
f :: c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f -> c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f -> c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f -> c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f
c_g :: c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f -> c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f
g :: c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f -> c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f
encArg :: cons_f:cons_g -> c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f
cons_f :: cons_f:cons_g -> cons_f:cons_g -> cons_f:cons_g -> cons_f:cons_g
cons_g :: cons_f:cons_g -> cons_f:cons_g
encode_f :: cons_f:cons_g -> cons_f:cons_g -> cons_f:cons_g -> c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f
encode_g :: cons_f:cons_g -> c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f
null_encArg :: c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f
null_encode_f :: c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f
null_encode_g :: c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f
null_g :: c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f
null_f :: c_g:null_encArg:null_encode_f:null_encode_g:null_g:null_f
const :: cons_f:cons_g

Rewrite Strategy: INNERMOST
----------------------------------------

(13) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID))
Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction.
The constant constructors are abstracted as follows:

   null_encArg => 0
   null_encode_f => 0
   null_encode_g => 0
   null_g => 0
   null_f => 0
   const => 0

----------------------------------------

(14)
Obligation:
Complexity RNTS consisting of the following rules:

   encArg(z) -{ 0 }-> g(encArg(x_1)) :|: z = 1 + x_1, x_1 >= 0
   encArg(z) -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, z = 1 + x_1 + x_2 + x_3, x_3 >= 0, x_2 >= 0
   encArg(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   encode_f(z, z', z'') -{ 0 }-> f(encArg(x_1), encArg(x_2), encArg(x_3)) :|: x_1 >= 0, x_3 >= 0, x_2 >= 0, z = x_1, z' = x_2, z'' = x_3
   encode_f(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   encode_g(z) -{ 0 }-> g(encArg(x_1)) :|: x_1 >= 0, z = x_1
   encode_g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   f(z, z', z'') -{ 1 }-> f(y, y, g(y)) :|: z' = x, z'' = y, x >= 0, y >= 0, z = 1 + x
   f(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0
   g(z) -{ 1 }-> g(x) :|: x >= 0, z = 1 + x
   g(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0
   g(z) -{ 0 }-> 1 + x0 :|: z = x0, x0 >= 0

Only complete derivations are relevant for the runtime complexity.

----------------------------------------

(15) CompleteCoflocoProof (FINISHED)
Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo:

eq(start(V1, V, V2),0,[f(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]).
eq(start(V1, V, V2),0,[g(V1, Out)],[V1 >= 0]).
eq(start(V1, V, V2),0,[encArg(V1, Out)],[V1 >= 0]).
eq(start(V1, V, V2),0,[fun(V1, V, V2, Out)],[V1 >= 0,V >= 0,V2 >= 0]).
eq(start(V1, V, V2),0,[fun1(V1, Out)],[V1 >= 0]).
eq(f(V1, V, V2, Out),1,[g(V3, Ret2),f(V3, V3, Ret2, Ret)],[Out = Ret,V = V4,V2 = V3,V4 >= 0,V3 >= 0,V1 = 1 + V4]).
eq(g(V1, Out),1,[g(V5, Ret1)],[Out = Ret1,V5 >= 0,V1 = 1 + V5]).
eq(encArg(V1, Out),0,[encArg(V8, Ret0),encArg(V7, Ret11),encArg(V6, Ret21),f(Ret0, Ret11, Ret21, Ret3)],[Out = Ret3,V8 >= 0,V1 = 1 + V6 + V7 + V8,V6 >= 0,V7 >= 0]).
eq(encArg(V1, Out),0,[encArg(V9, Ret01),g(Ret01, Ret4)],[Out = Ret4,V1 = 1 + V9,V9 >= 0]).
eq(fun(V1, V, V2, Out),0,[encArg(V10, Ret02),encArg(V12, Ret12),encArg(V11, Ret22),f(Ret02, Ret12, Ret22, Ret5)],[Out = Ret5,V10 >= 0,V11 >= 0,V12 >= 0,V1 = V10,V = V12,V2 = V11]).
eq(fun1(V1, Out),0,[encArg(V13, Ret03),g(Ret03, Ret6)],[Out = Ret6,V13 >= 0,V1 = V13]).
eq(g(V1, Out),0,[],[Out = 1 + V14,V1 = V14,V14 >= 0]).
eq(encArg(V1, Out),0,[],[Out = 0,V15 >= 0,V1 = V15]).
eq(fun(V1, V, V2, Out),0,[],[Out = 0,V17 >= 0,V2 = V18,V16 >= 0,V1 = V17,V = V16,V18 >= 0]).
eq(fun1(V1, Out),0,[],[Out = 0,V19 >= 0,V1 = V19]).
eq(g(V1, Out),0,[],[Out = 0,V20 >= 0,V1 = V20]).
eq(f(V1, V, V2, Out),0,[],[Out = 0,V21 >= 0,V2 = V22,V23 >= 0,V1 = V21,V = V23,V22 >= 0]).
input_output_vars(f(V1,V,V2,Out),[V1,V,V2],[Out]).
input_output_vars(g(V1,Out),[V1],[Out]).
input_output_vars(encArg(V1,Out),[V1],[Out]).
input_output_vars(fun(V1,V,V2,Out),[V1,V,V2],[Out]).
input_output_vars(fun1(V1,Out),[V1],[Out]).


CoFloCo proof output:
Preprocessing Cost Relations
=====================================

#### Computed strongly connected components 
0. recursive  : [g/2]
1. recursive  : [f/4]
2. recursive [non_tail,multiple] : [encArg/2]
3. non_recursive  : [fun/4]
4. non_recursive  : [fun1/2]
5. non_recursive  : [start/3]

#### Obtained direct recursion through partial evaluation 
0. SCC is partially evaluated into g/2
1. SCC is partially evaluated into f/4
2. SCC is partially evaluated into encArg/2
3. SCC is partially evaluated into fun/4
4. SCC is partially evaluated into fun1/2
5. SCC is partially evaluated into start/3

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

### Specialization of cost equations g/2 
* CE 9 is refined into CE [18] 
* CE 10 is refined into CE [19] 
* CE 8 is refined into CE [20] 


### Cost equations --> "Loop" of g/2 
* CEs [20] --> Loop 12 
* CEs [18] --> Loop 13 
* CEs [19] --> Loop 14 

### Ranking functions of CR g(V1,Out) 
* RF of phase [12]: [V1]

#### Partial ranking functions of CR g(V1,Out) 
* Partial RF of phase [12]:
  - RF of loop [12:1]:
    V1


### Specialization of cost equations f/4 
* CE 7 is refined into CE [21] 
* CE 6 is refined into CE [22,23,24] 


### Cost equations --> "Loop" of f/4 
* CEs [24] --> Loop 15 
* CEs [23] --> Loop 16 
* CEs [22] --> Loop 17 
* CEs [21] --> Loop 18 

### Ranking functions of CR f(V1,V,V2,Out) 

#### Partial ranking functions of CR f(V1,V,V2,Out) 


### Specialization of cost equations encArg/2 
* CE 13 is refined into CE [25] 
* CE 12 is refined into CE [26,27,28] 
* CE 11 is refined into CE [29] 


### Cost equations --> "Loop" of encArg/2 
* CEs [29] --> Loop 19 
* CEs [28] --> Loop 20 
* CEs [27] --> Loop 21 
* CEs [26] --> Loop 22 
* CEs [25] --> Loop 23 

### Ranking functions of CR encArg(V1,Out) 
* RF of phase [19,20,21,22]: [V1]

#### Partial ranking functions of CR encArg(V1,Out) 
* Partial RF of phase [19,20,21,22]:
  - RF of loop [19:1,19:2,19:3,20:1,21:1,22:1]:
    V1


### Specialization of cost equations fun/4 
* CE 14 is refined into CE [30,31,32,33,34,35,36,37] 
* CE 15 is refined into CE [38] 


### Cost equations --> "Loop" of fun/4 
* CEs [30,31,32,33,34,35,36,37,38] --> Loop 24 

### Ranking functions of CR fun(V1,V,V2,Out) 

#### Partial ranking functions of CR fun(V1,V,V2,Out) 


### Specialization of cost equations fun1/2 
* CE 16 is refined into CE [39,40,41,42,43] 
* CE 17 is refined into CE [44] 


### Cost equations --> "Loop" of fun1/2 
* CEs [42,43] --> Loop 25 
* CEs [40] --> Loop 26 
* CEs [39,41,44] --> Loop 27 

### Ranking functions of CR fun1(V1,Out) 

#### Partial ranking functions of CR fun1(V1,Out) 


### Specialization of cost equations start/3 
* CE 1 is refined into CE [45] 
* CE 2 is refined into CE [46,47,48] 
* CE 3 is refined into CE [49,50] 
* CE 4 is refined into CE [51] 
* CE 5 is refined into CE [52,53,54] 


### Cost equations --> "Loop" of start/3 
* CEs [45,46,47,48,49,50,51,52,53,54] --> Loop 28 

### Ranking functions of CR start(V1,V,V2) 

#### Partial ranking functions of CR start(V1,V,V2) 


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

#### Cost of chains of g(V1,Out):
* Chain [[12],14]: 1*it(12)+0
  Such that:it(12) =< V1

  with precondition: [Out=0,V1>=1] 

* Chain [[12],13]: 1*it(12)+0
  Such that:it(12) =< V1-Out+1

  with precondition: [Out>=1,V1>=Out] 

* Chain [14]: 0
  with precondition: [Out=0,V1>=0] 

* Chain [13]: 0
  with precondition: [V1+1=Out,V1>=0] 


#### Cost of chains of f(V1,V,V2,Out):
* Chain [18]: 0
  with precondition: [Out=0,V1>=0,V>=0,V2>=0] 

* Chain [17,18]: 1*s(2)+1
  Such that:s(2) =< V2

  with precondition: [Out=0,V1=V+1,V1>=1,V2>=0] 

* Chain [16,18]: 1
  with precondition: [Out=0,V1=V+1,V1>=1,V2>=0] 

* Chain [15,18]: 1*s(3)+1
  Such that:s(3) =< V2

  with precondition: [Out=0,V1=V+1,V1>=1,V2>=1] 


#### Cost of chains of encArg(V1,Out):
* Chain [23]: 0
  with precondition: [Out=0,V1>=0] 

* Chain [multiple([19,20,21,22],[[23]])]: 1*it(19)+2*s(14)+1*s(16)+1*s(17)+0
  Such that:aux(5) =< V1
it(19) =< aux(5)
it(20) =< aux(5)
aux(4) =< aux(5)+1
aux(3) =< aux(5)
s(15) =< it(19)*aux(5)
s(17) =< it(20)*aux(4)
s(16) =< it(20)*aux(3)
s(14) =< s(15)

  with precondition: [V1>=1,Out>=0,V1>=Out] 


#### Cost of chains of fun(V1,V,V2,Out):
* Chain [24]: 12*s(21)+4*s(26)+4*s(27)+8*s(28)+4*s(32)+4*s(37)+4*s(38)+8*s(39)+4*s(63)+4*s(68)+4*s(69)+8*s(70)+1
  Such that:aux(10) =< V1
aux(11) =< V
aux(12) =< V2
s(63) =< aux(10)
s(65) =< aux(10)+1
s(66) =< aux(10)
s(67) =< s(63)*aux(10)
s(68) =< aux(10)*s(65)
s(69) =< aux(10)*s(66)
s(70) =< s(67)
s(21) =< aux(12)
s(23) =< aux(12)+1
s(24) =< aux(12)
s(25) =< s(21)*aux(12)
s(26) =< aux(12)*s(23)
s(27) =< aux(12)*s(24)
s(28) =< s(25)
s(32) =< aux(11)
s(34) =< aux(11)+1
s(35) =< aux(11)
s(36) =< s(32)*aux(11)
s(37) =< aux(11)*s(34)
s(38) =< aux(11)*s(35)
s(39) =< s(36)

  with precondition: [Out=0,V1>=0,V>=0,V2>=0] 


#### Cost of chains of fun1(V1,Out):
* Chain [27]: 2*s(144)+1*s(149)+1*s(150)+2*s(151)+0
  Such that:aux(13) =< V1
s(144) =< aux(13)
s(146) =< aux(13)+1
s(147) =< aux(13)
s(148) =< s(144)*aux(13)
s(149) =< aux(13)*s(146)
s(150) =< aux(13)*s(147)
s(151) =< s(148)

  with precondition: [Out=0,V1>=0] 

* Chain [26]: 0
  with precondition: [Out=1,V1>=0] 

* Chain [25]: 3*s(154)+2*s(159)+2*s(160)+4*s(161)+0
  Such that:aux(15) =< V1
s(154) =< aux(15)
s(156) =< aux(15)+1
s(157) =< aux(15)
s(158) =< s(154)*aux(15)
s(159) =< aux(15)*s(156)
s(160) =< aux(15)*s(157)
s(161) =< s(158)

  with precondition: [V1>=1,Out>=1,V1+1>=Out] 


#### Cost of chains of start(V1,V,V2):
* Chain [28]: 14*s(173)+12*s(174)+8*s(182)+8*s(183)+16*s(184)+4*s(199)+4*s(200)+8*s(201)+4*s(202)+4*s(206)+4*s(207)+8*s(208)+1
  Such that:s(186) =< V
aux(16) =< V1
aux(17) =< V2
s(174) =< aux(16)
s(179) =< aux(16)+1
s(180) =< aux(16)
s(181) =< s(174)*aux(16)
s(182) =< aux(16)*s(179)
s(183) =< aux(16)*s(180)
s(184) =< s(181)
s(173) =< aux(17)
s(196) =< aux(17)+1
s(197) =< aux(17)
s(198) =< s(173)*aux(17)
s(199) =< aux(17)*s(196)
s(200) =< aux(17)*s(197)
s(201) =< s(198)
s(202) =< s(186)
s(203) =< s(186)+1
s(204) =< s(186)
s(205) =< s(202)*s(186)
s(206) =< s(186)*s(203)
s(207) =< s(186)*s(204)
s(208) =< s(205)

  with precondition: [V1>=0] 


Closed-form bounds of start(V1,V,V2): 
-------------------------------------
* Chain [28] with precondition: [V1>=0] 
    - Upper bound: 20*V1+1+32*V1*V1+nat(V)*8+nat(V)*16*nat(V)+nat(V2)*18+nat(V2)*16*nat(V2) 
    - Complexity: n^2 

### Maximum cost of start(V1,V,V2): 20*V1+1+32*V1*V1+nat(V)*8+nat(V)*16*nat(V)+nat(V2)*18+nat(V2)*16*nat(V2) 
Asymptotic class: n^2 
* Total analysis performed in 370 ms.


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(16)
BOUNDS(1, n^2)