/export/starexec/sandbox2/solver/bin/starexec_run_complexity /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- WORST_CASE(Omega(n^1), O(n^3)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). (0) CpxRelTRS (1) SInnermostTerminationProof [BOTH CONCRETE BOUNDS(ID, ID), 225 ms] (2) CpxRelTRS (3) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxWeightedTrs (5) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (6) CpxTypedWeightedTrs (7) CompletionProof [UPPER BOUND(ID), 0 ms] (8) CpxTypedWeightedCompleteTrs (9) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (10) CpxRNTS (11) CompleteCoflocoProof [FINISHED, 109.4 s] (12) BOUNDS(1, n^3) (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxRelTRS (15) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (16) typed CpxTrs (17) OrderProof [LOWER BOUND(ID), 0 ms] (18) typed CpxTrs (19) RewriteLemmaProof [LOWER BOUND(ID), 260 ms] (20) BEST (21) proven lower bound (22) LowerBoundPropagationProof [FINISHED, 0 ms] (23) BOUNDS(n^1, INF) (24) typed CpxTrs (25) RewriteLemmaProof [LOWER BOUND(ID), 1 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 66 ms] (28) typed CpxTrs (29) RewriteLemmaProof [LOWER BOUND(ID), 45 ms] (30) typed CpxTrs ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) @(Nil, ys) -> ys gt0(Cons(x, xs), Nil) -> True gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) gcd(Nil, Nil) -> Nil gcd(Nil, Cons(x, xs)) -> Nil gcd(Cons(x, xs), Nil) -> Nil gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) eqList(Cons(x, xs), Nil) -> False eqList(Nil, Cons(y, ys)) -> False eqList(Nil, Nil) -> True lgth(Nil) -> Nil gt0(Nil, y) -> False monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) goal(x, y) -> gcd(x, y) The (relative) TRS S consists of the following rules: and(False, False) -> False and(True, False) -> False and(False, True) -> False and(True, True) -> True monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) monus[Ite](True, Cons(x, xs), y) -> xs gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) gcd[Ite](True, x, y) -> x gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x) gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y)) Rewrite Strategy: INNERMOST ---------------------------------------- (1) SInnermostTerminationProof (BOTH CONCRETE BOUNDS(ID, ID)) proved innermost termination of relative rules ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, n^3). The TRS R consists of the following rules: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) @(Nil, ys) -> ys gt0(Cons(x, xs), Nil) -> True gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) gcd(Nil, Nil) -> Nil gcd(Nil, Cons(x, xs)) -> Nil gcd(Cons(x, xs), Nil) -> Nil gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) eqList(Cons(x, xs), Nil) -> False eqList(Nil, Cons(y, ys)) -> False eqList(Nil, Nil) -> True lgth(Nil) -> Nil gt0(Nil, y) -> False monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) goal(x, y) -> gcd(x, y) The (relative) TRS S consists of the following rules: and(False, False) -> False and(True, False) -> False and(False, True) -> False and(True, True) -> True monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) monus[Ite](True, Cons(x, xs), y) -> xs gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) gcd[Ite](True, x, y) -> x gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x) gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y)) Rewrite Strategy: INNERMOST ---------------------------------------- (3) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (4) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^3). The TRS R consists of the following rules: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) [1] @(Nil, ys) -> ys [1] gt0(Cons(x, xs), Nil) -> True [1] gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) [1] gcd(Nil, Nil) -> Nil [1] gcd(Nil, Cons(x, xs)) -> Nil [1] gcd(Cons(x, xs), Nil) -> Nil [1] gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) [1] lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) [1] eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) [1] eqList(Cons(x, xs), Nil) -> False [1] eqList(Nil, Cons(y, ys)) -> False [1] eqList(Nil, Nil) -> True [1] lgth(Nil) -> Nil [1] gt0(Nil, y) -> False [1] monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) [1] goal(x, y) -> gcd(x, y) [1] and(False, False) -> False [0] and(True, False) -> False [0] and(False, True) -> False [0] and(True, True) -> True [0] monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) [0] monus[Ite](True, Cons(x, xs), y) -> xs [0] gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) [0] gcd[Ite](True, x, y) -> x [0] gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x) [0] gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y)) [0] Rewrite Strategy: INNERMOST ---------------------------------------- (5) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (6) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) [1] @(Nil, ys) -> ys [1] gt0(Cons(x, xs), Nil) -> True [1] gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) [1] gcd(Nil, Nil) -> Nil [1] gcd(Nil, Cons(x, xs)) -> Nil [1] gcd(Cons(x, xs), Nil) -> Nil [1] gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) [1] lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) [1] eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) [1] eqList(Cons(x, xs), Nil) -> False [1] eqList(Nil, Cons(y, ys)) -> False [1] eqList(Nil, Nil) -> True [1] lgth(Nil) -> Nil [1] gt0(Nil, y) -> False [1] monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) [1] goal(x, y) -> gcd(x, y) [1] and(False, False) -> False [0] and(True, False) -> False [0] and(False, True) -> False [0] and(True, True) -> True [0] monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) [0] monus[Ite](True, Cons(x, xs), y) -> xs [0] gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) [0] gcd[Ite](True, x, y) -> x [0] gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x) [0] gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y)) [0] The TRS has the following type information: @ :: Cons:Nil -> Cons:Nil -> Cons:Nil Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil Nil :: Cons:Nil gt0 :: Cons:Nil -> Cons:Nil -> True:False True :: True:False gcd :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil eqList :: Cons:Nil -> Cons:Nil -> True:False lgth :: Cons:Nil -> Cons:Nil and :: True:False -> True:False -> True:False False :: True:False monus :: Cons:Nil -> Cons:Nil -> Cons:Nil monus[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil goal :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[False][Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil Rewrite Strategy: INNERMOST ---------------------------------------- (7) 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: and(v0, v1) -> null_and [0] monus[Ite](v0, v1, v2) -> null_monus[Ite] [0] gcd[Ite](v0, v1, v2) -> null_gcd[Ite] [0] gcd[False][Ite](v0, v1, v2) -> null_gcd[False][Ite] [0] @(v0, v1) -> null_@ [0] gt0(v0, v1) -> null_gt0 [0] gcd(v0, v1) -> null_gcd [0] lgth(v0) -> null_lgth [0] eqList(v0, v1) -> null_eqList [0] And the following fresh constants: null_and, null_monus[Ite], null_gcd[Ite], null_gcd[False][Ite], null_@, null_gt0, null_gcd, null_lgth, null_eqList ---------------------------------------- (8) 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: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) [1] @(Nil, ys) -> ys [1] gt0(Cons(x, xs), Nil) -> True [1] gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) [1] gcd(Nil, Nil) -> Nil [1] gcd(Nil, Cons(x, xs)) -> Nil [1] gcd(Cons(x, xs), Nil) -> Nil [1] gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) [1] lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) [1] eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) [1] eqList(Cons(x, xs), Nil) -> False [1] eqList(Nil, Cons(y, ys)) -> False [1] eqList(Nil, Nil) -> True [1] lgth(Nil) -> Nil [1] gt0(Nil, y) -> False [1] monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) [1] goal(x, y) -> gcd(x, y) [1] and(False, False) -> False [0] and(True, False) -> False [0] and(False, True) -> False [0] and(True, True) -> True [0] monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) [0] monus[Ite](True, Cons(x, xs), y) -> xs [0] gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) [0] gcd[Ite](True, x, y) -> x [0] gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x) [0] gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y)) [0] and(v0, v1) -> null_and [0] monus[Ite](v0, v1, v2) -> null_monus[Ite] [0] gcd[Ite](v0, v1, v2) -> null_gcd[Ite] [0] gcd[False][Ite](v0, v1, v2) -> null_gcd[False][Ite] [0] @(v0, v1) -> null_@ [0] gt0(v0, v1) -> null_gt0 [0] gcd(v0, v1) -> null_gcd [0] lgth(v0) -> null_lgth [0] eqList(v0, v1) -> null_eqList [0] The TRS has the following type information: @ :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth Cons :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth Nil :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth gt0 :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> True:False:null_and:null_gt0:null_eqList True :: True:False:null_and:null_gt0:null_eqList gcd :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth gcd[Ite] :: True:False:null_and:null_gt0:null_eqList -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth eqList :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> True:False:null_and:null_gt0:null_eqList lgth :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth and :: True:False:null_and:null_gt0:null_eqList -> True:False:null_and:null_gt0:null_eqList -> True:False:null_and:null_gt0:null_eqList False :: True:False:null_and:null_gt0:null_eqList monus :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth monus[Ite] :: True:False:null_and:null_gt0:null_eqList -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth goal :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth gcd[False][Ite] :: True:False:null_and:null_gt0:null_eqList -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth -> Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth null_and :: True:False:null_and:null_gt0:null_eqList null_monus[Ite] :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth null_gcd[Ite] :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth null_gcd[False][Ite] :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth null_@ :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth null_gt0 :: True:False:null_and:null_gt0:null_eqList null_gcd :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth null_lgth :: Cons:Nil:null_monus[Ite]:null_gcd[Ite]:null_gcd[False][Ite]:null_@:null_gcd:null_lgth null_eqList :: True:False:null_and:null_gt0:null_eqList Rewrite Strategy: INNERMOST ---------------------------------------- (9) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: Nil => 0 True => 2 False => 1 null_and => 0 null_monus[Ite] => 0 null_gcd[Ite] => 0 null_gcd[False][Ite] => 0 null_@ => 0 null_gt0 => 0 null_gcd => 0 null_lgth => 0 null_eqList => 0 ---------------------------------------- (10) Obligation: Complexity RNTS consisting of the following rules: @(z, z') -{ 1 }-> ys :|: z' = ys, ys >= 0, z = 0 @(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 @(z, z') -{ 1 }-> 1 + x + @(xs, ys) :|: z = 1 + x + xs, xs >= 0, z' = ys, ys >= 0, x >= 0 and(z, z') -{ 0 }-> 2 :|: z = 2, z' = 2 and(z, z') -{ 0 }-> 1 :|: z = 1, z' = 1 and(z, z') -{ 0 }-> 1 :|: z = 2, z' = 1 and(z, z') -{ 0 }-> 1 :|: z' = 2, z = 1 and(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 eqList(z, z') -{ 1 }-> and(eqList(x, y), eqList(xs, ys)) :|: z = 1 + x + xs, xs >= 0, ys >= 0, x >= 0, y >= 0, z' = 1 + y + ys eqList(z, z') -{ 1 }-> 2 :|: z = 0, z' = 0 eqList(z, z') -{ 1 }-> 1 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 eqList(z, z') -{ 1 }-> 1 :|: ys >= 0, y >= 0, z = 0, z' = 1 + y + ys eqList(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 gcd(z, z') -{ 1 }-> gcd[Ite](eqList(1 + x' + xs', 1 + x + xs), 1 + x' + xs', 1 + x + xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs' gcd(z, z') -{ 1 }-> 0 :|: z = 0, z' = 0 gcd(z, z') -{ 1 }-> 0 :|: xs >= 0, z' = 1 + x + xs, x >= 0, z = 0 gcd(z, z') -{ 1 }-> 0 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 gcd(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 gcd[False][Ite](z, z', z'') -{ 0 }-> gcd(y, monus(x, y)) :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0 gcd[False][Ite](z, z', z'') -{ 0 }-> gcd(monus(y, x), x) :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0 gcd[False][Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 gcd[Ite](z, z', z'') -{ 0 }-> x :|: z = 2, z' = x, z'' = y, x >= 0, y >= 0 gcd[Ite](z, z', z'') -{ 0 }-> gcd[False][Ite](gt0(x, y), x, y) :|: z' = x, z'' = y, z = 1, x >= 0, y >= 0 gcd[Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 goal(z, z') -{ 1 }-> gcd(x, y) :|: x >= 0, y >= 0, z = x, z' = y gt0(z, z') -{ 1 }-> gt0(xs', xs) :|: xs >= 0, z' = 1 + x + xs, x' >= 0, xs' >= 0, x >= 0, z = 1 + x' + xs' gt0(z, z') -{ 1 }-> 2 :|: z = 1 + x + xs, xs >= 0, x >= 0, z' = 0 gt0(z, z') -{ 1 }-> 1 :|: y >= 0, z = 0, z' = y gt0(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 lgth(z) -{ 1 }-> @(1 + 0 + 0, lgth(xs)) :|: z = 1 + x + xs, xs >= 0, x >= 0 lgth(z) -{ 1 }-> 0 :|: z = 0 lgth(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 monus(z, z') -{ 1 }-> monus[Ite](eqList(lgth(y), 1 + 0 + 0), x, y) :|: x >= 0, y >= 0, z = x, z' = y monus[Ite](z, z', z'') -{ 0 }-> xs :|: z = 2, xs >= 0, z' = 1 + x + xs, z'' = y, x >= 0, y >= 0 monus[Ite](z, z', z'') -{ 0 }-> monus(xs', xs) :|: xs >= 0, z = 1, x' >= 0, xs' >= 0, x >= 0, z' = 1 + x' + xs', z'' = 1 + x + xs monus[Ite](z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (11) CompleteCoflocoProof (FINISHED) Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: eq(start(V1, V, V35),0,[fun(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V35),0,[gt0(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V35),0,[gcd(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V35),0,[lgth(V1, Out)],[V1 >= 0]). eq(start(V1, V, V35),0,[eqList(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V35),0,[monus(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V35),0,[goal(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V35),0,[and(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V35),0,[fun2(V1, V, V35, Out)],[V1 >= 0,V >= 0,V35 >= 0]). eq(start(V1, V, V35),0,[fun1(V1, V, V35, Out)],[V1 >= 0,V >= 0,V35 >= 0]). eq(start(V1, V, V35),0,[fun3(V1, V, V35, Out)],[V1 >= 0,V >= 0,V35 >= 0]). eq(fun(V1, V, Out),1,[fun(V2, V3, Ret1)],[Out = 1 + Ret1 + V4,V1 = 1 + V2 + V4,V2 >= 0,V = V3,V3 >= 0,V4 >= 0]). eq(fun(V1, V, Out),1,[],[Out = V5,V = V5,V5 >= 0,V1 = 0]). eq(gt0(V1, V, Out),1,[],[Out = 2,V1 = 1 + V6 + V7,V7 >= 0,V6 >= 0,V = 0]). eq(gt0(V1, V, Out),1,[gt0(V8, V10, Ret)],[Out = Ret,V10 >= 0,V = 1 + V10 + V9,V11 >= 0,V8 >= 0,V9 >= 0,V1 = 1 + V11 + V8]). eq(gcd(V1, V, Out),1,[],[Out = 0,V1 = 0,V = 0]). eq(gcd(V1, V, Out),1,[],[Out = 0,V13 >= 0,V = 1 + V12 + V13,V12 >= 0,V1 = 0]). eq(gcd(V1, V, Out),1,[],[Out = 0,V1 = 1 + V14 + V15,V15 >= 0,V14 >= 0,V = 0]). eq(gcd(V1, V, Out),1,[eqList(1 + V19 + V17, 1 + V18 + V16, Ret0),fun1(Ret0, 1 + V19 + V17, 1 + V18 + V16, Ret2)],[Out = Ret2,V16 >= 0,V = 1 + V16 + V18,V19 >= 0,V17 >= 0,V18 >= 0,V1 = 1 + V17 + V19]). eq(lgth(V1, Out),1,[lgth(V20, Ret11),fun(1 + 0 + 0, Ret11, Ret3)],[Out = Ret3,V1 = 1 + V20 + V21,V20 >= 0,V21 >= 0]). eq(eqList(V1, V, Out),1,[eqList(V22, V25, Ret01),eqList(V23, V24, Ret12),and(Ret01, Ret12, Ret4)],[Out = Ret4,V1 = 1 + V22 + V23,V23 >= 0,V24 >= 0,V22 >= 0,V25 >= 0,V = 1 + V24 + V25]). eq(eqList(V1, V, Out),1,[],[Out = 1,V1 = 1 + V26 + V27,V26 >= 0,V27 >= 0,V = 0]). eq(eqList(V1, V, Out),1,[],[Out = 1,V28 >= 0,V29 >= 0,V1 = 0,V = 1 + V28 + V29]). eq(eqList(V1, V, Out),1,[],[Out = 2,V1 = 0,V = 0]). eq(lgth(V1, Out),1,[],[Out = 0,V1 = 0]). eq(gt0(V1, V, Out),1,[],[Out = 1,V30 >= 0,V1 = 0,V = V30]). eq(monus(V1, V, Out),1,[lgth(V31, Ret00),eqList(Ret00, 1 + 0 + 0, Ret02),fun2(Ret02, V32, V31, Ret5)],[Out = Ret5,V32 >= 0,V31 >= 0,V1 = V32,V = V31]). eq(goal(V1, V, Out),1,[gcd(V34, V33, Ret6)],[Out = Ret6,V34 >= 0,V33 >= 0,V1 = V34,V = V33]). eq(and(V1, V, Out),0,[],[Out = 1,V1 = 1,V = 1]). eq(and(V1, V, Out),0,[],[Out = 1,V1 = 2,V = 1]). eq(and(V1, V, Out),0,[],[Out = 1,V = 2,V1 = 1]). eq(and(V1, V, Out),0,[],[Out = 2,V1 = 2,V = 2]). eq(fun2(V1, V, V35, Out),0,[monus(V36, V37, Ret7)],[Out = Ret7,V37 >= 0,V1 = 1,V39 >= 0,V36 >= 0,V38 >= 0,V = 1 + V36 + V39,V35 = 1 + V37 + V38]). eq(fun2(V1, V, V35, Out),0,[],[Out = V42,V1 = 2,V42 >= 0,V = 1 + V41 + V42,V35 = V40,V41 >= 0,V40 >= 0]). eq(fun1(V1, V, V35, Out),0,[gt0(V43, V44, Ret03),fun3(Ret03, V43, V44, Ret8)],[Out = Ret8,V = V43,V35 = V44,V1 = 1,V43 >= 0,V44 >= 0]). eq(fun1(V1, V, V35, Out),0,[],[Out = V45,V1 = 2,V = V45,V35 = V46,V45 >= 0,V46 >= 0]). eq(fun3(V1, V, V35, Out),0,[monus(V47, V48, Ret04),gcd(Ret04, V48, Ret9)],[Out = Ret9,V = V48,V35 = V47,V1 = 1,V48 >= 0,V47 >= 0]). eq(fun3(V1, V, V35, Out),0,[monus(V49, V50, Ret13),gcd(V50, Ret13, Ret10)],[Out = Ret10,V1 = 2,V = V49,V35 = V50,V49 >= 0,V50 >= 0]). eq(and(V1, V, Out),0,[],[Out = 0,V52 >= 0,V51 >= 0,V1 = V52,V = V51]). eq(fun2(V1, V, V35, Out),0,[],[Out = 0,V54 >= 0,V35 = V55,V53 >= 0,V1 = V54,V = V53,V55 >= 0]). eq(fun1(V1, V, V35, Out),0,[],[Out = 0,V58 >= 0,V35 = V56,V57 >= 0,V1 = V58,V = V57,V56 >= 0]). eq(fun3(V1, V, V35, Out),0,[],[Out = 0,V59 >= 0,V35 = V60,V61 >= 0,V1 = V59,V = V61,V60 >= 0]). eq(fun(V1, V, Out),0,[],[Out = 0,V63 >= 0,V62 >= 0,V1 = V63,V = V62]). eq(gt0(V1, V, Out),0,[],[Out = 0,V65 >= 0,V64 >= 0,V1 = V65,V = V64]). eq(gcd(V1, V, Out),0,[],[Out = 0,V67 >= 0,V66 >= 0,V1 = V67,V = V66]). eq(lgth(V1, Out),0,[],[Out = 0,V68 >= 0,V1 = V68]). eq(eqList(V1, V, Out),0,[],[Out = 0,V69 >= 0,V70 >= 0,V1 = V69,V = V70]). input_output_vars(fun(V1,V,Out),[V1,V],[Out]). input_output_vars(gt0(V1,V,Out),[V1,V],[Out]). input_output_vars(gcd(V1,V,Out),[V1,V],[Out]). input_output_vars(lgth(V1,Out),[V1],[Out]). input_output_vars(eqList(V1,V,Out),[V1,V],[Out]). input_output_vars(monus(V1,V,Out),[V1,V],[Out]). input_output_vars(goal(V1,V,Out),[V1,V],[Out]). input_output_vars(and(V1,V,Out),[V1,V],[Out]). input_output_vars(fun2(V1,V,V35,Out),[V1,V,V35],[Out]). input_output_vars(fun1(V1,V,V35,Out),[V1,V,V35],[Out]). input_output_vars(fun3(V1,V,V35,Out),[V1,V,V35],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. non_recursive : [and/3] 1. recursive [non_tail,multiple] : [eqList/3] 2. recursive : [fun/3] 3. recursive [non_tail] : [lgth/2] 4. recursive : [fun2/4,monus/3] 5. recursive : [gt0/3] 6. recursive : [fun1/4,fun3/4,gcd/3] 7. non_recursive : [goal/3] 8. non_recursive : [start/3] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into and/3 1. SCC is partially evaluated into eqList/3 2. SCC is partially evaluated into fun/3 3. SCC is partially evaluated into lgth/2 4. SCC is partially evaluated into monus/3 5. SCC is partially evaluated into gt0/3 6. SCC is partially evaluated into gcd/3 7. SCC is completely evaluated into other SCCs 8. SCC is partially evaluated into start/3 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations and/3 * CE 47 is refined into CE [48] * CE 46 is refined into CE [49] * CE 44 is refined into CE [50] * CE 45 is refined into CE [51] * CE 43 is refined into CE [52] ### Cost equations --> "Loop" of and/3 * CEs [48] --> Loop 31 * CEs [49] --> Loop 32 * CEs [50] --> Loop 33 * CEs [51] --> Loop 34 * CEs [52] --> Loop 35 ### Ranking functions of CR and(V1,V,Out) #### Partial ranking functions of CR and(V1,V,Out) ### Specialization of cost equations eqList/3 * CE 42 is refined into CE [53] * CE 39 is refined into CE [54] * CE 40 is refined into CE [55] * CE 41 is refined into CE [56] * CE 38 is refined into CE [57,58,59,60,61] ### Cost equations --> "Loop" of eqList/3 * CEs [60] --> Loop 36 * CEs [59] --> Loop 37 * CEs [58] --> Loop 38 * CEs [57] --> Loop 39 * CEs [61] --> Loop 40 * CEs [53] --> Loop 41 * CEs [54] --> Loop 42 * CEs [55] --> Loop 43 * CEs [56] --> Loop 44 ### Ranking functions of CR eqList(V1,V,Out) * RF of phase [36]: [V,V1] * RF of phase [37,38,39]: [V,V1] * RF of phase [40]: [V,V1] #### Partial ranking functions of CR eqList(V1,V,Out) * Partial RF of phase [36]: - RF of loop [36:1,36:2]: V V1 * Partial RF of phase [37,38,39]: - RF of loop [37:1,37:2,38:1,38:2,39:1,39:2]: V V1 * Partial RF of phase [40]: - RF of loop [40:1,40:2]: V V1 ### Specialization of cost equations fun/3 * CE 34 is refined into CE [62] * CE 33 is refined into CE [63] * CE 32 is refined into CE [64] ### Cost equations --> "Loop" of fun/3 * CEs [64] --> Loop 45 * CEs [62] --> Loop 46 * CEs [63] --> Loop 47 ### Ranking functions of CR fun(V1,V,Out) * RF of phase [45]: [V1] #### Partial ranking functions of CR fun(V1,V,Out) * Partial RF of phase [45]: - RF of loop [45:1]: V1 ### Specialization of cost equations lgth/2 * CE 36 is refined into CE [65] * CE 37 is refined into CE [66] * CE 35 is refined into CE [67,68,69] ### Cost equations --> "Loop" of lgth/2 * CEs [68] --> Loop 48 * CEs [69] --> Loop 49 * CEs [67] --> Loop 50 * CEs [65,66] --> Loop 51 ### Ranking functions of CR lgth(V1,Out) * RF of phase [48,49,50]: [V1] #### Partial ranking functions of CR lgth(V1,Out) * Partial RF of phase [48,49,50]: - RF of loop [48:1,49:1,50:1]: V1 ### Specialization of cost equations monus/3 * CE 22 is refined into CE [70,71,72] * CE 21 is refined into CE [73] * CE 20 is refined into CE [74,75,76,77,78,79] ### Cost equations --> "Loop" of monus/3 * CEs [73] --> Loop 52 * CEs [74,75,76,77,78,79] --> Loop 53 * CEs [70,71,72] --> Loop 54 ### Ranking functions of CR monus(V1,V,Out) * RF of phase [54]: [V,V1] #### Partial ranking functions of CR monus(V1,V,Out) * Partial RF of phase [54]: - RF of loop [54:1]: V V1 ### Specialization of cost equations gt0/3 * CE 19 is refined into CE [80] * CE 16 is refined into CE [81] * CE 18 is refined into CE [82] * CE 17 is refined into CE [83] ### Cost equations --> "Loop" of gt0/3 * CEs [83] --> Loop 55 * CEs [80] --> Loop 56 * CEs [81] --> Loop 57 * CEs [82] --> Loop 58 ### Ranking functions of CR gt0(V1,V,Out) * RF of phase [55]: [V,V1] #### Partial ranking functions of CR gt0(V1,V,Out) * Partial RF of phase [55]: - RF of loop [55:1]: V V1 ### Specialization of cost equations gcd/3 * CE 27 is refined into CE [84] * CE 30 is refined into CE [85] * CE 29 is refined into CE [86] * CE 23 is refined into CE [87,88,89] * CE 26 is refined into CE [90,91,92] * CE 28 is refined into CE [93] * CE 31 is refined into CE [94] * CE 25 is refined into CE [95,96] * CE 24 is refined into CE [97,98] ### Cost equations --> "Loop" of gcd/3 * CEs [97,98] --> Loop 59 * CEs [95,96] --> Loop 60 * CEs [84] --> Loop 61 * CEs [92] --> Loop 62 * CEs [85] --> Loop 63 * CEs [86] --> Loop 64 * CEs [87,88,89,90,91,93,94] --> Loop 65 ### Ranking functions of CR gcd(V1,V,Out) * RF of phase [59,60]: [V1+V-2] #### Partial ranking functions of CR gcd(V1,V,Out) * Partial RF of phase [59,60]: - RF of loop [59:1,60:1]: V1+V-2 ### Specialization of cost equations start/3 * CE 4 is refined into CE [99,100,101,102,103,104,105] * CE 1 is refined into CE [106,107,108,109,110] * CE 2 is refined into CE [111] * CE 3 is refined into CE [112,113,114,115,116,117,118,119] * CE 5 is refined into CE [120,121,122,123,124,125] * CE 6 is refined into CE [126,127,128,129,130] * CE 7 is refined into CE [131,132] * CE 8 is refined into CE [133,134,135,136] * CE 9 is refined into CE [137,138,139,140,141] * CE 10 is refined into CE [142,143,144,145,146] * CE 11 is refined into CE [147,148] * CE 12 is refined into CE [149,150,151,152,153,154] * CE 13 is refined into CE [155,156] * CE 14 is refined into CE [157,158,159,160,161] * CE 15 is refined into CE [162,163,164,165,166] ### Cost equations --> "Loop" of start/3 * CEs [138,143,151,158] --> Loop 66 * CEs [99,100,101,102,103,104,105] --> Loop 67 * CEs [165] --> Loop 68 * CEs [164] --> Loop 69 * CEs [107,112] --> Loop 70 * CEs [163] --> Loop 71 * CEs [144,145,154,159,160,162] --> Loop 72 * CEs [106,108,109,110,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132] --> Loop 73 * CEs [111,133,134,135,136,137,139,140,141,142,146,147,148,149,150,152,153,155,156,157,161,166] --> Loop 74 ### Ranking functions of CR start(V1,V,V35) #### Partial ranking functions of CR start(V1,V,V35) Computing Bounds ===================================== #### Cost of chains of and(V1,V,Out): * Chain [35]: 0 with precondition: [V1=1,V=1,Out=1] * Chain [34]: 0 with precondition: [V1=1,V=2,Out=1] * Chain [33]: 0 with precondition: [V1=2,V=1,Out=1] * Chain [32]: 0 with precondition: [V1=2,V=2,Out=2] * Chain [31]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of eqList(V1,V,Out): * Chain [44]: 1 with precondition: [V1=0,V=0,Out=2] * Chain [43]: 1 with precondition: [V1=0,Out=1,V>=1] * Chain [42]: 1 with precondition: [V=0,Out=1,V1>=1] * Chain [41]: 0 with precondition: [Out=0,V1>=0,V>=0] * Chain [multiple([40],[[multiple([37,38,39],[[multiple([36],[[44]])],[44],[43],[42]])],[multiple([36],[[44]])],[44],[43],[42],[41]])]: 1*it(40)+1*it([42])+1*it([43])+1*it([44])+5*s(1)+1*s(3)+1*s(4)+1*s(5)+1*s(6)+1*s(7)+0 Such that:aux(11) =< V1 aux(12) =< V1+1 aux(13) =< V1/2+1/2 aux(14) =< V1/3+V/3+2/3 aux(15) =< V+1 aux(16) =< V/2+1/2 it(40) =< aux(11) it([42]) =< aux(11) it([42]) =< aux(12) it([43]) =< aux(12) it([44]) =< aux(12) it([42]) =< aux(13) it([44]) =< aux(15) s(1) =< aux(15) it([43]) =< aux(16) s(11) =< aux(15)*(1/2) s(9) =< aux(14)*(6/5) s(6) =< aux(13) s(5) =< aux(14) s(3) =< s(9) s(4) =< s(9) s(5) =< s(9) s(4) =< aux(15) s(5) =< aux(15) s(7) =< aux(15) s(7) =< s(11) s(5) =< s(1)*(1/3)+aux(14) s(3) =< s(1)*(1/5)+s(9) s(4) =< s(1)*(1/5)+s(9) s(5) =< s(1)*(1/5)+s(9) with precondition: [Out=0,V1>=1,V>=1] * Chain [multiple([37,38,39],[[multiple([36],[[44]])],[44],[43],[42]])]: 1*it(37)+1*it(38)+1*it(39)+1*it([42])+1*it([43])+3*it([44])+0 Such that:aux(3) =< V1/2+1/2 aux(4) =< V1/3+V/3 aux(5) =< 2/5*V1+2/5*V aux(6) =< V aux(7) =< V+1 aux(8) =< V/2+1/2 it([42]) =< aux(3) it(39) =< aux(4) it(37) =< aux(5) it(38) =< aux(5) it(39) =< aux(5) it(38) =< aux(6) it(39) =< aux(6) it([43]) =< aux(6) it([44]) =< aux(7) it([43]) =< aux(8) it(39) =< it([44])*(1/3)+aux(4) it(37) =< it([44])*(1/5)+aux(5) it(38) =< it([44])*(1/5)+aux(5) it(39) =< it([44])*(1/5)+aux(5) with precondition: [Out=1,V1>=1,V>=1,V+V1>=3] * Chain [multiple([36],[[44]])]: 1*it(36)+1*it([44])+0 Such that:it(36) =< V it([44]) =< V+1 with precondition: [Out=2,V1=V,V1>=1] #### Cost of chains of fun(V1,V,Out): * Chain [[45],47]: 1*it(45)+1 Such that:it(45) =< -V+Out with precondition: [V+V1=Out,V1>=1,V>=0] * Chain [[45],46]: 1*it(45)+0 Such that:it(45) =< Out with precondition: [V>=0,Out>=1,V1>=Out] * Chain [47]: 1 with precondition: [V1=0,V=Out,V>=0] * Chain [46]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of lgth(V1,Out): * Chain [[48,49,50],51]: 6*it(48)+1 Such that:aux(21) =< V1 it(48) =< aux(21) with precondition: [V1>=1,Out>=0,V1>=Out] * Chain [51]: 1 with precondition: [Out=0,V1>=0] #### Cost of chains of monus(V1,V,Out): * Chain [[54],53]: 3*it(54)+3*s(47)+1*s(48)+14*s(49)+1*s(52)+1*s(53)+1*s(54)+1*s(55)+2*s(56)+25*s(58)+1*s(68)+1*s(69)+1*s(70)+2*s(74)+1*s(75)+1*s(76)+1*s(77)+1*s(88)+1*s(89)+1*s(90)+12*s(126)+1*s(127)+1*s(128)+1*s(129)+1*s(130)+1*s(131)+3*s(132)+3 Such that:aux(25) =< 1 aux(26) =< 2 s(41) =< 1/2 s(64) =< V+3 aux(41) =< V1 aux(42) =< V aux(43) =< V+1 aux(44) =< 2*V+2 s(47) =< aux(25) s(49) =< aux(26) s(58) =< aux(42) s(68) =< aux(42) s(68) =< aux(43) s(69) =< aux(43) s(70) =< aux(43) s(70) =< aux(26) s(69) =< aux(25) s(50) =< aux(26)*(1/2) s(73) =< s(64)*(6/5) s(74) =< aux(43) s(75) =< s(64) s(76) =< s(73) s(77) =< s(73) s(75) =< s(73) s(77) =< aux(26) s(75) =< aux(26) s(56) =< aux(26) s(56) =< s(50) s(75) =< s(49)*(1/3)+s(64) s(76) =< s(49)*(1/5)+s(73) s(77) =< s(49)*(1/5)+s(73) s(75) =< s(49)*(1/5)+s(73) s(48) =< aux(25) s(48) =< aux(26) s(51) =< aux(25)*(6/5) s(52) =< s(41) s(53) =< aux(25) s(54) =< s(51) s(55) =< s(51) s(53) =< s(51) s(55) =< aux(26) s(53) =< aux(26) s(53) =< s(49)*(1/3)+aux(25) s(54) =< s(49)*(1/5)+s(51) s(55) =< s(49)*(1/5)+s(51) s(53) =< s(49)*(1/5)+s(51) s(88) =< aux(43) s(89) =< aux(44) s(90) =< aux(44) s(88) =< aux(44) s(90) =< aux(25) s(88) =< aux(25) s(88) =< s(49)*(1/3)+aux(43) s(89) =< s(49)*(1/5)+aux(44) s(90) =< s(49)*(1/5)+aux(44) s(88) =< s(49)*(1/5)+aux(44) aux(31) =< aux(41) it(54) =< aux(41) aux(31) =< aux(42) it(54) =< aux(42) aux(31) =< aux(44) it(54) =< aux(44) aux(34) =< aux(42)*(1/2)+1/2 s(133) =< it(54)*aux(42) s(136) =< aux(31)*2 aux(35) =< it(54)*aux(34) s(134) =< aux(35)*(4/5) s(135) =< aux(35)*(2/3) s(127) =< aux(35) s(128) =< s(135) s(129) =< s(134) s(130) =< s(134) s(128) =< s(134) s(130) =< aux(31) s(128) =< aux(31) s(131) =< aux(31) s(132) =< s(136) s(128) =< s(132)*(1/3)+s(135) s(129) =< s(132)*(1/5)+s(134) s(130) =< s(132)*(1/5)+s(134) s(128) =< s(132)*(1/5)+s(134) s(126) =< s(133) with precondition: [Out=0,V1>=1,V>=1] * Chain [[54],52]: 3*it(54)+12*s(126)+1*s(127)+1*s(128)+1*s(129)+1*s(130)+1*s(131)+3*s(132)+6*s(140)+1*s(141)+1*s(142)+2 Such that:s(141) =< 1 s(142) =< 2 aux(37) =< V1 aux(38) =< V1-Out aux(45) =< V s(140) =< aux(45) aux(31) =< aux(37) it(54) =< aux(37) aux(31) =< aux(38) it(54) =< aux(38) aux(31) =< aux(45) it(54) =< aux(45) aux(34) =< aux(45)*(1/2)+1/2 s(133) =< it(54)*aux(45) s(136) =< aux(31)*2 aux(35) =< it(54)*aux(34) s(134) =< aux(35)*(4/5) s(135) =< aux(35)*(2/3) s(127) =< aux(35) s(128) =< s(135) s(129) =< s(134) s(130) =< s(134) s(128) =< s(134) s(130) =< aux(31) s(128) =< aux(31) s(131) =< aux(31) s(132) =< s(136) s(128) =< s(132)*(1/3)+s(135) s(129) =< s(132)*(1/5)+s(134) s(130) =< s(132)*(1/5)+s(134) s(128) =< s(132)*(1/5)+s(134) s(126) =< s(133) with precondition: [V>=2,Out>=0,V1>=Out+2] * Chain [53]: 3*s(47)+1*s(48)+14*s(49)+1*s(52)+1*s(53)+1*s(54)+1*s(55)+2*s(56)+25*s(58)+1*s(68)+1*s(69)+1*s(70)+2*s(74)+1*s(75)+1*s(76)+1*s(77)+1*s(88)+1*s(89)+1*s(90)+3 Such that:s(41) =< 1/2 s(62) =< V+1 s(64) =< V/3+1 s(82) =< V/3+1/3 s(83) =< 2/5*V+2/5 aux(25) =< 1 aux(26) =< 2 aux(27) =< V aux(28) =< V/2+1/2 s(47) =< aux(25) s(49) =< aux(26) s(58) =< aux(27) s(68) =< aux(27) s(68) =< s(62) s(69) =< s(62) s(70) =< s(62) s(68) =< aux(28) s(70) =< aux(26) s(69) =< aux(25) s(50) =< aux(26)*(1/2) s(73) =< s(64)*(6/5) s(74) =< aux(28) s(75) =< s(64) s(76) =< s(73) s(77) =< s(73) s(75) =< s(73) s(77) =< aux(26) s(75) =< aux(26) s(56) =< aux(26) s(56) =< s(50) s(75) =< s(49)*(1/3)+s(64) s(76) =< s(49)*(1/5)+s(73) s(77) =< s(49)*(1/5)+s(73) s(75) =< s(49)*(1/5)+s(73) s(48) =< aux(25) s(48) =< aux(26) s(51) =< aux(25)*(6/5) s(52) =< s(41) s(53) =< aux(25) s(54) =< s(51) s(55) =< s(51) s(53) =< s(51) s(55) =< aux(26) s(53) =< aux(26) s(53) =< s(49)*(1/3)+aux(25) s(54) =< s(49)*(1/5)+s(51) s(55) =< s(49)*(1/5)+s(51) s(53) =< s(49)*(1/5)+s(51) s(88) =< s(82) s(89) =< s(83) s(90) =< s(83) s(88) =< s(83) s(90) =< aux(25) s(88) =< aux(25) s(88) =< s(49)*(1/3)+s(82) s(89) =< s(49)*(1/5)+s(83) s(90) =< s(49)*(1/5)+s(83) s(88) =< s(49)*(1/5)+s(83) with precondition: [Out=0,V1>=0,V>=0] * Chain [52]: 6*s(140)+1*s(141)+1*s(142)+2 Such that:s(141) =< 1 s(142) =< 2 s(139) =< V s(140) =< s(139) with precondition: [V>=1,Out>=0,V1>=Out+1] #### Cost of chains of gt0(V1,V,Out): * Chain [[55],58]: 1*it(55)+1 Such that:it(55) =< V with precondition: [Out=1,V1>=1,V>=1] * Chain [[55],57]: 1*it(55)+1 Such that:it(55) =< V with precondition: [Out=2,V1>=2,V>=1] * Chain [[55],56]: 1*it(55)+0 Such that:it(55) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [58]: 1 with precondition: [V1=0,Out=1,V>=0] * Chain [57]: 1 with precondition: [V=0,Out=2,V1>=1] * Chain [56]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of gcd(V1,V,Out): * Chain [[59,60],65]: 30*it(59)+24*s(251)+4*s(252)+4*s(253)+4*s(254)+5*s(255)+1*s(298)+1*s(299)+1*s(300)+1*s(301)+2*s(704)+3*s(705)+3*s(706)+3*s(707)+4*s(708)+16*s(709)+128*s(710)+60*s(712)+2*s(713)+4*s(714)+4*s(715)+2*s(716)+2*s(717)+2*s(718)+8*s(719)+4*s(720)+4*s(721)+4*s(722)+4*s(723)+4*s(724)+2*s(725)+2*s(726)+2*s(727)+6*s(728)+1*s(729)+1*s(730)+1*s(731)+1*s(732)+2*s(733)+6*s(734)+12*s(735)+2*s(736)+6*s(737)+2*s(738)+2*s(739)+2*s(740)+2*s(741)+2*s(742)+2*s(743)+1*s(744)+1*s(745)+1*s(746)+6*s(750)+2*s(751)+2*s(752)+2*s(753)+2*s(754)+2*s(755)+6*s(756)+24*s(757)+1*s(822)+1*s(823)+1*s(824)+1*s(825)+12*s(828)+2 Such that:s(287) =< V1+V+2 aux(59) =< 2*V1+2*V aux(88) =< V1/3+V/3 aux(121) =< V1+V aux(122) =< V1+V+1 it(59) =< aux(121) s(255) =< aux(121) s(255) =< aux(122) s(251) =< aux(122) s(295) =< aux(122)*(1/2) s(296) =< s(287)*(6/5) s(298) =< s(287) s(299) =< s(296) s(300) =< s(296) s(298) =< s(296) s(300) =< aux(122) s(298) =< aux(122) s(301) =< aux(122) s(301) =< s(295) s(298) =< s(251)*(1/3)+s(287) s(299) =< s(251)*(1/5)+s(296) s(300) =< s(251)*(1/5)+s(296) s(298) =< s(251)*(1/5)+s(296) s(252) =< aux(121) s(253) =< aux(59) s(254) =< aux(59) s(252) =< aux(59) s(254) =< aux(121) s(252) =< s(251)*(1/3)+aux(121) s(253) =< s(251)*(1/5)+aux(59) s(254) =< s(251)*(1/5)+aux(59) s(252) =< s(251)*(1/5)+aux(59) aux(93) =< aux(121)+1 aux(86) =< aux(121) aux(89) =< aux(88) aux(97) =< aux(121)+3 aux(87) =< aux(121)*(1/2)+1/2 s(791) =< aux(121)*(1/2) s(781) =< aux(121)*2 aux(90) =< it(59)*aux(88) aux(94) =< it(59)*aux(93) s(762) =< it(59)*aux(86) aux(91) =< it(59)*aux(89) aux(100) =< it(59)*aux(97) s(758) =< aux(90)*(6/5) s(775) =< it(59)*aux(87) s(760) =< aux(94)*(1/2) s(771) =< aux(91)*(6/5) s(776) =< aux(94)*(2/5) s(777) =< aux(94)*(1/3) s(780) =< aux(100)*(1/3) s(789) =< aux(94)*2 s(710) =< s(762) s(712) =< s(781) s(713) =< s(762) s(713) =< aux(94) s(714) =< aux(94) s(715) =< aux(94) s(715) =< s(781) s(714) =< aux(121) s(794) =< s(781)*(1/2) s(792) =< aux(100)*(6/5) s(709) =< aux(94) s(716) =< aux(100) s(717) =< s(792) s(718) =< s(792) s(716) =< s(792) s(718) =< s(781) s(716) =< s(781) s(719) =< s(781) s(719) =< s(794) s(716) =< s(712)*(1/3)+aux(100) s(717) =< s(712)*(1/5)+s(792) s(718) =< s(712)*(1/5)+s(792) s(716) =< s(712)*(1/5)+s(792) s(720) =< aux(121) s(720) =< s(781) s(790) =< aux(121)*(6/5) s(721) =< s(791) s(722) =< aux(121) s(723) =< s(790) s(724) =< s(790) s(722) =< s(790) s(724) =< s(781) s(722) =< s(781) s(722) =< s(712)*(1/3)+aux(121) s(723) =< s(712)*(1/5)+s(790) s(724) =< s(712)*(1/5)+s(790) s(722) =< s(712)*(1/5)+s(790) s(725) =< aux(94) s(726) =< s(789) s(727) =< s(789) s(725) =< s(789) s(727) =< aux(121) s(725) =< aux(121) s(725) =< s(712)*(1/3)+aux(94) s(726) =< s(712)*(1/5)+s(789) s(727) =< s(712)*(1/5)+s(789) s(725) =< s(712)*(1/5)+s(789) s(787) =< s(762) s(728) =< s(762) s(787) =< s(789) s(728) =< s(789) s(865) =< s(728)*aux(121) s(786) =< s(787)*2 s(870) =< s(728)*aux(87) s(866) =< s(870)*(4/5) s(867) =< s(870)*(2/3) s(822) =< s(870) s(823) =< s(867) s(824) =< s(866) s(825) =< s(866) s(823) =< s(866) s(825) =< s(787) s(823) =< s(787) s(733) =< s(787) s(734) =< s(786) s(823) =< s(734)*(1/3)+s(867) s(824) =< s(734)*(1/5)+s(866) s(825) =< s(734)*(1/5)+s(866) s(823) =< s(734)*(1/5)+s(866) s(828) =< s(865) s(736) =< s(762) s(736) =< aux(94) s(736) =< s(760) s(779) =< s(780)*(6/5) s(737) =< s(760) s(738) =< s(780) s(739) =< s(779) s(740) =< s(779) s(738) =< s(779) s(740) =< s(781) s(738) =< s(781) s(738) =< s(712)*(1/3)+s(780) s(739) =< s(712)*(1/5)+s(779) s(740) =< s(712)*(1/5)+s(779) s(738) =< s(712)*(1/5)+s(779) s(741) =< s(777) s(742) =< s(776) s(743) =< s(776) s(741) =< s(776) s(743) =< aux(121) s(741) =< aux(121) s(741) =< s(712)*(1/3)+s(777) s(742) =< s(712)*(1/5)+s(776) s(743) =< s(712)*(1/5)+s(776) s(741) =< s(712)*(1/5)+s(776) s(705) =< aux(91) s(706) =< s(771) s(707) =< s(771) s(705) =< s(771) s(707) =< s(762) s(705) =< s(762) s(708) =< s(762) s(708) =< s(760) s(705) =< s(709)*(1/3)+aux(91) s(706) =< s(709)*(1/5)+s(771) s(707) =< s(709)*(1/5)+s(771) s(705) =< s(709)*(1/5)+s(771) s(767) =< s(762) s(750) =< s(762) s(767) =< aux(121) s(750) =< aux(121) s(763) =< s(750)*aux(121) s(766) =< s(767)*2 s(768) =< s(750)*aux(87) s(764) =< s(768)*(4/5) s(765) =< s(768)*(2/3) s(751) =< s(768) s(752) =< s(765) s(753) =< s(764) s(754) =< s(764) s(752) =< s(764) s(754) =< s(767) s(752) =< s(767) s(755) =< s(767) s(756) =< s(766) s(752) =< s(756)*(1/3)+s(765) s(753) =< s(756)*(1/5)+s(764) s(754) =< s(756)*(1/5)+s(764) s(752) =< s(756)*(1/5)+s(764) s(757) =< s(763) s(466) =< aux(86)*(1/2)+1/2 s(783) =< s(728)*aux(86) s(788) =< s(728)*s(466) s(784) =< s(788)*(4/5) s(785) =< s(788)*(2/3) s(729) =< s(788) s(730) =< s(785) s(731) =< s(784) s(732) =< s(784) s(730) =< s(784) s(732) =< s(787) s(730) =< s(787) s(730) =< s(734)*(1/3)+s(785) s(731) =< s(734)*(1/5)+s(784) s(732) =< s(734)*(1/5)+s(784) s(730) =< s(734)*(1/5)+s(784) s(735) =< s(783) s(704) =< s(775) s(744) =< aux(90) s(745) =< s(758) s(746) =< s(758) s(744) =< s(758) s(746) =< s(762) s(744) =< s(762) s(744) =< s(709)*(1/3)+aux(90) s(745) =< s(709)*(1/5)+s(758) s(746) =< s(709)*(1/5)+s(758) s(744) =< s(709)*(1/5)+s(758) with precondition: [Out=0,V1>=1,V>=1,V+V1>=3] * Chain [[59,60],64]: 26*it(59)+2*s(704)+3*s(705)+3*s(706)+3*s(707)+4*s(708)+16*s(709)+128*s(710)+60*s(712)+2*s(713)+4*s(714)+4*s(715)+2*s(716)+2*s(717)+2*s(718)+8*s(719)+4*s(720)+4*s(721)+4*s(722)+4*s(723)+4*s(724)+2*s(725)+2*s(726)+2*s(727)+6*s(728)+1*s(729)+1*s(730)+1*s(731)+1*s(732)+2*s(733)+6*s(734)+12*s(735)+2*s(736)+6*s(737)+2*s(738)+2*s(739)+2*s(740)+2*s(741)+2*s(742)+2*s(743)+1*s(744)+1*s(745)+1*s(746)+6*s(750)+2*s(751)+2*s(752)+2*s(753)+2*s(754)+2*s(755)+6*s(756)+24*s(757)+1*s(822)+1*s(823)+1*s(824)+1*s(825)+12*s(828)+1 Such that:aux(88) =< V1/3+V/3 aux(123) =< V1+V it(59) =< aux(123) aux(93) =< aux(123)+1 aux(86) =< aux(123) aux(89) =< aux(88) aux(97) =< aux(123)+3 aux(87) =< aux(123)*(1/2)+1/2 s(791) =< aux(123)*(1/2) s(781) =< aux(123)*2 aux(90) =< it(59)*aux(88) aux(94) =< it(59)*aux(93) s(762) =< it(59)*aux(86) aux(91) =< it(59)*aux(89) aux(100) =< it(59)*aux(97) s(758) =< aux(90)*(6/5) s(775) =< it(59)*aux(87) s(760) =< aux(94)*(1/2) s(771) =< aux(91)*(6/5) s(776) =< aux(94)*(2/5) s(777) =< aux(94)*(1/3) s(780) =< aux(100)*(1/3) s(789) =< aux(94)*2 s(710) =< s(762) s(712) =< s(781) s(713) =< s(762) s(713) =< aux(94) s(714) =< aux(94) s(715) =< aux(94) s(715) =< s(781) s(714) =< aux(123) s(794) =< s(781)*(1/2) s(792) =< aux(100)*(6/5) s(709) =< aux(94) s(716) =< aux(100) s(717) =< s(792) s(718) =< s(792) s(716) =< s(792) s(718) =< s(781) s(716) =< s(781) s(719) =< s(781) s(719) =< s(794) s(716) =< s(712)*(1/3)+aux(100) s(717) =< s(712)*(1/5)+s(792) s(718) =< s(712)*(1/5)+s(792) s(716) =< s(712)*(1/5)+s(792) s(720) =< aux(123) s(720) =< s(781) s(790) =< aux(123)*(6/5) s(721) =< s(791) s(722) =< aux(123) s(723) =< s(790) s(724) =< s(790) s(722) =< s(790) s(724) =< s(781) s(722) =< s(781) s(722) =< s(712)*(1/3)+aux(123) s(723) =< s(712)*(1/5)+s(790) s(724) =< s(712)*(1/5)+s(790) s(722) =< s(712)*(1/5)+s(790) s(725) =< aux(94) s(726) =< s(789) s(727) =< s(789) s(725) =< s(789) s(727) =< aux(123) s(725) =< aux(123) s(725) =< s(712)*(1/3)+aux(94) s(726) =< s(712)*(1/5)+s(789) s(727) =< s(712)*(1/5)+s(789) s(725) =< s(712)*(1/5)+s(789) s(787) =< s(762) s(728) =< s(762) s(787) =< s(789) s(728) =< s(789) s(865) =< s(728)*aux(123) s(786) =< s(787)*2 s(870) =< s(728)*aux(87) s(866) =< s(870)*(4/5) s(867) =< s(870)*(2/3) s(822) =< s(870) s(823) =< s(867) s(824) =< s(866) s(825) =< s(866) s(823) =< s(866) s(825) =< s(787) s(823) =< s(787) s(733) =< s(787) s(734) =< s(786) s(823) =< s(734)*(1/3)+s(867) s(824) =< s(734)*(1/5)+s(866) s(825) =< s(734)*(1/5)+s(866) s(823) =< s(734)*(1/5)+s(866) s(828) =< s(865) s(736) =< s(762) s(736) =< aux(94) s(736) =< s(760) s(779) =< s(780)*(6/5) s(737) =< s(760) s(738) =< s(780) s(739) =< s(779) s(740) =< s(779) s(738) =< s(779) s(740) =< s(781) s(738) =< s(781) s(738) =< s(712)*(1/3)+s(780) s(739) =< s(712)*(1/5)+s(779) s(740) =< s(712)*(1/5)+s(779) s(738) =< s(712)*(1/5)+s(779) s(741) =< s(777) s(742) =< s(776) s(743) =< s(776) s(741) =< s(776) s(743) =< aux(123) s(741) =< aux(123) s(741) =< s(712)*(1/3)+s(777) s(742) =< s(712)*(1/5)+s(776) s(743) =< s(712)*(1/5)+s(776) s(741) =< s(712)*(1/5)+s(776) s(705) =< aux(91) s(706) =< s(771) s(707) =< s(771) s(705) =< s(771) s(707) =< s(762) s(705) =< s(762) s(708) =< s(762) s(708) =< s(760) s(705) =< s(709)*(1/3)+aux(91) s(706) =< s(709)*(1/5)+s(771) s(707) =< s(709)*(1/5)+s(771) s(705) =< s(709)*(1/5)+s(771) s(767) =< s(762) s(750) =< s(762) s(767) =< aux(123) s(750) =< aux(123) s(763) =< s(750)*aux(123) s(766) =< s(767)*2 s(768) =< s(750)*aux(87) s(764) =< s(768)*(4/5) s(765) =< s(768)*(2/3) s(751) =< s(768) s(752) =< s(765) s(753) =< s(764) s(754) =< s(764) s(752) =< s(764) s(754) =< s(767) s(752) =< s(767) s(755) =< s(767) s(756) =< s(766) s(752) =< s(756)*(1/3)+s(765) s(753) =< s(756)*(1/5)+s(764) s(754) =< s(756)*(1/5)+s(764) s(752) =< s(756)*(1/5)+s(764) s(757) =< s(763) s(466) =< aux(86)*(1/2)+1/2 s(783) =< s(728)*aux(86) s(788) =< s(728)*s(466) s(784) =< s(788)*(4/5) s(785) =< s(788)*(2/3) s(729) =< s(788) s(730) =< s(785) s(731) =< s(784) s(732) =< s(784) s(730) =< s(784) s(732) =< s(787) s(730) =< s(787) s(730) =< s(734)*(1/3)+s(785) s(731) =< s(734)*(1/5)+s(784) s(732) =< s(734)*(1/5)+s(784) s(730) =< s(734)*(1/5)+s(784) s(735) =< s(783) s(704) =< s(775) s(744) =< aux(90) s(745) =< s(758) s(746) =< s(758) s(744) =< s(758) s(746) =< s(762) s(744) =< s(762) s(744) =< s(709)*(1/3)+aux(90) s(745) =< s(709)*(1/5)+s(758) s(746) =< s(709)*(1/5)+s(758) s(744) =< s(709)*(1/5)+s(758) with precondition: [Out=0,V1>=1,V>=1,V+V1>=3] * Chain [[59,60],63]: 26*it(59)+2*s(704)+3*s(705)+3*s(706)+3*s(707)+4*s(708)+16*s(709)+128*s(710)+60*s(712)+2*s(713)+4*s(714)+4*s(715)+2*s(716)+2*s(717)+2*s(718)+8*s(719)+4*s(720)+4*s(721)+4*s(722)+4*s(723)+4*s(724)+2*s(725)+2*s(726)+2*s(727)+6*s(728)+1*s(729)+1*s(730)+1*s(731)+1*s(732)+2*s(733)+6*s(734)+12*s(735)+2*s(736)+6*s(737)+2*s(738)+2*s(739)+2*s(740)+2*s(741)+2*s(742)+2*s(743)+1*s(744)+1*s(745)+1*s(746)+6*s(750)+2*s(751)+2*s(752)+2*s(753)+2*s(754)+2*s(755)+6*s(756)+24*s(757)+1*s(822)+1*s(823)+1*s(824)+1*s(825)+12*s(828)+1 Such that:aux(88) =< V1/3+V/3 aux(124) =< V1+V it(59) =< aux(124) aux(93) =< aux(124)+1 aux(86) =< aux(124) aux(89) =< aux(88) aux(97) =< aux(124)+3 aux(87) =< aux(124)*(1/2)+1/2 s(791) =< aux(124)*(1/2) s(781) =< aux(124)*2 aux(90) =< it(59)*aux(88) aux(94) =< it(59)*aux(93) s(762) =< it(59)*aux(86) aux(91) =< it(59)*aux(89) aux(100) =< it(59)*aux(97) s(758) =< aux(90)*(6/5) s(775) =< it(59)*aux(87) s(760) =< aux(94)*(1/2) s(771) =< aux(91)*(6/5) s(776) =< aux(94)*(2/5) s(777) =< aux(94)*(1/3) s(780) =< aux(100)*(1/3) s(789) =< aux(94)*2 s(710) =< s(762) s(712) =< s(781) s(713) =< s(762) s(713) =< aux(94) s(714) =< aux(94) s(715) =< aux(94) s(715) =< s(781) s(714) =< aux(124) s(794) =< s(781)*(1/2) s(792) =< aux(100)*(6/5) s(709) =< aux(94) s(716) =< aux(100) s(717) =< s(792) s(718) =< s(792) s(716) =< s(792) s(718) =< s(781) s(716) =< s(781) s(719) =< s(781) s(719) =< s(794) s(716) =< s(712)*(1/3)+aux(100) s(717) =< s(712)*(1/5)+s(792) s(718) =< s(712)*(1/5)+s(792) s(716) =< s(712)*(1/5)+s(792) s(720) =< aux(124) s(720) =< s(781) s(790) =< aux(124)*(6/5) s(721) =< s(791) s(722) =< aux(124) s(723) =< s(790) s(724) =< s(790) s(722) =< s(790) s(724) =< s(781) s(722) =< s(781) s(722) =< s(712)*(1/3)+aux(124) s(723) =< s(712)*(1/5)+s(790) s(724) =< s(712)*(1/5)+s(790) s(722) =< s(712)*(1/5)+s(790) s(725) =< aux(94) s(726) =< s(789) s(727) =< s(789) s(725) =< s(789) s(727) =< aux(124) s(725) =< aux(124) s(725) =< s(712)*(1/3)+aux(94) s(726) =< s(712)*(1/5)+s(789) s(727) =< s(712)*(1/5)+s(789) s(725) =< s(712)*(1/5)+s(789) s(787) =< s(762) s(728) =< s(762) s(787) =< s(789) s(728) =< s(789) s(865) =< s(728)*aux(124) s(786) =< s(787)*2 s(870) =< s(728)*aux(87) s(866) =< s(870)*(4/5) s(867) =< s(870)*(2/3) s(822) =< s(870) s(823) =< s(867) s(824) =< s(866) s(825) =< s(866) s(823) =< s(866) s(825) =< s(787) s(823) =< s(787) s(733) =< s(787) s(734) =< s(786) s(823) =< s(734)*(1/3)+s(867) s(824) =< s(734)*(1/5)+s(866) s(825) =< s(734)*(1/5)+s(866) s(823) =< s(734)*(1/5)+s(866) s(828) =< s(865) s(736) =< s(762) s(736) =< aux(94) s(736) =< s(760) s(779) =< s(780)*(6/5) s(737) =< s(760) s(738) =< s(780) s(739) =< s(779) s(740) =< s(779) s(738) =< s(779) s(740) =< s(781) s(738) =< s(781) s(738) =< s(712)*(1/3)+s(780) s(739) =< s(712)*(1/5)+s(779) s(740) =< s(712)*(1/5)+s(779) s(738) =< s(712)*(1/5)+s(779) s(741) =< s(777) s(742) =< s(776) s(743) =< s(776) s(741) =< s(776) s(743) =< aux(124) s(741) =< aux(124) s(741) =< s(712)*(1/3)+s(777) s(742) =< s(712)*(1/5)+s(776) s(743) =< s(712)*(1/5)+s(776) s(741) =< s(712)*(1/5)+s(776) s(705) =< aux(91) s(706) =< s(771) s(707) =< s(771) s(705) =< s(771) s(707) =< s(762) s(705) =< s(762) s(708) =< s(762) s(708) =< s(760) s(705) =< s(709)*(1/3)+aux(91) s(706) =< s(709)*(1/5)+s(771) s(707) =< s(709)*(1/5)+s(771) s(705) =< s(709)*(1/5)+s(771) s(767) =< s(762) s(750) =< s(762) s(767) =< aux(124) s(750) =< aux(124) s(763) =< s(750)*aux(124) s(766) =< s(767)*2 s(768) =< s(750)*aux(87) s(764) =< s(768)*(4/5) s(765) =< s(768)*(2/3) s(751) =< s(768) s(752) =< s(765) s(753) =< s(764) s(754) =< s(764) s(752) =< s(764) s(754) =< s(767) s(752) =< s(767) s(755) =< s(767) s(756) =< s(766) s(752) =< s(756)*(1/3)+s(765) s(753) =< s(756)*(1/5)+s(764) s(754) =< s(756)*(1/5)+s(764) s(752) =< s(756)*(1/5)+s(764) s(757) =< s(763) s(466) =< aux(86)*(1/2)+1/2 s(783) =< s(728)*aux(86) s(788) =< s(728)*s(466) s(784) =< s(788)*(4/5) s(785) =< s(788)*(2/3) s(729) =< s(788) s(730) =< s(785) s(731) =< s(784) s(732) =< s(784) s(730) =< s(784) s(732) =< s(787) s(730) =< s(787) s(730) =< s(734)*(1/3)+s(785) s(731) =< s(734)*(1/5)+s(784) s(732) =< s(734)*(1/5)+s(784) s(730) =< s(734)*(1/5)+s(784) s(735) =< s(783) s(704) =< s(775) s(744) =< aux(90) s(745) =< s(758) s(746) =< s(758) s(744) =< s(758) s(746) =< s(762) s(744) =< s(762) s(744) =< s(709)*(1/3)+aux(90) s(745) =< s(709)*(1/5)+s(758) s(746) =< s(709)*(1/5)+s(758) s(744) =< s(709)*(1/5)+s(758) with precondition: [Out=0,V1>=1,V>=1,V+2*V1>=5] * Chain [[59,60],62]: 10*it(59)+2*s(704)+3*s(705)+3*s(706)+3*s(707)+4*s(708)+16*s(709)+128*s(710)+16*s(711)+60*s(712)+2*s(713)+4*s(714)+4*s(715)+2*s(716)+2*s(717)+2*s(718)+8*s(719)+4*s(720)+4*s(721)+4*s(722)+4*s(723)+4*s(724)+2*s(725)+2*s(726)+2*s(727)+6*s(728)+1*s(729)+1*s(730)+1*s(731)+1*s(732)+2*s(733)+6*s(734)+12*s(735)+2*s(736)+6*s(737)+2*s(738)+2*s(739)+2*s(740)+2*s(741)+2*s(742)+2*s(743)+1*s(744)+1*s(745)+1*s(746)+6*s(750)+2*s(751)+2*s(752)+2*s(753)+2*s(754)+2*s(755)+6*s(756)+24*s(757)+1*s(822)+1*s(823)+1*s(824)+1*s(825)+12*s(828)+1*s(877)+1*s(878)+1 Such that:aux(88) =< V1/3+V/3 aux(125) =< V1+V aux(126) =< V1+V+2 s(877) =< aux(125) s(878) =< aux(126) aux(83) =< aux(125) it(59) =< aux(125) aux(83) =< aux(126) it(59) =< aux(126) aux(93) =< aux(125)+1 aux(86) =< aux(125) aux(89) =< aux(88) aux(97) =< aux(125)+3 aux(87) =< aux(125)*(1/2)+1/2 s(791) =< aux(83)*(1/2) s(781) =< aux(83)*2 aux(90) =< it(59)*aux(88) aux(94) =< it(59)*aux(93) s(762) =< it(59)*aux(86) aux(91) =< it(59)*aux(89) aux(100) =< it(59)*aux(97) s(758) =< aux(90)*(6/5) s(775) =< it(59)*aux(87) s(760) =< aux(94)*(1/2) s(771) =< aux(91)*(6/5) s(776) =< aux(94)*(2/5) s(777) =< aux(94)*(1/3) s(780) =< aux(100)*(1/3) s(789) =< aux(94)*2 s(710) =< s(762) s(711) =< aux(83) s(712) =< s(781) s(713) =< s(762) s(713) =< aux(94) s(714) =< aux(94) s(715) =< aux(94) s(715) =< s(781) s(714) =< aux(83) s(794) =< s(781)*(1/2) s(792) =< aux(100)*(6/5) s(709) =< aux(94) s(716) =< aux(100) s(717) =< s(792) s(718) =< s(792) s(716) =< s(792) s(718) =< s(781) s(716) =< s(781) s(719) =< s(781) s(719) =< s(794) s(716) =< s(712)*(1/3)+aux(100) s(717) =< s(712)*(1/5)+s(792) s(718) =< s(712)*(1/5)+s(792) s(716) =< s(712)*(1/5)+s(792) s(720) =< aux(83) s(720) =< s(781) s(790) =< aux(83)*(6/5) s(721) =< s(791) s(722) =< aux(83) s(723) =< s(790) s(724) =< s(790) s(722) =< s(790) s(724) =< s(781) s(722) =< s(781) s(722) =< s(712)*(1/3)+aux(83) s(723) =< s(712)*(1/5)+s(790) s(724) =< s(712)*(1/5)+s(790) s(722) =< s(712)*(1/5)+s(790) s(725) =< aux(94) s(726) =< s(789) s(727) =< s(789) s(725) =< s(789) s(727) =< aux(83) s(725) =< aux(83) s(725) =< s(712)*(1/3)+aux(94) s(726) =< s(712)*(1/5)+s(789) s(727) =< s(712)*(1/5)+s(789) s(725) =< s(712)*(1/5)+s(789) s(787) =< s(762) s(728) =< s(762) s(787) =< s(789) s(728) =< s(789) s(865) =< s(728)*aux(125) s(786) =< s(787)*2 s(870) =< s(728)*aux(87) s(866) =< s(870)*(4/5) s(867) =< s(870)*(2/3) s(822) =< s(870) s(823) =< s(867) s(824) =< s(866) s(825) =< s(866) s(823) =< s(866) s(825) =< s(787) s(823) =< s(787) s(733) =< s(787) s(734) =< s(786) s(823) =< s(734)*(1/3)+s(867) s(824) =< s(734)*(1/5)+s(866) s(825) =< s(734)*(1/5)+s(866) s(823) =< s(734)*(1/5)+s(866) s(828) =< s(865) s(736) =< s(762) s(736) =< aux(94) s(736) =< s(760) s(779) =< s(780)*(6/5) s(737) =< s(760) s(738) =< s(780) s(739) =< s(779) s(740) =< s(779) s(738) =< s(779) s(740) =< s(781) s(738) =< s(781) s(738) =< s(712)*(1/3)+s(780) s(739) =< s(712)*(1/5)+s(779) s(740) =< s(712)*(1/5)+s(779) s(738) =< s(712)*(1/5)+s(779) s(741) =< s(777) s(742) =< s(776) s(743) =< s(776) s(741) =< s(776) s(743) =< aux(83) s(741) =< aux(83) s(741) =< s(712)*(1/3)+s(777) s(742) =< s(712)*(1/5)+s(776) s(743) =< s(712)*(1/5)+s(776) s(741) =< s(712)*(1/5)+s(776) s(705) =< aux(91) s(706) =< s(771) s(707) =< s(771) s(705) =< s(771) s(707) =< s(762) s(705) =< s(762) s(708) =< s(762) s(708) =< s(760) s(705) =< s(709)*(1/3)+aux(91) s(706) =< s(709)*(1/5)+s(771) s(707) =< s(709)*(1/5)+s(771) s(705) =< s(709)*(1/5)+s(771) s(767) =< s(762) s(750) =< s(762) s(767) =< aux(83) s(750) =< aux(83) s(763) =< s(750)*aux(125) s(766) =< s(767)*2 s(768) =< s(750)*aux(87) s(764) =< s(768)*(4/5) s(765) =< s(768)*(2/3) s(751) =< s(768) s(752) =< s(765) s(753) =< s(764) s(754) =< s(764) s(752) =< s(764) s(754) =< s(767) s(752) =< s(767) s(755) =< s(767) s(756) =< s(766) s(752) =< s(756)*(1/3)+s(765) s(753) =< s(756)*(1/5)+s(764) s(754) =< s(756)*(1/5)+s(764) s(752) =< s(756)*(1/5)+s(764) s(757) =< s(763) s(466) =< aux(86)*(1/2)+1/2 s(783) =< s(728)*aux(86) s(788) =< s(728)*s(466) s(784) =< s(788)*(4/5) s(785) =< s(788)*(2/3) s(729) =< s(788) s(730) =< s(785) s(731) =< s(784) s(732) =< s(784) s(730) =< s(784) s(732) =< s(787) s(730) =< s(787) s(730) =< s(734)*(1/3)+s(785) s(731) =< s(734)*(1/5)+s(784) s(732) =< s(734)*(1/5)+s(784) s(730) =< s(734)*(1/5)+s(784) s(735) =< s(783) s(704) =< s(775) s(744) =< aux(90) s(745) =< s(758) s(746) =< s(758) s(744) =< s(758) s(746) =< s(762) s(744) =< s(762) s(744) =< s(709)*(1/3)+aux(90) s(745) =< s(709)*(1/5)+s(758) s(746) =< s(709)*(1/5)+s(758) s(744) =< s(709)*(1/5)+s(758) with precondition: [Out=0,V1>=1,V>=1,V+V1>=3] * Chain [[59,60],61]: 10*it(59)+2*s(704)+3*s(705)+3*s(706)+3*s(707)+4*s(708)+16*s(709)+128*s(710)+16*s(711)+60*s(712)+2*s(713)+4*s(714)+4*s(715)+2*s(716)+2*s(717)+2*s(718)+8*s(719)+4*s(720)+4*s(721)+4*s(722)+4*s(723)+4*s(724)+2*s(725)+2*s(726)+2*s(727)+6*s(728)+1*s(729)+1*s(730)+1*s(731)+1*s(732)+2*s(733)+6*s(734)+12*s(735)+2*s(736)+6*s(737)+2*s(738)+2*s(739)+2*s(740)+2*s(741)+2*s(742)+2*s(743)+1*s(744)+1*s(745)+1*s(746)+6*s(750)+2*s(751)+2*s(752)+2*s(753)+2*s(754)+2*s(755)+6*s(756)+24*s(757)+1*s(822)+1*s(823)+1*s(824)+1*s(825)+12*s(828)+1*s(879)+1*s(880)+1 Such that:aux(119) =< V1+V aux(120) =< V1+V-2*Out aux(88) =< V1/3+V/3 s(879) =< Out s(880) =< Out+1 aux(83) =< aux(119) it(59) =< aux(119) aux(83) =< aux(120) it(59) =< aux(120) aux(93) =< aux(119)+1 aux(86) =< aux(119) aux(89) =< aux(88) aux(97) =< aux(119)+3 aux(87) =< aux(119)*(1/2)+1/2 s(791) =< aux(83)*(1/2) s(781) =< aux(83)*2 aux(90) =< it(59)*aux(88) aux(94) =< it(59)*aux(93) s(762) =< it(59)*aux(86) aux(91) =< it(59)*aux(89) aux(100) =< it(59)*aux(97) s(758) =< aux(90)*(6/5) s(775) =< it(59)*aux(87) s(760) =< aux(94)*(1/2) s(771) =< aux(91)*(6/5) s(776) =< aux(94)*(2/5) s(777) =< aux(94)*(1/3) s(780) =< aux(100)*(1/3) s(789) =< aux(94)*2 s(710) =< s(762) s(711) =< aux(83) s(712) =< s(781) s(713) =< s(762) s(713) =< aux(94) s(714) =< aux(94) s(715) =< aux(94) s(715) =< s(781) s(714) =< aux(83) s(794) =< s(781)*(1/2) s(792) =< aux(100)*(6/5) s(709) =< aux(94) s(716) =< aux(100) s(717) =< s(792) s(718) =< s(792) s(716) =< s(792) s(718) =< s(781) s(716) =< s(781) s(719) =< s(781) s(719) =< s(794) s(716) =< s(712)*(1/3)+aux(100) s(717) =< s(712)*(1/5)+s(792) s(718) =< s(712)*(1/5)+s(792) s(716) =< s(712)*(1/5)+s(792) s(720) =< aux(83) s(720) =< s(781) s(790) =< aux(83)*(6/5) s(721) =< s(791) s(722) =< aux(83) s(723) =< s(790) s(724) =< s(790) s(722) =< s(790) s(724) =< s(781) s(722) =< s(781) s(722) =< s(712)*(1/3)+aux(83) s(723) =< s(712)*(1/5)+s(790) s(724) =< s(712)*(1/5)+s(790) s(722) =< s(712)*(1/5)+s(790) s(725) =< aux(94) s(726) =< s(789) s(727) =< s(789) s(725) =< s(789) s(727) =< aux(83) s(725) =< aux(83) s(725) =< s(712)*(1/3)+aux(94) s(726) =< s(712)*(1/5)+s(789) s(727) =< s(712)*(1/5)+s(789) s(725) =< s(712)*(1/5)+s(789) s(787) =< s(762) s(728) =< s(762) s(787) =< s(789) s(728) =< s(789) s(865) =< s(728)*aux(119) s(786) =< s(787)*2 s(870) =< s(728)*aux(87) s(866) =< s(870)*(4/5) s(867) =< s(870)*(2/3) s(822) =< s(870) s(823) =< s(867) s(824) =< s(866) s(825) =< s(866) s(823) =< s(866) s(825) =< s(787) s(823) =< s(787) s(733) =< s(787) s(734) =< s(786) s(823) =< s(734)*(1/3)+s(867) s(824) =< s(734)*(1/5)+s(866) s(825) =< s(734)*(1/5)+s(866) s(823) =< s(734)*(1/5)+s(866) s(828) =< s(865) s(736) =< s(762) s(736) =< aux(94) s(736) =< s(760) s(779) =< s(780)*(6/5) s(737) =< s(760) s(738) =< s(780) s(739) =< s(779) s(740) =< s(779) s(738) =< s(779) s(740) =< s(781) s(738) =< s(781) s(738) =< s(712)*(1/3)+s(780) s(739) =< s(712)*(1/5)+s(779) s(740) =< s(712)*(1/5)+s(779) s(738) =< s(712)*(1/5)+s(779) s(741) =< s(777) s(742) =< s(776) s(743) =< s(776) s(741) =< s(776) s(743) =< aux(83) s(741) =< aux(83) s(741) =< s(712)*(1/3)+s(777) s(742) =< s(712)*(1/5)+s(776) s(743) =< s(712)*(1/5)+s(776) s(741) =< s(712)*(1/5)+s(776) s(705) =< aux(91) s(706) =< s(771) s(707) =< s(771) s(705) =< s(771) s(707) =< s(762) s(705) =< s(762) s(708) =< s(762) s(708) =< s(760) s(705) =< s(709)*(1/3)+aux(91) s(706) =< s(709)*(1/5)+s(771) s(707) =< s(709)*(1/5)+s(771) s(705) =< s(709)*(1/5)+s(771) s(767) =< s(762) s(750) =< s(762) s(767) =< aux(83) s(750) =< aux(83) s(763) =< s(750)*aux(119) s(766) =< s(767)*2 s(768) =< s(750)*aux(87) s(764) =< s(768)*(4/5) s(765) =< s(768)*(2/3) s(751) =< s(768) s(752) =< s(765) s(753) =< s(764) s(754) =< s(764) s(752) =< s(764) s(754) =< s(767) s(752) =< s(767) s(755) =< s(767) s(756) =< s(766) s(752) =< s(756)*(1/3)+s(765) s(753) =< s(756)*(1/5)+s(764) s(754) =< s(756)*(1/5)+s(764) s(752) =< s(756)*(1/5)+s(764) s(757) =< s(763) s(466) =< aux(86)*(1/2)+1/2 s(783) =< s(728)*aux(86) s(788) =< s(728)*s(466) s(784) =< s(788)*(4/5) s(785) =< s(788)*(2/3) s(729) =< s(788) s(730) =< s(785) s(731) =< s(784) s(732) =< s(784) s(730) =< s(784) s(732) =< s(787) s(730) =< s(787) s(730) =< s(734)*(1/3)+s(785) s(731) =< s(734)*(1/5)+s(784) s(732) =< s(734)*(1/5)+s(784) s(730) =< s(734)*(1/5)+s(784) s(735) =< s(783) s(704) =< s(775) s(744) =< aux(90) s(745) =< s(758) s(746) =< s(758) s(744) =< s(758) s(746) =< s(762) s(744) =< s(762) s(744) =< s(709)*(1/3)+aux(90) s(745) =< s(709)*(1/5)+s(758) s(746) =< s(709)*(1/5)+s(758) s(744) =< s(709)*(1/5)+s(758) with precondition: [Out>=1,V1>=Out,V>=Out,V+V1>=2*Out+1] * Chain [65]: 5*s(251)+4*s(252)+4*s(253)+4*s(254)+4*s(255)+17*s(256)+3*s(257)+1*s(290)+1*s(291)+1*s(292)+1*s(293)+1*s(298)+1*s(299)+1*s(300)+1*s(301)+2 Such that:s(284) =< V1 s(285) =< V1+1 s(287) =< V1/3+V/3+2/3 aux(57) =< V1/2+1/2 aux(58) =< V1/3+V/3 aux(59) =< 2/5*V1+2/5*V aux(60) =< V aux(61) =< V+1 aux(62) =< V/2+1/2 s(290) =< s(284) s(291) =< s(284) s(291) =< s(285) s(292) =< s(285) s(293) =< s(285) s(291) =< aux(57) s(293) =< aux(61) s(256) =< aux(61) s(292) =< aux(62) s(295) =< aux(61)*(1/2) s(296) =< s(287)*(6/5) s(251) =< aux(57) s(298) =< s(287) s(299) =< s(296) s(300) =< s(296) s(298) =< s(296) s(300) =< aux(61) s(298) =< aux(61) s(301) =< aux(61) s(301) =< s(295) s(298) =< s(256)*(1/3)+s(287) s(299) =< s(256)*(1/5)+s(296) s(300) =< s(256)*(1/5)+s(296) s(298) =< s(256)*(1/5)+s(296) s(257) =< aux(60) s(252) =< aux(58) s(253) =< aux(59) s(254) =< aux(59) s(252) =< aux(59) s(254) =< aux(60) s(252) =< aux(60) s(255) =< aux(60) s(255) =< aux(62) s(252) =< s(256)*(1/3)+aux(58) s(253) =< s(256)*(1/5)+aux(59) s(254) =< s(256)*(1/5)+aux(59) s(252) =< s(256)*(1/5)+aux(59) with precondition: [Out=0,V1>=0,V>=0] * Chain [64]: 1 with precondition: [V1=0,Out=0,V>=1] * Chain [63]: 1 with precondition: [V=0,Out=0,V1>=1] * Chain [62]: 1*s(877)+1*s(878)+1 Such that:s(877) =< V s(878) =< V+1 with precondition: [Out=0,V1=V,V1>=1] * Chain [61]: 1*s(879)+1*s(880)+1 Such that:s(879) =< V s(880) =< V+1 with precondition: [V1=V,V1=Out,V1>=1] #### Cost of chains of start(V1,V,V35): * Chain [74]: 11*s(1322)+71*s(1324)+3*s(1341)+3*s(1342)+3*s(1343)+44*s(1344)+12*s(1347)+3*s(1348)+3*s(1349)+3*s(1350)+3*s(1351)+9*s(1353)+9*s(1354)+9*s(1355)+9*s(1356)+220*s(1357)+10*s(1358)+48*s(1359)+2*s(1362)+2*s(1363)+2*s(1364)+2*s(1365)+8*s(1366)+8*s(1367)+8*s(1368)+1024*s(1389)+480*s(1390)+16*s(1391)+32*s(1392)+32*s(1393)+128*s(1396)+16*s(1397)+16*s(1398)+16*s(1399)+64*s(1400)+32*s(1401)+32*s(1403)+32*s(1404)+32*s(1405)+32*s(1406)+16*s(1407)+16*s(1408)+16*s(1409)+48*s(1411)+8*s(1417)+8*s(1418)+8*s(1419)+8*s(1420)+16*s(1421)+48*s(1422)+96*s(1423)+16*s(1424)+48*s(1426)+16*s(1427)+16*s(1428)+16*s(1429)+16*s(1430)+16*s(1431)+16*s(1432)+24*s(1433)+24*s(1434)+24*s(1435)+32*s(1436)+48*s(1438)+16*s(1444)+16*s(1445)+16*s(1446)+16*s(1447)+16*s(1448)+48*s(1449)+192*s(1450)+8*s(1456)+8*s(1457)+8*s(1458)+8*s(1459)+96*s(1460)+16*s(1461)+8*s(1462)+8*s(1463)+8*s(1464)+4*s(1465)+20*s(1467)+256*s(1483)+32*s(1484)+120*s(1485)+4*s(1486)+8*s(1487)+8*s(1488)+32*s(1491)+4*s(1492)+4*s(1493)+4*s(1494)+16*s(1495)+8*s(1496)+8*s(1498)+8*s(1499)+8*s(1500)+8*s(1501)+4*s(1502)+4*s(1503)+4*s(1504)+12*s(1506)+2*s(1512)+2*s(1513)+2*s(1514)+2*s(1515)+4*s(1516)+12*s(1517)+24*s(1518)+4*s(1519)+12*s(1521)+4*s(1522)+4*s(1523)+4*s(1524)+4*s(1525)+4*s(1526)+4*s(1527)+6*s(1528)+6*s(1529)+6*s(1530)+8*s(1531)+12*s(1533)+4*s(1539)+4*s(1540)+4*s(1541)+4*s(1542)+4*s(1543)+12*s(1544)+48*s(1545)+2*s(1550)+2*s(1551)+2*s(1552)+2*s(1553)+24*s(1554)+4*s(1555)+2*s(1556)+2*s(1557)+2*s(1558)+8*s(1707)+30*s(1708)+1*s(1710)+2*s(1711)+2*s(1712)+1*s(1716)+1*s(1717)+1*s(1718)+4*s(1719)+2*s(1720)+2*s(1722)+2*s(1723)+2*s(1724)+2*s(1725)+1*s(1726)+1*s(1727)+1*s(1728)+3*s(1730)+1*s(1737)+1*s(1738)+1*s(1739)+1*s(1740)+1*s(1741)+3*s(1742)+12*s(1743)+1*s(1744)+2*s(1746)+1*s(1747)+1*s(1748)+1*s(1749)+1*s(1750)+1*s(1751)+1*s(1752)+3*s(1762)+1*s(1769)+1*s(1770)+1*s(1771)+1*s(1772)+1*s(1773)+3*s(1774)+12*s(1775)+3 Such that:s(1704) =< 1/2 s(1696) =< V+3 s(1697) =< 2*V+2 s(1699) =< V/3+1 s(1700) =< V/3+1/3 s(1701) =< 2/5*V+2/5 aux(133) =< 1 aux(134) =< 2 aux(135) =< V1 aux(136) =< V1+1 aux(137) =< V1+V aux(138) =< V1+V+1 aux(139) =< V1+V+2 aux(140) =< 2*V1+2*V aux(141) =< V1/2+1/2 aux(142) =< V1/3+V/3 aux(143) =< V1/3+V/3+2/3 aux(144) =< 2/5*V1+2/5*V aux(145) =< V aux(146) =< V+1 aux(147) =< V/2+1/2 s(1322) =< aux(135) s(1465) =< aux(139) s(1324) =< aux(145) s(1707) =< aux(133) s(1708) =< aux(134) s(1710) =< aux(145) s(1710) =< aux(146) s(1711) =< aux(146) s(1712) =< aux(146) s(1712) =< aux(134) s(1711) =< aux(133) s(1713) =< aux(134)*(1/2) s(1714) =< s(1696)*(6/5) s(1344) =< aux(146) s(1716) =< s(1696) s(1717) =< s(1714) s(1718) =< s(1714) s(1716) =< s(1714) s(1718) =< aux(134) s(1716) =< aux(134) s(1719) =< aux(134) s(1719) =< s(1713) s(1716) =< s(1708)*(1/3)+s(1696) s(1717) =< s(1708)*(1/5)+s(1714) s(1718) =< s(1708)*(1/5)+s(1714) s(1716) =< s(1708)*(1/5)+s(1714) s(1720) =< aux(133) s(1720) =< aux(134) s(1721) =< aux(133)*(6/5) s(1722) =< s(1704) s(1723) =< aux(133) s(1724) =< s(1721) s(1725) =< s(1721) s(1723) =< s(1721) s(1725) =< aux(134) s(1723) =< aux(134) s(1723) =< s(1708)*(1/3)+aux(133) s(1724) =< s(1708)*(1/5)+s(1721) s(1725) =< s(1708)*(1/5)+s(1721) s(1723) =< s(1708)*(1/5)+s(1721) s(1726) =< aux(146) s(1727) =< s(1697) s(1728) =< s(1697) s(1726) =< s(1697) s(1728) =< aux(133) s(1726) =< aux(133) s(1726) =< s(1708)*(1/3)+aux(146) s(1727) =< s(1708)*(1/5)+s(1697) s(1728) =< s(1708)*(1/5)+s(1697) s(1726) =< s(1708)*(1/5)+s(1697) s(1729) =< aux(135) s(1730) =< aux(135) s(1729) =< aux(145) s(1730) =< aux(145) s(1729) =< s(1697) s(1730) =< s(1697) s(1731) =< aux(145)*(1/2)+1/2 s(1732) =< s(1730)*aux(145) s(1733) =< s(1729)*2 s(1734) =< s(1730)*s(1731) s(1735) =< s(1734)*(4/5) s(1736) =< s(1734)*(2/3) s(1737) =< s(1734) s(1738) =< s(1736) s(1739) =< s(1735) s(1740) =< s(1735) s(1738) =< s(1735) s(1740) =< s(1729) s(1738) =< s(1729) s(1741) =< s(1729) s(1742) =< s(1733) s(1738) =< s(1742)*(1/3)+s(1736) s(1739) =< s(1742)*(1/5)+s(1735) s(1740) =< s(1742)*(1/5)+s(1735) s(1738) =< s(1742)*(1/5)+s(1735) s(1743) =< s(1732) s(1744) =< aux(145) s(1744) =< aux(146) s(1744) =< aux(147) s(1745) =< s(1699)*(6/5) s(1746) =< aux(147) s(1747) =< s(1699) s(1748) =< s(1745) s(1749) =< s(1745) s(1747) =< s(1745) s(1749) =< aux(134) s(1747) =< aux(134) s(1747) =< s(1708)*(1/3)+s(1699) s(1748) =< s(1708)*(1/5)+s(1745) s(1749) =< s(1708)*(1/5)+s(1745) s(1747) =< s(1708)*(1/5)+s(1745) s(1750) =< s(1700) s(1751) =< s(1701) s(1752) =< s(1701) s(1750) =< s(1701) s(1752) =< aux(133) s(1750) =< aux(133) s(1750) =< s(1708)*(1/3)+s(1700) s(1751) =< s(1708)*(1/5)+s(1701) s(1752) =< s(1708)*(1/5)+s(1701) s(1750) =< s(1708)*(1/5)+s(1701) s(1761) =< aux(135) s(1762) =< aux(135) s(1761) =< aux(145) s(1762) =< aux(145) s(1764) =< s(1762)*aux(145) s(1765) =< s(1761)*2 s(1766) =< s(1762)*s(1731) s(1767) =< s(1766)*(4/5) s(1768) =< s(1766)*(2/3) s(1769) =< s(1766) s(1770) =< s(1768) s(1771) =< s(1767) s(1772) =< s(1767) s(1770) =< s(1767) s(1772) =< s(1761) s(1770) =< s(1761) s(1773) =< s(1761) s(1774) =< s(1765) s(1770) =< s(1774)*(1/3)+s(1768) s(1771) =< s(1774)*(1/5)+s(1767) s(1772) =< s(1774)*(1/5)+s(1767) s(1770) =< s(1774)*(1/5)+s(1767) s(1775) =< s(1764) s(1341) =< aux(135) s(1341) =< aux(136) s(1342) =< aux(136) s(1343) =< aux(136) s(1341) =< aux(141) s(1343) =< aux(146) s(1342) =< aux(147) s(1345) =< aux(146)*(1/2) s(1346) =< aux(143)*(6/5) s(1347) =< aux(141) s(1348) =< aux(143) s(1349) =< s(1346) s(1350) =< s(1346) s(1348) =< s(1346) s(1350) =< aux(146) s(1348) =< aux(146) s(1351) =< aux(146) s(1351) =< s(1345) s(1348) =< s(1344)*(1/3)+aux(143) s(1349) =< s(1344)*(1/5)+s(1346) s(1350) =< s(1344)*(1/5)+s(1346) s(1348) =< s(1344)*(1/5)+s(1346) s(1353) =< aux(142) s(1354) =< aux(144) s(1355) =< aux(144) s(1353) =< aux(144) s(1355) =< aux(145) s(1353) =< aux(145) s(1356) =< aux(145) s(1356) =< aux(147) s(1353) =< s(1344)*(1/3)+aux(142) s(1354) =< s(1344)*(1/5)+aux(144) s(1355) =< s(1344)*(1/5)+aux(144) s(1353) =< s(1344)*(1/5)+aux(144) s(1357) =< aux(137) s(1358) =< aux(137) s(1358) =< aux(138) s(1359) =< aux(138) s(1360) =< aux(138)*(1/2) s(1361) =< aux(139)*(6/5) s(1362) =< aux(139) s(1363) =< s(1361) s(1364) =< s(1361) s(1362) =< s(1361) s(1364) =< aux(138) s(1362) =< aux(138) s(1365) =< aux(138) s(1365) =< s(1360) s(1362) =< s(1359)*(1/3)+aux(139) s(1363) =< s(1359)*(1/5)+s(1361) s(1364) =< s(1359)*(1/5)+s(1361) s(1362) =< s(1359)*(1/5)+s(1361) s(1366) =< aux(137) s(1367) =< aux(140) s(1368) =< aux(140) s(1366) =< aux(140) s(1368) =< aux(137) s(1366) =< s(1359)*(1/3)+aux(137) s(1367) =< s(1359)*(1/5)+aux(140) s(1368) =< s(1359)*(1/5)+aux(140) s(1366) =< s(1359)*(1/5)+aux(140) s(1369) =< aux(137)+1 s(1370) =< aux(137) s(1371) =< aux(142) s(1372) =< aux(137)+3 s(1373) =< aux(137)*(1/2)+1/2 s(1374) =< aux(137)*(1/2) s(1375) =< aux(137)*2 s(1376) =< s(1357)*aux(142) s(1377) =< s(1357)*s(1369) s(1378) =< s(1357)*s(1370) s(1379) =< s(1357)*s(1371) s(1380) =< s(1357)*s(1372) s(1381) =< s(1376)*(6/5) s(1382) =< s(1357)*s(1373) s(1383) =< s(1377)*(1/2) s(1384) =< s(1379)*(6/5) s(1385) =< s(1377)*(2/5) s(1386) =< s(1377)*(1/3) s(1387) =< s(1380)*(1/3) s(1388) =< s(1377)*2 s(1389) =< s(1378) s(1390) =< s(1375) s(1391) =< s(1378) s(1391) =< s(1377) s(1392) =< s(1377) s(1393) =< s(1377) s(1393) =< s(1375) s(1392) =< aux(137) s(1394) =< s(1375)*(1/2) s(1395) =< s(1380)*(6/5) s(1396) =< s(1377) s(1397) =< s(1380) s(1398) =< s(1395) s(1399) =< s(1395) s(1397) =< s(1395) s(1399) =< s(1375) s(1397) =< s(1375) s(1400) =< s(1375) s(1400) =< s(1394) s(1397) =< s(1390)*(1/3)+s(1380) s(1398) =< s(1390)*(1/5)+s(1395) s(1399) =< s(1390)*(1/5)+s(1395) s(1397) =< s(1390)*(1/5)+s(1395) s(1401) =< aux(137) s(1401) =< s(1375) s(1402) =< aux(137)*(6/5) s(1403) =< s(1374) s(1404) =< aux(137) s(1405) =< s(1402) s(1406) =< s(1402) s(1404) =< s(1402) s(1406) =< s(1375) s(1404) =< s(1375) s(1404) =< s(1390)*(1/3)+aux(137) s(1405) =< s(1390)*(1/5)+s(1402) s(1406) =< s(1390)*(1/5)+s(1402) s(1404) =< s(1390)*(1/5)+s(1402) s(1407) =< s(1377) s(1408) =< s(1388) s(1409) =< s(1388) s(1407) =< s(1388) s(1409) =< aux(137) s(1407) =< aux(137) s(1407) =< s(1390)*(1/3)+s(1377) s(1408) =< s(1390)*(1/5)+s(1388) s(1409) =< s(1390)*(1/5)+s(1388) s(1407) =< s(1390)*(1/5)+s(1388) s(1410) =< s(1378) s(1411) =< s(1378) s(1410) =< s(1388) s(1411) =< s(1388) s(1412) =< s(1411)*aux(137) s(1413) =< s(1410)*2 s(1414) =< s(1411)*s(1373) s(1415) =< s(1414)*(4/5) s(1416) =< s(1414)*(2/3) s(1417) =< s(1414) s(1418) =< s(1416) s(1419) =< s(1415) s(1420) =< s(1415) s(1418) =< s(1415) s(1420) =< s(1410) s(1418) =< s(1410) s(1421) =< s(1410) s(1422) =< s(1413) s(1418) =< s(1422)*(1/3)+s(1416) s(1419) =< s(1422)*(1/5)+s(1415) s(1420) =< s(1422)*(1/5)+s(1415) s(1418) =< s(1422)*(1/5)+s(1415) s(1423) =< s(1412) s(1424) =< s(1378) s(1424) =< s(1377) s(1424) =< s(1383) s(1425) =< s(1387)*(6/5) s(1426) =< s(1383) s(1427) =< s(1387) s(1428) =< s(1425) s(1429) =< s(1425) s(1427) =< s(1425) s(1429) =< s(1375) s(1427) =< s(1375) s(1427) =< s(1390)*(1/3)+s(1387) s(1428) =< s(1390)*(1/5)+s(1425) s(1429) =< s(1390)*(1/5)+s(1425) s(1427) =< s(1390)*(1/5)+s(1425) s(1430) =< s(1386) s(1431) =< s(1385) s(1432) =< s(1385) s(1430) =< s(1385) s(1432) =< aux(137) s(1430) =< aux(137) s(1430) =< s(1390)*(1/3)+s(1386) s(1431) =< s(1390)*(1/5)+s(1385) s(1432) =< s(1390)*(1/5)+s(1385) s(1430) =< s(1390)*(1/5)+s(1385) s(1433) =< s(1379) s(1434) =< s(1384) s(1435) =< s(1384) s(1433) =< s(1384) s(1435) =< s(1378) s(1433) =< s(1378) s(1436) =< s(1378) s(1436) =< s(1383) s(1433) =< s(1396)*(1/3)+s(1379) s(1434) =< s(1396)*(1/5)+s(1384) s(1435) =< s(1396)*(1/5)+s(1384) s(1433) =< s(1396)*(1/5)+s(1384) s(1437) =< s(1378) s(1438) =< s(1378) s(1437) =< aux(137) s(1438) =< aux(137) s(1439) =< s(1438)*aux(137) s(1440) =< s(1437)*2 s(1441) =< s(1438)*s(1373) s(1442) =< s(1441)*(4/5) s(1443) =< s(1441)*(2/3) s(1444) =< s(1441) s(1445) =< s(1443) s(1446) =< s(1442) s(1447) =< s(1442) s(1445) =< s(1442) s(1447) =< s(1437) s(1445) =< s(1437) s(1448) =< s(1437) s(1449) =< s(1440) s(1445) =< s(1449)*(1/3)+s(1443) s(1446) =< s(1449)*(1/5)+s(1442) s(1447) =< s(1449)*(1/5)+s(1442) s(1445) =< s(1449)*(1/5)+s(1442) s(1450) =< s(1439) s(1451) =< s(1370)*(1/2)+1/2 s(1452) =< s(1411)*s(1370) s(1453) =< s(1411)*s(1451) s(1454) =< s(1453)*(4/5) s(1455) =< s(1453)*(2/3) s(1456) =< s(1453) s(1457) =< s(1455) s(1458) =< s(1454) s(1459) =< s(1454) s(1457) =< s(1454) s(1459) =< s(1410) s(1457) =< s(1410) s(1457) =< s(1422)*(1/3)+s(1455) s(1458) =< s(1422)*(1/5)+s(1454) s(1459) =< s(1422)*(1/5)+s(1454) s(1457) =< s(1422)*(1/5)+s(1454) s(1460) =< s(1452) s(1461) =< s(1382) s(1462) =< s(1376) s(1463) =< s(1381) s(1464) =< s(1381) s(1462) =< s(1381) s(1464) =< s(1378) s(1462) =< s(1378) s(1462) =< s(1396)*(1/3)+s(1376) s(1463) =< s(1396)*(1/5)+s(1381) s(1464) =< s(1396)*(1/5)+s(1381) s(1462) =< s(1396)*(1/5)+s(1381) s(1466) =< aux(137) s(1467) =< aux(137) s(1466) =< aux(139) s(1467) =< aux(139) s(1468) =< s(1466)*(1/2) s(1469) =< s(1466)*2 s(1470) =< s(1467)*aux(142) s(1471) =< s(1467)*s(1369) s(1472) =< s(1467)*s(1370) s(1473) =< s(1467)*s(1371) s(1474) =< s(1467)*s(1372) s(1475) =< s(1470)*(6/5) s(1476) =< s(1467)*s(1373) s(1477) =< s(1471)*(1/2) s(1478) =< s(1473)*(6/5) s(1479) =< s(1471)*(2/5) s(1480) =< s(1471)*(1/3) s(1481) =< s(1474)*(1/3) s(1482) =< s(1471)*2 s(1483) =< s(1472) s(1484) =< s(1466) s(1485) =< s(1469) s(1486) =< s(1472) s(1486) =< s(1471) s(1487) =< s(1471) s(1488) =< s(1471) s(1488) =< s(1469) s(1487) =< s(1466) s(1489) =< s(1469)*(1/2) s(1490) =< s(1474)*(6/5) s(1491) =< s(1471) s(1492) =< s(1474) s(1493) =< s(1490) s(1494) =< s(1490) s(1492) =< s(1490) s(1494) =< s(1469) s(1492) =< s(1469) s(1495) =< s(1469) s(1495) =< s(1489) s(1492) =< s(1485)*(1/3)+s(1474) s(1493) =< s(1485)*(1/5)+s(1490) s(1494) =< s(1485)*(1/5)+s(1490) s(1492) =< s(1485)*(1/5)+s(1490) s(1496) =< s(1466) s(1496) =< s(1469) s(1497) =< s(1466)*(6/5) s(1498) =< s(1468) s(1499) =< s(1466) s(1500) =< s(1497) s(1501) =< s(1497) s(1499) =< s(1497) s(1501) =< s(1469) s(1499) =< s(1469) s(1499) =< s(1485)*(1/3)+s(1466) s(1500) =< s(1485)*(1/5)+s(1497) s(1501) =< s(1485)*(1/5)+s(1497) s(1499) =< s(1485)*(1/5)+s(1497) s(1502) =< s(1471) s(1503) =< s(1482) s(1504) =< s(1482) s(1502) =< s(1482) s(1504) =< s(1466) s(1502) =< s(1466) s(1502) =< s(1485)*(1/3)+s(1471) s(1503) =< s(1485)*(1/5)+s(1482) s(1504) =< s(1485)*(1/5)+s(1482) s(1502) =< s(1485)*(1/5)+s(1482) s(1505) =< s(1472) s(1506) =< s(1472) s(1505) =< s(1482) s(1506) =< s(1482) s(1507) =< s(1506)*aux(137) s(1508) =< s(1505)*2 s(1509) =< s(1506)*s(1373) s(1510) =< s(1509)*(4/5) s(1511) =< s(1509)*(2/3) s(1512) =< s(1509) s(1513) =< s(1511) s(1514) =< s(1510) s(1515) =< s(1510) s(1513) =< s(1510) s(1515) =< s(1505) s(1513) =< s(1505) s(1516) =< s(1505) s(1517) =< s(1508) s(1513) =< s(1517)*(1/3)+s(1511) s(1514) =< s(1517)*(1/5)+s(1510) s(1515) =< s(1517)*(1/5)+s(1510) s(1513) =< s(1517)*(1/5)+s(1510) s(1518) =< s(1507) s(1519) =< s(1472) s(1519) =< s(1471) s(1519) =< s(1477) s(1520) =< s(1481)*(6/5) s(1521) =< s(1477) s(1522) =< s(1481) s(1523) =< s(1520) s(1524) =< s(1520) s(1522) =< s(1520) s(1524) =< s(1469) s(1522) =< s(1469) s(1522) =< s(1485)*(1/3)+s(1481) s(1523) =< s(1485)*(1/5)+s(1520) s(1524) =< s(1485)*(1/5)+s(1520) s(1522) =< s(1485)*(1/5)+s(1520) s(1525) =< s(1480) s(1526) =< s(1479) s(1527) =< s(1479) s(1525) =< s(1479) s(1527) =< s(1466) s(1525) =< s(1466) s(1525) =< s(1485)*(1/3)+s(1480) s(1526) =< s(1485)*(1/5)+s(1479) s(1527) =< s(1485)*(1/5)+s(1479) s(1525) =< s(1485)*(1/5)+s(1479) s(1528) =< s(1473) s(1529) =< s(1478) s(1530) =< s(1478) s(1528) =< s(1478) s(1530) =< s(1472) s(1528) =< s(1472) s(1531) =< s(1472) s(1531) =< s(1477) s(1528) =< s(1491)*(1/3)+s(1473) s(1529) =< s(1491)*(1/5)+s(1478) s(1530) =< s(1491)*(1/5)+s(1478) s(1528) =< s(1491)*(1/5)+s(1478) s(1532) =< s(1472) s(1533) =< s(1472) s(1532) =< s(1466) s(1533) =< s(1466) s(1534) =< s(1533)*aux(137) s(1535) =< s(1532)*2 s(1536) =< s(1533)*s(1373) s(1537) =< s(1536)*(4/5) s(1538) =< s(1536)*(2/3) s(1539) =< s(1536) s(1540) =< s(1538) s(1541) =< s(1537) s(1542) =< s(1537) s(1540) =< s(1537) s(1542) =< s(1532) s(1540) =< s(1532) s(1543) =< s(1532) s(1544) =< s(1535) s(1540) =< s(1544)*(1/3)+s(1538) s(1541) =< s(1544)*(1/5)+s(1537) s(1542) =< s(1544)*(1/5)+s(1537) s(1540) =< s(1544)*(1/5)+s(1537) s(1545) =< s(1534) s(1546) =< s(1506)*s(1370) s(1547) =< s(1506)*s(1451) s(1548) =< s(1547)*(4/5) s(1549) =< s(1547)*(2/3) s(1550) =< s(1547) s(1551) =< s(1549) s(1552) =< s(1548) s(1553) =< s(1548) s(1551) =< s(1548) s(1553) =< s(1505) s(1551) =< s(1505) s(1551) =< s(1517)*(1/3)+s(1549) s(1552) =< s(1517)*(1/5)+s(1548) s(1553) =< s(1517)*(1/5)+s(1548) s(1551) =< s(1517)*(1/5)+s(1548) s(1554) =< s(1546) s(1555) =< s(1476) s(1556) =< s(1470) s(1557) =< s(1475) s(1558) =< s(1475) s(1556) =< s(1475) s(1558) =< s(1472) s(1556) =< s(1472) s(1556) =< s(1491)*(1/3)+s(1470) s(1557) =< s(1491)*(1/5)+s(1475) s(1558) =< s(1491)*(1/5)+s(1475) s(1556) =< s(1491)*(1/5)+s(1475) with precondition: [V1>=0] * Chain [73]: 329*s(2112)+127*s(2128)+197*s(2129)+9*s(2131)+5*s(2132)+4*s(2133)+40*s(2136)+2*s(2137)+2*s(2138)+2*s(2139)+24*s(2140)+14*s(2141)+29*s(2143)+13*s(2144)+13*s(2145)+13*s(2146)+2*s(2147)+2*s(2148)+2*s(2149)+6*s(2151)+2*s(2158)+2*s(2159)+2*s(2160)+2*s(2161)+2*s(2162)+6*s(2163)+24*s(2164)+4*s(2165)+14*s(2167)+2*s(2168)+2*s(2169)+2*s(2170)+2*s(2171)+2*s(2172)+2*s(2173)+1*s(2189)+1*s(2195)+1*s(2196)+1*s(2197)+3*s(2198)+4*s(2201)+1*s(2209)+1*s(2210)+1*s(2211)+1*s(2212)+4*s(2213)+4*s(2214)+4*s(2215)+384*s(2236)+180*s(2237)+6*s(2238)+12*s(2239)+12*s(2240)+48*s(2243)+6*s(2244)+6*s(2245)+6*s(2246)+24*s(2247)+12*s(2248)+12*s(2250)+12*s(2251)+12*s(2252)+12*s(2253)+6*s(2254)+6*s(2255)+6*s(2256)+18*s(2258)+3*s(2264)+3*s(2265)+3*s(2266)+3*s(2267)+6*s(2268)+18*s(2269)+36*s(2270)+6*s(2271)+18*s(2273)+6*s(2274)+6*s(2275)+6*s(2276)+6*s(2277)+6*s(2278)+6*s(2279)+9*s(2280)+9*s(2281)+9*s(2282)+12*s(2283)+18*s(2285)+6*s(2291)+6*s(2292)+6*s(2293)+6*s(2294)+6*s(2295)+18*s(2296)+72*s(2297)+3*s(2303)+3*s(2304)+3*s(2305)+3*s(2306)+36*s(2307)+6*s(2308)+3*s(2309)+3*s(2310)+3*s(2311)+1*s(2312)+10*s(2314)+128*s(2330)+16*s(2331)+60*s(2332)+2*s(2333)+4*s(2334)+4*s(2335)+16*s(2338)+2*s(2339)+2*s(2340)+2*s(2341)+8*s(2342)+4*s(2343)+4*s(2345)+4*s(2346)+4*s(2347)+4*s(2348)+2*s(2349)+2*s(2350)+2*s(2351)+6*s(2353)+1*s(2359)+1*s(2360)+1*s(2361)+1*s(2362)+2*s(2363)+6*s(2364)+12*s(2365)+2*s(2366)+6*s(2368)+2*s(2369)+2*s(2370)+2*s(2371)+2*s(2372)+2*s(2373)+2*s(2374)+3*s(2375)+3*s(2376)+3*s(2377)+4*s(2378)+6*s(2380)+2*s(2386)+2*s(2387)+2*s(2388)+2*s(2389)+2*s(2390)+6*s(2391)+24*s(2392)+1*s(2397)+1*s(2398)+1*s(2399)+1*s(2400)+12*s(2401)+2*s(2402)+1*s(2403)+1*s(2404)+1*s(2405)+15*s(2475)+2*s(2482)+2*s(2483)+2*s(2484)+2*s(2485)+5*s(2486)+15*s(2487)+24*s(2488)+4*s(2504)+141*s(2506)+3*s(2510)+3*s(2511)+3*s(2512)+7*s(2513)+381*s(2514)+12*s(2515)+12*s(2516)+12*s(2517)+16*s(2518)+304*s(2519)+15*s(2520)+72*s(2521)+3*s(2524)+3*s(2525)+3*s(2526)+3*s(2527)+12*s(2528)+12*s(2529)+12*s(2530)+1408*s(2551)+660*s(2552)+22*s(2553)+44*s(2554)+44*s(2555)+176*s(2558)+22*s(2559)+22*s(2560)+22*s(2561)+88*s(2562)+44*s(2563)+44*s(2565)+44*s(2566)+44*s(2567)+44*s(2568)+22*s(2569)+22*s(2570)+22*s(2571)+66*s(2573)+11*s(2579)+11*s(2580)+11*s(2581)+11*s(2582)+22*s(2583)+66*s(2584)+132*s(2585)+22*s(2586)+66*s(2588)+22*s(2589)+22*s(2590)+22*s(2591)+22*s(2592)+22*s(2593)+22*s(2594)+33*s(2595)+33*s(2596)+33*s(2597)+44*s(2598)+66*s(2600)+22*s(2606)+22*s(2607)+22*s(2608)+22*s(2609)+22*s(2610)+66*s(2611)+264*s(2612)+11*s(2618)+11*s(2619)+11*s(2620)+11*s(2621)+132*s(2622)+22*s(2623)+11*s(2624)+11*s(2625)+11*s(2626)+6*s(2627)+40*s(2629)+512*s(2645)+64*s(2646)+240*s(2647)+8*s(2648)+16*s(2649)+16*s(2650)+64*s(2653)+8*s(2654)+8*s(2655)+8*s(2656)+32*s(2657)+16*s(2658)+16*s(2660)+16*s(2661)+16*s(2662)+16*s(2663)+8*s(2664)+8*s(2665)+8*s(2666)+24*s(2668)+4*s(2674)+4*s(2675)+4*s(2676)+4*s(2677)+8*s(2678)+24*s(2679)+48*s(2680)+8*s(2681)+24*s(2683)+8*s(2684)+8*s(2685)+8*s(2686)+8*s(2687)+8*s(2688)+8*s(2689)+12*s(2690)+12*s(2691)+12*s(2692)+16*s(2693)+24*s(2695)+8*s(2701)+8*s(2702)+8*s(2703)+8*s(2704)+8*s(2705)+24*s(2706)+96*s(2707)+4*s(2712)+4*s(2713)+4*s(2714)+4*s(2715)+48*s(2716)+8*s(2717)+4*s(2718)+4*s(2719)+4*s(2720)+6*s(2731)+2*s(2738)+2*s(2739)+2*s(2740)+2*s(2741)+2*s(2742)+6*s(2743)+24*s(2744)+6*s(2755)+2*s(2762)+2*s(2763)+2*s(2764)+2*s(2765)+2*s(2766)+6*s(2767)+24*s(2768)+1*s(2946)+1*s(2947)+1*s(2948)+1*s(2956)+1*s(2957)+1*s(2958)+1*s(2980)+1*s(2981)+1*s(2982)+1*s(2998)+1*s(3004)+1*s(3005)+1*s(3006)+1*s(3018)+1*s(3019)+1*s(3020)+6*s(3232)+4*s(3233)+2*s(3237)+2*s(3238)+2*s(3239)+2*s(3247)+2*s(3248)+2*s(3249)+6*s(3251)+2*s(3258)+2*s(3259)+2*s(3260)+2*s(3261)+2*s(3262)+6*s(3263)+24*s(3264)+2*s(3265)+4*s(3267)+2*s(3268)+2*s(3269)+2*s(3270)+2*s(3271)+2*s(3272)+2*s(3273)+2*s(3289)+2*s(3295)+2*s(3296)+2*s(3297)+8*s(3300)+8*s(3301)+8*s(3302)+16*s(3303)+2*s(3309)+2*s(3310)+2*s(3311)+8*s(3313)+8*s(3314)+8*s(3315)+768*s(3336)+360*s(3337)+12*s(3338)+24*s(3339)+24*s(3340)+96*s(3343)+12*s(3344)+12*s(3345)+12*s(3346)+48*s(3347)+24*s(3348)+24*s(3350)+24*s(3351)+24*s(3352)+24*s(3353)+12*s(3354)+12*s(3355)+12*s(3356)+36*s(3358)+6*s(3364)+6*s(3365)+6*s(3366)+6*s(3367)+12*s(3368)+36*s(3369)+72*s(3370)+12*s(3371)+36*s(3373)+12*s(3374)+12*s(3375)+12*s(3376)+12*s(3377)+12*s(3378)+12*s(3379)+18*s(3380)+18*s(3381)+18*s(3382)+24*s(3383)+36*s(3385)+12*s(3391)+12*s(3392)+12*s(3393)+12*s(3394)+12*s(3395)+36*s(3396)+144*s(3397)+6*s(3403)+6*s(3404)+6*s(3405)+6*s(3406)+72*s(3407)+12*s(3408)+6*s(3409)+6*s(3410)+6*s(3411)+2*s(3412)+20*s(3414)+256*s(3430)+32*s(3431)+120*s(3432)+4*s(3433)+8*s(3434)+8*s(3435)+32*s(3438)+4*s(3439)+4*s(3440)+4*s(3441)+16*s(3442)+8*s(3443)+8*s(3445)+8*s(3446)+8*s(3447)+8*s(3448)+4*s(3449)+4*s(3450)+4*s(3451)+12*s(3453)+2*s(3459)+2*s(3460)+2*s(3461)+2*s(3462)+4*s(3463)+12*s(3464)+24*s(3465)+4*s(3466)+12*s(3468)+4*s(3469)+4*s(3470)+4*s(3471)+4*s(3472)+4*s(3473)+4*s(3474)+6*s(3475)+6*s(3476)+6*s(3477)+8*s(3478)+12*s(3480)+4*s(3486)+4*s(3487)+4*s(3488)+4*s(3489)+4*s(3490)+12*s(3491)+48*s(3492)+2*s(3497)+2*s(3498)+2*s(3499)+2*s(3500)+24*s(3501)+4*s(3502)+2*s(3503)+2*s(3504)+2*s(3505)+3*s(3523)+3*s(3524)+3*s(3525)+3*s(3526)+36*s(3529)+2*s(3545)+12*s(3772)+4*s(3779)+4*s(3780)+4*s(3781)+4*s(3782)+4*s(3783)+12*s(3784)+48*s(3785)+3*s(4546)+1*s(4553)+1*s(4554)+1*s(4555)+1*s(4556)+1*s(4557)+3*s(4558)+12*s(4559)+2*s(4680)+2*s(4681)+1*s(4685)+1*s(4686)+1*s(4687)+1*s(4695)+1*s(4696)+1*s(4697)+3*s(4699)+1*s(4706)+1*s(4707)+1*s(4708)+1*s(4709)+1*s(4710)+3*s(4711)+12*s(4712)+1*s(4713)+2*s(4715)+1*s(4716)+1*s(4717)+1*s(4718)+1*s(4719)+1*s(4720)+1*s(4721)+6 Such that:s(2926) =< 3 s(2930) =< 1/3 s(2988) =< 2/3 s(2931) =< 2/5 s(4667) =< V35/2 aux(205) =< 1 aux(206) =< 2 aux(207) =< 1/2 aux(208) =< -V+V35 aux(209) =< V aux(210) =< V+1 aux(211) =< V+2 aux(212) =< V+3 aux(213) =< V-V35 aux(214) =< V+V35 aux(215) =< V+V35+1 aux(216) =< V+V35+2 aux(217) =< 2*V aux(218) =< 2*V+2 aux(219) =< 2*V+2*V35 aux(220) =< V/2+1/2 aux(221) =< V/3 aux(222) =< V/3+1 aux(223) =< V/3+1/3 aux(224) =< V/3+2/3 aux(225) =< 2/5*V aux(226) =< 2/5*V+2/5 aux(227) =< V35 aux(228) =< V35+1 aux(229) =< V35+2 aux(230) =< V35+3 aux(231) =< 2*V35 aux(232) =< 2*V35+2 aux(233) =< V35/2+1/2 aux(234) =< V35/3 aux(235) =< V35/3+1 aux(236) =< V35/3+1/3 aux(237) =< V35/3+2/3 aux(238) =< 2/5*V35 aux(239) =< 2/5*V35+2/5 s(2506) =< aux(210) s(2627) =< aux(216) s(2112) =< aux(227) s(2136) =< aux(228) s(2128) =< aux(205) s(2129) =< aux(206) s(2131) =< aux(227) s(2131) =< aux(228) s(2132) =< aux(228) s(2133) =< aux(228) s(2133) =< aux(206) s(2132) =< aux(205) s(2134) =< aux(206)*(1/2) s(2135) =< aux(230)*(6/5) s(2137) =< aux(230) s(2138) =< s(2135) s(2139) =< s(2135) s(2137) =< s(2135) s(2139) =< aux(206) s(2137) =< aux(206) s(2140) =< aux(206) s(2140) =< s(2134) s(2137) =< s(2129)*(1/3)+aux(230) s(2138) =< s(2129)*(1/5)+s(2135) s(2139) =< s(2129)*(1/5)+s(2135) s(2137) =< s(2129)*(1/5)+s(2135) s(2141) =< aux(205) s(2141) =< aux(206) s(2142) =< aux(205)*(6/5) s(2143) =< aux(207) s(2144) =< aux(205) s(2145) =< s(2142) s(2146) =< s(2142) s(2144) =< s(2142) s(2146) =< aux(206) s(2144) =< aux(206) s(2144) =< s(2129)*(1/3)+aux(205) s(2145) =< s(2129)*(1/5)+s(2142) s(2146) =< s(2129)*(1/5)+s(2142) s(2144) =< s(2129)*(1/5)+s(2142) s(2147) =< aux(228) s(2148) =< aux(232) s(2149) =< aux(232) s(2147) =< aux(232) s(2149) =< aux(205) s(2147) =< aux(205) s(2147) =< s(2129)*(1/3)+aux(228) s(2148) =< s(2129)*(1/5)+aux(232) s(2149) =< s(2129)*(1/5)+aux(232) s(2147) =< s(2129)*(1/5)+aux(232) s(2150) =< aux(209) s(2151) =< aux(209) s(2150) =< aux(227) s(2151) =< aux(227) s(2150) =< aux(232) s(2151) =< aux(232) s(2152) =< aux(227)*(1/2)+1/2 s(2153) =< s(2151)*aux(227) s(2154) =< s(2150)*2 s(2155) =< s(2151)*s(2152) s(2156) =< s(2155)*(4/5) s(2157) =< s(2155)*(2/3) s(2158) =< s(2155) s(2159) =< s(2157) s(2160) =< s(2156) s(2161) =< s(2156) s(2159) =< s(2156) s(2161) =< s(2150) s(2159) =< s(2150) s(2162) =< s(2150) s(2163) =< s(2154) s(2159) =< s(2163)*(1/3)+s(2157) s(2160) =< s(2163)*(1/5)+s(2156) s(2161) =< s(2163)*(1/5)+s(2156) s(2159) =< s(2163)*(1/5)+s(2156) s(2164) =< s(2153) s(2165) =< aux(227) s(2165) =< aux(228) s(2165) =< aux(233) s(2166) =< aux(235)*(6/5) s(2167) =< aux(233) s(2168) =< aux(235) s(2169) =< s(2166) s(2170) =< s(2166) s(2168) =< s(2166) s(2170) =< aux(206) s(2168) =< aux(206) s(2168) =< s(2129)*(1/3)+aux(235) s(2169) =< s(2129)*(1/5)+s(2166) s(2170) =< s(2129)*(1/5)+s(2166) s(2168) =< s(2129)*(1/5)+s(2166) s(2171) =< aux(236) s(2172) =< aux(239) s(2173) =< aux(239) s(2171) =< aux(239) s(2173) =< aux(205) s(2171) =< aux(205) s(2171) =< s(2129)*(1/3)+aux(236) s(2172) =< s(2129)*(1/5)+aux(239) s(2173) =< s(2129)*(1/5)+aux(239) s(2171) =< s(2129)*(1/5)+aux(239) s(2504) =< aux(228) s(2504) =< aux(210) s(2507) =< aux(210)*(1/2) s(2508) =< aux(216)*(6/5) s(2510) =< aux(216) s(2511) =< s(2508) s(2512) =< s(2508) s(2510) =< s(2508) s(2512) =< aux(210) s(2510) =< aux(210) s(2513) =< aux(210) s(2513) =< s(2507) s(2510) =< s(2506)*(1/3)+aux(216) s(2511) =< s(2506)*(1/5)+s(2508) s(2512) =< s(2506)*(1/5)+s(2508) s(2510) =< s(2506)*(1/5)+s(2508) s(2514) =< aux(209) s(2515) =< aux(214) s(2516) =< aux(219) s(2517) =< aux(219) s(2515) =< aux(219) s(2517) =< aux(209) s(2515) =< aux(209) s(2518) =< aux(209) s(2518) =< aux(210) s(2515) =< s(2506)*(1/3)+aux(214) s(2516) =< s(2506)*(1/5)+aux(219) s(2517) =< s(2506)*(1/5)+aux(219) s(2515) =< s(2506)*(1/5)+aux(219) s(2519) =< aux(214) s(2520) =< aux(214) s(2520) =< aux(215) s(2521) =< aux(215) s(2522) =< aux(215)*(1/2) s(2524) =< aux(216) s(2525) =< s(2508) s(2526) =< s(2508) s(2524) =< s(2508) s(2526) =< aux(215) s(2524) =< aux(215) s(2527) =< aux(215) s(2527) =< s(2522) s(2524) =< s(2521)*(1/3)+aux(216) s(2525) =< s(2521)*(1/5)+s(2508) s(2526) =< s(2521)*(1/5)+s(2508) s(2524) =< s(2521)*(1/5)+s(2508) s(2528) =< aux(214) s(2529) =< aux(219) s(2530) =< aux(219) s(2528) =< aux(219) s(2530) =< aux(214) s(2528) =< s(2521)*(1/3)+aux(214) s(2529) =< s(2521)*(1/5)+aux(219) s(2530) =< s(2521)*(1/5)+aux(219) s(2528) =< s(2521)*(1/5)+aux(219) s(2531) =< aux(214)+1 s(2532) =< aux(214) s(2534) =< aux(214)+3 s(2535) =< aux(214)*(1/2)+1/2 s(2536) =< aux(214)*(1/2) s(2537) =< aux(214)*2 s(2538) =< s(2519)*aux(214) s(2539) =< s(2519)*s(2531) s(2540) =< s(2519)*s(2532) s(2542) =< s(2519)*s(2534) s(2543) =< s(2538)*(6/5) s(2544) =< s(2519)*s(2535) s(2545) =< s(2539)*(1/2) s(2546) =< s(2540)*(6/5) s(2547) =< s(2539)*(2/5) s(2548) =< s(2539)*(1/3) s(2549) =< s(2542)*(1/3) s(2550) =< s(2539)*2 s(2551) =< s(2540) s(2552) =< s(2537) s(2553) =< s(2540) s(2553) =< s(2539) s(2554) =< s(2539) s(2555) =< s(2539) s(2555) =< s(2537) s(2554) =< aux(214) s(2556) =< s(2537)*(1/2) s(2557) =< s(2542)*(6/5) s(2558) =< s(2539) s(2559) =< s(2542) s(2560) =< s(2557) s(2561) =< s(2557) s(2559) =< s(2557) s(2561) =< s(2537) s(2559) =< s(2537) s(2562) =< s(2537) s(2562) =< s(2556) s(2559) =< s(2552)*(1/3)+s(2542) s(2560) =< s(2552)*(1/5)+s(2557) s(2561) =< s(2552)*(1/5)+s(2557) s(2559) =< s(2552)*(1/5)+s(2557) s(2563) =< aux(214) s(2563) =< s(2537) s(2564) =< aux(214)*(6/5) s(2565) =< s(2536) s(2566) =< aux(214) s(2567) =< s(2564) s(2568) =< s(2564) s(2566) =< s(2564) s(2568) =< s(2537) s(2566) =< s(2537) s(2566) =< s(2552)*(1/3)+aux(214) s(2567) =< s(2552)*(1/5)+s(2564) s(2568) =< s(2552)*(1/5)+s(2564) s(2566) =< s(2552)*(1/5)+s(2564) s(2569) =< s(2539) s(2570) =< s(2550) s(2571) =< s(2550) s(2569) =< s(2550) s(2571) =< aux(214) s(2569) =< aux(214) s(2569) =< s(2552)*(1/3)+s(2539) s(2570) =< s(2552)*(1/5)+s(2550) s(2571) =< s(2552)*(1/5)+s(2550) s(2569) =< s(2552)*(1/5)+s(2550) s(2572) =< s(2540) s(2573) =< s(2540) s(2572) =< s(2550) s(2573) =< s(2550) s(2574) =< s(2573)*aux(214) s(2575) =< s(2572)*2 s(2576) =< s(2573)*s(2535) s(2577) =< s(2576)*(4/5) s(2578) =< s(2576)*(2/3) s(2579) =< s(2576) s(2580) =< s(2578) s(2581) =< s(2577) s(2582) =< s(2577) s(2580) =< s(2577) s(2582) =< s(2572) s(2580) =< s(2572) s(2583) =< s(2572) s(2584) =< s(2575) s(2580) =< s(2584)*(1/3)+s(2578) s(2581) =< s(2584)*(1/5)+s(2577) s(2582) =< s(2584)*(1/5)+s(2577) s(2580) =< s(2584)*(1/5)+s(2577) s(2585) =< s(2574) s(2586) =< s(2540) s(2586) =< s(2539) s(2586) =< s(2545) s(2587) =< s(2549)*(6/5) s(2588) =< s(2545) s(2589) =< s(2549) s(2590) =< s(2587) s(2591) =< s(2587) s(2589) =< s(2587) s(2591) =< s(2537) s(2589) =< s(2537) s(2589) =< s(2552)*(1/3)+s(2549) s(2590) =< s(2552)*(1/5)+s(2587) s(2591) =< s(2552)*(1/5)+s(2587) s(2589) =< s(2552)*(1/5)+s(2587) s(2592) =< s(2548) s(2593) =< s(2547) s(2594) =< s(2547) s(2592) =< s(2547) s(2594) =< aux(214) s(2592) =< aux(214) s(2592) =< s(2552)*(1/3)+s(2548) s(2593) =< s(2552)*(1/5)+s(2547) s(2594) =< s(2552)*(1/5)+s(2547) s(2592) =< s(2552)*(1/5)+s(2547) s(2595) =< s(2540) s(2596) =< s(2546) s(2597) =< s(2546) s(2595) =< s(2546) s(2597) =< s(2540) s(2598) =< s(2540) s(2598) =< s(2545) s(2595) =< s(2558)*(1/3)+s(2540) s(2596) =< s(2558)*(1/5)+s(2546) s(2597) =< s(2558)*(1/5)+s(2546) s(2595) =< s(2558)*(1/5)+s(2546) s(2599) =< s(2540) s(2600) =< s(2540) s(2599) =< aux(214) s(2600) =< aux(214) s(2601) =< s(2600)*aux(214) s(2602) =< s(2599)*2 s(2603) =< s(2600)*s(2535) s(2604) =< s(2603)*(4/5) s(2605) =< s(2603)*(2/3) s(2606) =< s(2603) s(2607) =< s(2605) s(2608) =< s(2604) s(2609) =< s(2604) s(2607) =< s(2604) s(2609) =< s(2599) s(2607) =< s(2599) s(2610) =< s(2599) s(2611) =< s(2602) s(2607) =< s(2611)*(1/3)+s(2605) s(2608) =< s(2611)*(1/5)+s(2604) s(2609) =< s(2611)*(1/5)+s(2604) s(2607) =< s(2611)*(1/5)+s(2604) s(2612) =< s(2601) s(2613) =< s(2532)*(1/2)+1/2 s(2614) =< s(2573)*s(2532) s(2615) =< s(2573)*s(2613) s(2616) =< s(2615)*(4/5) s(2617) =< s(2615)*(2/3) s(2618) =< s(2615) s(2619) =< s(2617) s(2620) =< s(2616) s(2621) =< s(2616) s(2619) =< s(2616) s(2621) =< s(2572) s(2619) =< s(2572) s(2619) =< s(2584)*(1/3)+s(2617) s(2620) =< s(2584)*(1/5)+s(2616) s(2621) =< s(2584)*(1/5)+s(2616) s(2619) =< s(2584)*(1/5)+s(2616) s(2622) =< s(2614) s(2623) =< s(2544) s(2624) =< s(2538) s(2625) =< s(2543) s(2626) =< s(2543) s(2624) =< s(2543) s(2626) =< s(2540) s(2624) =< s(2540) s(2624) =< s(2558)*(1/3)+s(2538) s(2625) =< s(2558)*(1/5)+s(2543) s(2626) =< s(2558)*(1/5)+s(2543) s(2624) =< s(2558)*(1/5)+s(2543) s(2628) =< aux(214) s(2629) =< aux(214) s(2628) =< aux(216) s(2629) =< aux(216) s(2630) =< s(2628)*(1/2) s(2631) =< s(2628)*2 s(2632) =< s(2629)*aux(214) s(2633) =< s(2629)*s(2531) s(2634) =< s(2629)*s(2532) s(2636) =< s(2629)*s(2534) s(2637) =< s(2632)*(6/5) s(2638) =< s(2629)*s(2535) s(2639) =< s(2633)*(1/2) s(2640) =< s(2634)*(6/5) s(2641) =< s(2633)*(2/5) s(2642) =< s(2633)*(1/3) s(2643) =< s(2636)*(1/3) s(2644) =< s(2633)*2 s(2645) =< s(2634) s(2646) =< s(2628) s(2647) =< s(2631) s(2648) =< s(2634) s(2648) =< s(2633) s(2649) =< s(2633) s(2650) =< s(2633) s(2650) =< s(2631) s(2649) =< s(2628) s(2651) =< s(2631)*(1/2) s(2652) =< s(2636)*(6/5) s(2653) =< s(2633) s(2654) =< s(2636) s(2655) =< s(2652) s(2656) =< s(2652) s(2654) =< s(2652) s(2656) =< s(2631) s(2654) =< s(2631) s(2657) =< s(2631) s(2657) =< s(2651) s(2654) =< s(2647)*(1/3)+s(2636) s(2655) =< s(2647)*(1/5)+s(2652) s(2656) =< s(2647)*(1/5)+s(2652) s(2654) =< s(2647)*(1/5)+s(2652) s(2658) =< s(2628) s(2658) =< s(2631) s(2659) =< s(2628)*(6/5) s(2660) =< s(2630) s(2661) =< s(2628) s(2662) =< s(2659) s(2663) =< s(2659) s(2661) =< s(2659) s(2663) =< s(2631) s(2661) =< s(2631) s(2661) =< s(2647)*(1/3)+s(2628) s(2662) =< s(2647)*(1/5)+s(2659) s(2663) =< s(2647)*(1/5)+s(2659) s(2661) =< s(2647)*(1/5)+s(2659) s(2664) =< s(2633) s(2665) =< s(2644) s(2666) =< s(2644) s(2664) =< s(2644) s(2666) =< s(2628) s(2664) =< s(2628) s(2664) =< s(2647)*(1/3)+s(2633) s(2665) =< s(2647)*(1/5)+s(2644) s(2666) =< s(2647)*(1/5)+s(2644) s(2664) =< s(2647)*(1/5)+s(2644) s(2667) =< s(2634) s(2668) =< s(2634) s(2667) =< s(2644) s(2668) =< s(2644) s(2669) =< s(2668)*aux(214) s(2670) =< s(2667)*2 s(2671) =< s(2668)*s(2535) s(2672) =< s(2671)*(4/5) s(2673) =< s(2671)*(2/3) s(2674) =< s(2671) s(2675) =< s(2673) s(2676) =< s(2672) s(2677) =< s(2672) s(2675) =< s(2672) s(2677) =< s(2667) s(2675) =< s(2667) s(2678) =< s(2667) s(2679) =< s(2670) s(2675) =< s(2679)*(1/3)+s(2673) s(2676) =< s(2679)*(1/5)+s(2672) s(2677) =< s(2679)*(1/5)+s(2672) s(2675) =< s(2679)*(1/5)+s(2672) s(2680) =< s(2669) s(2681) =< s(2634) s(2681) =< s(2633) s(2681) =< s(2639) s(2682) =< s(2643)*(6/5) s(2683) =< s(2639) s(2684) =< s(2643) s(2685) =< s(2682) s(2686) =< s(2682) s(2684) =< s(2682) s(2686) =< s(2631) s(2684) =< s(2631) s(2684) =< s(2647)*(1/3)+s(2643) s(2685) =< s(2647)*(1/5)+s(2682) s(2686) =< s(2647)*(1/5)+s(2682) s(2684) =< s(2647)*(1/5)+s(2682) s(2687) =< s(2642) s(2688) =< s(2641) s(2689) =< s(2641) s(2687) =< s(2641) s(2689) =< s(2628) s(2687) =< s(2628) s(2687) =< s(2647)*(1/3)+s(2642) s(2688) =< s(2647)*(1/5)+s(2641) s(2689) =< s(2647)*(1/5)+s(2641) s(2687) =< s(2647)*(1/5)+s(2641) s(2690) =< s(2634) s(2691) =< s(2640) s(2692) =< s(2640) s(2690) =< s(2640) s(2692) =< s(2634) s(2693) =< s(2634) s(2693) =< s(2639) s(2690) =< s(2653)*(1/3)+s(2634) s(2691) =< s(2653)*(1/5)+s(2640) s(2692) =< s(2653)*(1/5)+s(2640) s(2690) =< s(2653)*(1/5)+s(2640) s(2694) =< s(2634) s(2695) =< s(2634) s(2694) =< s(2628) s(2695) =< s(2628) s(2696) =< s(2695)*aux(214) s(2697) =< s(2694)*2 s(2698) =< s(2695)*s(2535) s(2699) =< s(2698)*(4/5) s(2700) =< s(2698)*(2/3) s(2701) =< s(2698) s(2702) =< s(2700) s(2703) =< s(2699) s(2704) =< s(2699) s(2702) =< s(2699) s(2704) =< s(2694) s(2702) =< s(2694) s(2705) =< s(2694) s(2706) =< s(2697) s(2702) =< s(2706)*(1/3)+s(2700) s(2703) =< s(2706)*(1/5)+s(2699) s(2704) =< s(2706)*(1/5)+s(2699) s(2702) =< s(2706)*(1/5)+s(2699) s(2707) =< s(2696) s(2708) =< s(2668)*s(2532) s(2709) =< s(2668)*s(2613) s(2710) =< s(2709)*(4/5) s(2711) =< s(2709)*(2/3) s(2712) =< s(2709) s(2713) =< s(2711) s(2714) =< s(2710) s(2715) =< s(2710) s(2713) =< s(2710) s(2715) =< s(2667) s(2713) =< s(2667) s(2713) =< s(2679)*(1/3)+s(2711) s(2714) =< s(2679)*(1/5)+s(2710) s(2715) =< s(2679)*(1/5)+s(2710) s(2713) =< s(2679)*(1/5)+s(2710) s(2716) =< s(2708) s(2717) =< s(2638) s(2718) =< s(2632) s(2719) =< s(2637) s(2720) =< s(2637) s(2718) =< s(2637) s(2720) =< s(2634) s(2718) =< s(2634) s(2718) =< s(2653)*(1/3)+s(2632) s(2719) =< s(2653)*(1/5)+s(2637) s(2720) =< s(2653)*(1/5)+s(2637) s(2718) =< s(2653)*(1/5)+s(2637) s(2474) =< aux(209) s(2475) =< aux(209) s(2474) =< aux(214) s(2475) =< aux(214) s(2474) =< aux(227) s(2475) =< aux(227) s(2477) =< s(2475)*aux(227) s(2478) =< s(2474)*2 s(2479) =< s(2475)*s(2152) s(2480) =< s(2479)*(4/5) s(2481) =< s(2479)*(2/3) s(2482) =< s(2479) s(2483) =< s(2481) s(2484) =< s(2480) s(2485) =< s(2480) s(2483) =< s(2480) s(2485) =< s(2474) s(2483) =< s(2474) s(2486) =< s(2474) s(2487) =< s(2478) s(2483) =< s(2487)*(1/3)+s(2481) s(2484) =< s(2487)*(1/5)+s(2480) s(2485) =< s(2487)*(1/5)+s(2480) s(2483) =< s(2487)*(1/5)+s(2480) s(2488) =< s(2477) s(2730) =< aux(209) s(2731) =< aux(209) s(2730) =< aux(227) s(2731) =< aux(227) s(2733) =< s(2731)*aux(227) s(2734) =< s(2730)*2 s(2735) =< s(2731)*s(2152) s(2736) =< s(2735)*(4/5) s(2737) =< s(2735)*(2/3) s(2738) =< s(2735) s(2739) =< s(2737) s(2740) =< s(2736) s(2741) =< s(2736) s(2739) =< s(2736) s(2741) =< s(2730) s(2739) =< s(2730) s(2742) =< s(2730) s(2743) =< s(2734) s(2739) =< s(2743)*(1/3)+s(2737) s(2740) =< s(2743)*(1/5)+s(2736) s(2741) =< s(2743)*(1/5)+s(2736) s(2739) =< s(2743)*(1/5)+s(2736) s(2744) =< s(2733) s(2754) =< aux(209) s(2755) =< aux(209) s(2754) =< aux(213) s(2755) =< aux(213) s(2754) =< aux(227) s(2755) =< aux(227) s(2757) =< s(2755)*aux(227) s(2758) =< s(2754)*2 s(2759) =< s(2755)*s(2152) s(2760) =< s(2759)*(4/5) s(2761) =< s(2759)*(2/3) s(2762) =< s(2759) s(2763) =< s(2761) s(2764) =< s(2760) s(2765) =< s(2760) s(2763) =< s(2760) s(2765) =< s(2754) s(2763) =< s(2754) s(2766) =< s(2754) s(2767) =< s(2758) s(2763) =< s(2767)*(1/3)+s(2761) s(2764) =< s(2767)*(1/5)+s(2760) s(2765) =< s(2767)*(1/5)+s(2760) s(2763) =< s(2767)*(1/5)+s(2760) s(2768) =< s(2757) s(3545) =< aux(228) s(3545) =< aux(220) s(3303) =< aux(209) s(3303) =< aux(220) s(3252) =< aux(209)*(1/2)+1/2 s(3518) =< s(2475)*aux(209) s(3520) =< s(2475)*s(3252) s(3521) =< s(3520)*(4/5) s(3522) =< s(3520)*(2/3) s(3523) =< s(3520) s(3524) =< s(3522) s(3525) =< s(3521) s(3526) =< s(3521) s(3524) =< s(3521) s(3526) =< s(2474) s(3524) =< s(2474) s(3524) =< s(2487)*(1/3)+s(3522) s(3525) =< s(2487)*(1/5)+s(3521) s(3526) =< s(2487)*(1/5)+s(3521) s(3524) =< s(2487)*(1/5)+s(3521) s(3529) =< s(3518) s(3771) =< aux(227) s(3772) =< aux(227) s(3771) =< aux(208) s(3772) =< aux(208) s(3771) =< aux(209) s(3772) =< aux(209) s(3774) =< s(3772)*aux(209) s(3775) =< s(3771)*2 s(3776) =< s(3772)*s(3252) s(3777) =< s(3776)*(4/5) s(3778) =< s(3776)*(2/3) s(3779) =< s(3776) s(3780) =< s(3778) s(3781) =< s(3777) s(3782) =< s(3777) s(3780) =< s(3777) s(3782) =< s(3771) s(3780) =< s(3771) s(3783) =< s(3771) s(3784) =< s(3775) s(3780) =< s(3784)*(1/3)+s(3778) s(3781) =< s(3784)*(1/5)+s(3777) s(3782) =< s(3784)*(1/5)+s(3777) s(3780) =< s(3784)*(1/5)+s(3777) s(3785) =< s(3774) s(4545) =< aux(227) s(4546) =< aux(227) s(4545) =< aux(216) s(4546) =< aux(216) s(4545) =< aux(209) s(4546) =< aux(209) s(4548) =< s(4546)*aux(209) s(4549) =< s(4545)*2 s(4550) =< s(4546)*s(3252) s(4551) =< s(4550)*(4/5) s(4552) =< s(4550)*(2/3) s(4553) =< s(4550) s(4554) =< s(4552) s(4555) =< s(4551) s(4556) =< s(4551) s(4554) =< s(4551) s(4556) =< s(4545) s(4554) =< s(4545) s(4557) =< s(4545) s(4558) =< s(4549) s(4554) =< s(4558)*(1/3)+s(4552) s(4555) =< s(4558)*(1/5)+s(4551) s(4556) =< s(4558)*(1/5)+s(4551) s(4554) =< s(4558)*(1/5)+s(4551) s(4559) =< s(4548) s(4680) =< aux(227) s(4681) =< aux(227) s(4681) =< aux(206) s(4680) =< aux(205) s(2208) =< aux(229)*(6/5) s(4685) =< aux(229) s(4686) =< s(2208) s(4687) =< s(2208) s(4685) =< s(2208) s(4687) =< aux(206) s(4685) =< aux(206) s(4685) =< s(2129)*(1/3)+aux(229) s(4686) =< s(2129)*(1/5)+s(2208) s(4687) =< s(2129)*(1/5)+s(2208) s(4685) =< s(2129)*(1/5)+s(2208) s(4695) =< aux(227) s(4696) =< aux(231) s(4697) =< aux(231) s(4695) =< aux(231) s(4697) =< aux(205) s(4695) =< aux(205) s(4695) =< s(2129)*(1/3)+aux(227) s(4696) =< s(2129)*(1/5)+aux(231) s(4697) =< s(2129)*(1/5)+aux(231) s(4695) =< s(2129)*(1/5)+aux(231) s(4698) =< aux(209) s(4699) =< aux(209) s(4698) =< aux(227) s(4699) =< aux(227) s(4698) =< aux(231) s(4699) =< aux(231) s(4701) =< s(4699)*aux(227) s(4702) =< s(4698)*2 s(4703) =< s(4699)*s(2152) s(4704) =< s(4703)*(4/5) s(4705) =< s(4703)*(2/3) s(4706) =< s(4703) s(4707) =< s(4705) s(4708) =< s(4704) s(4709) =< s(4704) s(4707) =< s(4704) s(4709) =< s(4698) s(4707) =< s(4698) s(4710) =< s(4698) s(4711) =< s(4702) s(4707) =< s(4711)*(1/3)+s(4705) s(4708) =< s(4711)*(1/5)+s(4704) s(4709) =< s(4711)*(1/5)+s(4704) s(4707) =< s(4711)*(1/5)+s(4704) s(4712) =< s(4701) s(4713) =< aux(227) s(4713) =< s(4667) s(2193) =< aux(237)*(6/5) s(4715) =< s(4667) s(4716) =< aux(237) s(4717) =< s(2193) s(4718) =< s(2193) s(4716) =< s(2193) s(4718) =< aux(206) s(4716) =< aux(206) s(4716) =< s(2129)*(1/3)+aux(237) s(4717) =< s(2129)*(1/5)+s(2193) s(4718) =< s(2129)*(1/5)+s(2193) s(4716) =< s(2129)*(1/5)+s(2193) s(4719) =< aux(234) s(4720) =< aux(238) s(4721) =< aux(238) s(4719) =< aux(238) s(4721) =< aux(205) s(4719) =< aux(205) s(4719) =< s(2129)*(1/3)+aux(234) s(4720) =< s(2129)*(1/5)+aux(238) s(4721) =< s(2129)*(1/5)+aux(238) s(4719) =< s(2129)*(1/5)+aux(238) s(2189) =< aux(228) s(2189) =< aux(207) s(2192) =< aux(205)*(1/2) s(2195) =< aux(237) s(2196) =< s(2193) s(2197) =< s(2193) s(2195) =< s(2193) s(2197) =< aux(205) s(2195) =< aux(205) s(2198) =< aux(205) s(2198) =< s(2192) s(2195) =< s(2128)*(1/3)+aux(237) s(2196) =< s(2128)*(1/5)+s(2193) s(2197) =< s(2128)*(1/5)+s(2193) s(2195) =< s(2128)*(1/5)+s(2193) s(2201) =< aux(238) s(2201) =< s(2128)*(1/5)+aux(238) s(2207) =< aux(228)*(1/2) s(2209) =< aux(229) s(2210) =< s(2208) s(2211) =< s(2208) s(2209) =< s(2208) s(2211) =< aux(228) s(2209) =< aux(228) s(2212) =< aux(228) s(2212) =< s(2207) s(2209) =< s(2136)*(1/3)+aux(229) s(2210) =< s(2136)*(1/5)+s(2208) s(2211) =< s(2136)*(1/5)+s(2208) s(2209) =< s(2136)*(1/5)+s(2208) s(2213) =< aux(227) s(2214) =< aux(231) s(2215) =< aux(231) s(2213) =< aux(231) s(2215) =< aux(227) s(2213) =< s(2136)*(1/3)+aux(227) s(2214) =< s(2136)*(1/5)+aux(231) s(2215) =< s(2136)*(1/5)+aux(231) s(2213) =< s(2136)*(1/5)+aux(231) s(2216) =< aux(227)+1 s(2217) =< aux(227) s(2218) =< aux(234) s(2219) =< aux(227)+3 s(2221) =< aux(227)*(1/2) s(2222) =< aux(227)*2 s(2223) =< s(2112)*aux(234) s(2224) =< s(2112)*s(2216) s(2225) =< s(2112)*s(2217) s(2226) =< s(2112)*s(2218) s(2227) =< s(2112)*s(2219) s(2228) =< s(2223)*(6/5) s(2229) =< s(2112)*s(2152) s(2230) =< s(2224)*(1/2) s(2231) =< s(2226)*(6/5) s(2232) =< s(2224)*(2/5) s(2233) =< s(2224)*(1/3) s(2234) =< s(2227)*(1/3) s(2235) =< s(2224)*2 s(2236) =< s(2225) s(2237) =< s(2222) s(2238) =< s(2225) s(2238) =< s(2224) s(2239) =< s(2224) s(2240) =< s(2224) s(2240) =< s(2222) s(2239) =< aux(227) s(2241) =< s(2222)*(1/2) s(2242) =< s(2227)*(6/5) s(2243) =< s(2224) s(2244) =< s(2227) s(2245) =< s(2242) s(2246) =< s(2242) s(2244) =< s(2242) s(2246) =< s(2222) s(2244) =< s(2222) s(2247) =< s(2222) s(2247) =< s(2241) s(2244) =< s(2237)*(1/3)+s(2227) s(2245) =< s(2237)*(1/5)+s(2242) s(2246) =< s(2237)*(1/5)+s(2242) s(2244) =< s(2237)*(1/5)+s(2242) s(2248) =< aux(227) s(2248) =< s(2222) s(2249) =< aux(227)*(6/5) s(2250) =< s(2221) s(2251) =< aux(227) s(2252) =< s(2249) s(2253) =< s(2249) s(2251) =< s(2249) s(2253) =< s(2222) s(2251) =< s(2222) s(2251) =< s(2237)*(1/3)+aux(227) s(2252) =< s(2237)*(1/5)+s(2249) s(2253) =< s(2237)*(1/5)+s(2249) s(2251) =< s(2237)*(1/5)+s(2249) s(2254) =< s(2224) s(2255) =< s(2235) s(2256) =< s(2235) s(2254) =< s(2235) s(2256) =< aux(227) s(2254) =< aux(227) s(2254) =< s(2237)*(1/3)+s(2224) s(2255) =< s(2237)*(1/5)+s(2235) s(2256) =< s(2237)*(1/5)+s(2235) s(2254) =< s(2237)*(1/5)+s(2235) s(2257) =< s(2225) s(2258) =< s(2225) s(2257) =< s(2235) s(2258) =< s(2235) s(2259) =< s(2258)*aux(227) s(2260) =< s(2257)*2 s(2261) =< s(2258)*s(2152) s(2262) =< s(2261)*(4/5) s(2263) =< s(2261)*(2/3) s(2264) =< s(2261) s(2265) =< s(2263) s(2266) =< s(2262) s(2267) =< s(2262) s(2265) =< s(2262) s(2267) =< s(2257) s(2265) =< s(2257) s(2268) =< s(2257) s(2269) =< s(2260) s(2265) =< s(2269)*(1/3)+s(2263) s(2266) =< s(2269)*(1/5)+s(2262) s(2267) =< s(2269)*(1/5)+s(2262) s(2265) =< s(2269)*(1/5)+s(2262) s(2270) =< s(2259) s(2271) =< s(2225) s(2271) =< s(2224) s(2271) =< s(2230) s(2272) =< s(2234)*(6/5) s(2273) =< s(2230) s(2274) =< s(2234) s(2275) =< s(2272) s(2276) =< s(2272) s(2274) =< s(2272) s(2276) =< s(2222) s(2274) =< s(2222) s(2274) =< s(2237)*(1/3)+s(2234) s(2275) =< s(2237)*(1/5)+s(2272) s(2276) =< s(2237)*(1/5)+s(2272) s(2274) =< s(2237)*(1/5)+s(2272) s(2277) =< s(2233) s(2278) =< s(2232) s(2279) =< s(2232) s(2277) =< s(2232) s(2279) =< aux(227) s(2277) =< aux(227) s(2277) =< s(2237)*(1/3)+s(2233) s(2278) =< s(2237)*(1/5)+s(2232) s(2279) =< s(2237)*(1/5)+s(2232) s(2277) =< s(2237)*(1/5)+s(2232) s(2280) =< s(2226) s(2281) =< s(2231) s(2282) =< s(2231) s(2280) =< s(2231) s(2282) =< s(2225) s(2280) =< s(2225) s(2283) =< s(2225) s(2283) =< s(2230) s(2280) =< s(2243)*(1/3)+s(2226) s(2281) =< s(2243)*(1/5)+s(2231) s(2282) =< s(2243)*(1/5)+s(2231) s(2280) =< s(2243)*(1/5)+s(2231) s(2284) =< s(2225) s(2285) =< s(2225) s(2284) =< aux(227) s(2285) =< aux(227) s(2286) =< s(2285)*aux(227) s(2287) =< s(2284)*2 s(2288) =< s(2285)*s(2152) s(2289) =< s(2288)*(4/5) s(2290) =< s(2288)*(2/3) s(2291) =< s(2288) s(2292) =< s(2290) s(2293) =< s(2289) s(2294) =< s(2289) s(2292) =< s(2289) s(2294) =< s(2284) s(2292) =< s(2284) s(2295) =< s(2284) s(2296) =< s(2287) s(2292) =< s(2296)*(1/3)+s(2290) s(2293) =< s(2296)*(1/5)+s(2289) s(2294) =< s(2296)*(1/5)+s(2289) s(2292) =< s(2296)*(1/5)+s(2289) s(2297) =< s(2286) s(2298) =< s(2217)*(1/2)+1/2 s(2299) =< s(2258)*s(2217) s(2300) =< s(2258)*s(2298) s(2301) =< s(2300)*(4/5) s(2302) =< s(2300)*(2/3) s(2303) =< s(2300) s(2304) =< s(2302) s(2305) =< s(2301) s(2306) =< s(2301) s(2304) =< s(2301) s(2306) =< s(2257) s(2304) =< s(2257) s(2304) =< s(2269)*(1/3)+s(2302) s(2305) =< s(2269)*(1/5)+s(2301) s(2306) =< s(2269)*(1/5)+s(2301) s(2304) =< s(2269)*(1/5)+s(2301) s(2307) =< s(2299) s(2308) =< s(2229) s(2309) =< s(2223) s(2310) =< s(2228) s(2311) =< s(2228) s(2309) =< s(2228) s(2311) =< s(2225) s(2309) =< s(2225) s(2309) =< s(2243)*(1/3)+s(2223) s(2310) =< s(2243)*(1/5)+s(2228) s(2311) =< s(2243)*(1/5)+s(2228) s(2309) =< s(2243)*(1/5)+s(2228) s(2312) =< aux(229) s(2313) =< aux(227) s(2314) =< aux(227) s(2313) =< aux(229) s(2314) =< aux(229) s(2315) =< s(2313)*(1/2) s(2316) =< s(2313)*2 s(2317) =< s(2314)*aux(234) s(2318) =< s(2314)*s(2216) s(2319) =< s(2314)*s(2217) s(2320) =< s(2314)*s(2218) s(2321) =< s(2314)*s(2219) s(2322) =< s(2317)*(6/5) s(2323) =< s(2314)*s(2152) s(2324) =< s(2318)*(1/2) s(2325) =< s(2320)*(6/5) s(2326) =< s(2318)*(2/5) s(2327) =< s(2318)*(1/3) s(2328) =< s(2321)*(1/3) s(2329) =< s(2318)*2 s(2330) =< s(2319) s(2331) =< s(2313) s(2332) =< s(2316) s(2333) =< s(2319) s(2333) =< s(2318) s(2334) =< s(2318) s(2335) =< s(2318) s(2335) =< s(2316) s(2334) =< s(2313) s(2336) =< s(2316)*(1/2) s(2337) =< s(2321)*(6/5) s(2338) =< s(2318) s(2339) =< s(2321) s(2340) =< s(2337) s(2341) =< s(2337) s(2339) =< s(2337) s(2341) =< s(2316) s(2339) =< s(2316) s(2342) =< s(2316) s(2342) =< s(2336) s(2339) =< s(2332)*(1/3)+s(2321) s(2340) =< s(2332)*(1/5)+s(2337) s(2341) =< s(2332)*(1/5)+s(2337) s(2339) =< s(2332)*(1/5)+s(2337) s(2343) =< s(2313) s(2343) =< s(2316) s(2344) =< s(2313)*(6/5) s(2345) =< s(2315) s(2346) =< s(2313) s(2347) =< s(2344) s(2348) =< s(2344) s(2346) =< s(2344) s(2348) =< s(2316) s(2346) =< s(2316) s(2346) =< s(2332)*(1/3)+s(2313) s(2347) =< s(2332)*(1/5)+s(2344) s(2348) =< s(2332)*(1/5)+s(2344) s(2346) =< s(2332)*(1/5)+s(2344) s(2349) =< s(2318) s(2350) =< s(2329) s(2351) =< s(2329) s(2349) =< s(2329) s(2351) =< s(2313) s(2349) =< s(2313) s(2349) =< s(2332)*(1/3)+s(2318) s(2350) =< s(2332)*(1/5)+s(2329) s(2351) =< s(2332)*(1/5)+s(2329) s(2349) =< s(2332)*(1/5)+s(2329) s(2352) =< s(2319) s(2353) =< s(2319) s(2352) =< s(2329) s(2353) =< s(2329) s(2354) =< s(2353)*aux(227) s(2355) =< s(2352)*2 s(2356) =< s(2353)*s(2152) s(2357) =< s(2356)*(4/5) s(2358) =< s(2356)*(2/3) s(2359) =< s(2356) s(2360) =< s(2358) s(2361) =< s(2357) s(2362) =< s(2357) s(2360) =< s(2357) s(2362) =< s(2352) s(2360) =< s(2352) s(2363) =< s(2352) s(2364) =< s(2355) s(2360) =< s(2364)*(1/3)+s(2358) s(2361) =< s(2364)*(1/5)+s(2357) s(2362) =< s(2364)*(1/5)+s(2357) s(2360) =< s(2364)*(1/5)+s(2357) s(2365) =< s(2354) s(2366) =< s(2319) s(2366) =< s(2318) s(2366) =< s(2324) s(2367) =< s(2328)*(6/5) s(2368) =< s(2324) s(2369) =< s(2328) s(2370) =< s(2367) s(2371) =< s(2367) s(2369) =< s(2367) s(2371) =< s(2316) s(2369) =< s(2316) s(2369) =< s(2332)*(1/3)+s(2328) s(2370) =< s(2332)*(1/5)+s(2367) s(2371) =< s(2332)*(1/5)+s(2367) s(2369) =< s(2332)*(1/5)+s(2367) s(2372) =< s(2327) s(2373) =< s(2326) s(2374) =< s(2326) s(2372) =< s(2326) s(2374) =< s(2313) s(2372) =< s(2313) s(2372) =< s(2332)*(1/3)+s(2327) s(2373) =< s(2332)*(1/5)+s(2326) s(2374) =< s(2332)*(1/5)+s(2326) s(2372) =< s(2332)*(1/5)+s(2326) s(2375) =< s(2320) s(2376) =< s(2325) s(2377) =< s(2325) s(2375) =< s(2325) s(2377) =< s(2319) s(2375) =< s(2319) s(2378) =< s(2319) s(2378) =< s(2324) s(2375) =< s(2338)*(1/3)+s(2320) s(2376) =< s(2338)*(1/5)+s(2325) s(2377) =< s(2338)*(1/5)+s(2325) s(2375) =< s(2338)*(1/5)+s(2325) s(2379) =< s(2319) s(2380) =< s(2319) s(2379) =< s(2313) s(2380) =< s(2313) s(2381) =< s(2380)*aux(227) s(2382) =< s(2379)*2 s(2383) =< s(2380)*s(2152) s(2384) =< s(2383)*(4/5) s(2385) =< s(2383)*(2/3) s(2386) =< s(2383) s(2387) =< s(2385) s(2388) =< s(2384) s(2389) =< s(2384) s(2387) =< s(2384) s(2389) =< s(2379) s(2387) =< s(2379) s(2390) =< s(2379) s(2391) =< s(2382) s(2387) =< s(2391)*(1/3)+s(2385) s(2388) =< s(2391)*(1/5)+s(2384) s(2389) =< s(2391)*(1/5)+s(2384) s(2387) =< s(2391)*(1/5)+s(2384) s(2392) =< s(2381) s(2393) =< s(2353)*s(2217) s(2394) =< s(2353)*s(2298) s(2395) =< s(2394)*(4/5) s(2396) =< s(2394)*(2/3) s(2397) =< s(2394) s(2398) =< s(2396) s(2399) =< s(2395) s(2400) =< s(2395) s(2398) =< s(2395) s(2400) =< s(2352) s(2398) =< s(2352) s(2398) =< s(2364)*(1/3)+s(2396) s(2399) =< s(2364)*(1/5)+s(2395) s(2400) =< s(2364)*(1/5)+s(2395) s(2398) =< s(2364)*(1/5)+s(2395) s(2401) =< s(2393) s(2402) =< s(2323) s(2403) =< s(2317) s(2404) =< s(2322) s(2405) =< s(2322) s(2403) =< s(2322) s(2405) =< s(2319) s(2403) =< s(2319) s(2403) =< s(2338)*(1/3)+s(2317) s(2404) =< s(2338)*(1/5)+s(2322) s(2405) =< s(2338)*(1/5)+s(2322) s(2403) =< s(2338)*(1/5)+s(2322) s(3289) =< aux(205) s(3232) =< aux(205) s(3232) =< aux(210) s(3289) =< aux(220) s(3293) =< aux(224)*(6/5) s(3295) =< aux(224) s(3296) =< s(3293) s(3297) =< s(3293) s(3295) =< s(3293) s(3297) =< aux(210) s(3295) =< aux(210) s(3295) =< s(2506)*(1/3)+aux(224) s(3296) =< s(2506)*(1/5)+s(3293) s(3297) =< s(2506)*(1/5)+s(3293) s(3295) =< s(2506)*(1/5)+s(3293) s(3300) =< aux(221) s(3301) =< aux(225) s(3302) =< aux(225) s(3300) =< aux(225) s(3302) =< aux(209) s(3300) =< aux(209) s(3300) =< s(2506)*(1/3)+aux(221) s(3301) =< s(2506)*(1/5)+aux(225) s(3302) =< s(2506)*(1/5)+aux(225) s(3300) =< s(2506)*(1/5)+aux(225) s(3308) =< aux(211)*(6/5) s(3309) =< aux(211) s(3310) =< s(3308) s(3311) =< s(3308) s(3309) =< s(3308) s(3311) =< aux(210) s(3309) =< aux(210) s(3309) =< s(2506)*(1/3)+aux(211) s(3310) =< s(2506)*(1/5)+s(3308) s(3311) =< s(2506)*(1/5)+s(3308) s(3309) =< s(2506)*(1/5)+s(3308) s(3313) =< aux(209) s(3314) =< aux(217) s(3315) =< aux(217) s(3313) =< aux(217) s(3315) =< aux(209) s(3313) =< s(2506)*(1/3)+aux(209) s(3314) =< s(2506)*(1/5)+aux(217) s(3315) =< s(2506)*(1/5)+aux(217) s(3313) =< s(2506)*(1/5)+aux(217) s(3316) =< aux(209)+1 s(3317) =< aux(209) s(3318) =< aux(221) s(3319) =< aux(209)+3 s(3321) =< aux(209)*(1/2) s(3322) =< aux(209)*2 s(3323) =< s(2514)*aux(221) s(3324) =< s(2514)*s(3316) s(3325) =< s(2514)*s(3317) s(3326) =< s(2514)*s(3318) s(3327) =< s(2514)*s(3319) s(3328) =< s(3323)*(6/5) s(3329) =< s(2514)*s(3252) s(3330) =< s(3324)*(1/2) s(3331) =< s(3326)*(6/5) s(3332) =< s(3324)*(2/5) s(3333) =< s(3324)*(1/3) s(3334) =< s(3327)*(1/3) s(3335) =< s(3324)*2 s(3336) =< s(3325) s(3337) =< s(3322) s(3338) =< s(3325) s(3338) =< s(3324) s(3339) =< s(3324) s(3340) =< s(3324) s(3340) =< s(3322) s(3339) =< aux(209) s(3341) =< s(3322)*(1/2) s(3342) =< s(3327)*(6/5) s(3343) =< s(3324) s(3344) =< s(3327) s(3345) =< s(3342) s(3346) =< s(3342) s(3344) =< s(3342) s(3346) =< s(3322) s(3344) =< s(3322) s(3347) =< s(3322) s(3347) =< s(3341) s(3344) =< s(3337)*(1/3)+s(3327) s(3345) =< s(3337)*(1/5)+s(3342) s(3346) =< s(3337)*(1/5)+s(3342) s(3344) =< s(3337)*(1/5)+s(3342) s(3348) =< aux(209) s(3348) =< s(3322) s(3349) =< aux(209)*(6/5) s(3350) =< s(3321) s(3351) =< aux(209) s(3352) =< s(3349) s(3353) =< s(3349) s(3351) =< s(3349) s(3353) =< s(3322) s(3351) =< s(3322) s(3351) =< s(3337)*(1/3)+aux(209) s(3352) =< s(3337)*(1/5)+s(3349) s(3353) =< s(3337)*(1/5)+s(3349) s(3351) =< s(3337)*(1/5)+s(3349) s(3354) =< s(3324) s(3355) =< s(3335) s(3356) =< s(3335) s(3354) =< s(3335) s(3356) =< aux(209) s(3354) =< aux(209) s(3354) =< s(3337)*(1/3)+s(3324) s(3355) =< s(3337)*(1/5)+s(3335) s(3356) =< s(3337)*(1/5)+s(3335) s(3354) =< s(3337)*(1/5)+s(3335) s(3357) =< s(3325) s(3358) =< s(3325) s(3357) =< s(3335) s(3358) =< s(3335) s(3359) =< s(3358)*aux(209) s(3360) =< s(3357)*2 s(3361) =< s(3358)*s(3252) s(3362) =< s(3361)*(4/5) s(3363) =< s(3361)*(2/3) s(3364) =< s(3361) s(3365) =< s(3363) s(3366) =< s(3362) s(3367) =< s(3362) s(3365) =< s(3362) s(3367) =< s(3357) s(3365) =< s(3357) s(3368) =< s(3357) s(3369) =< s(3360) s(3365) =< s(3369)*(1/3)+s(3363) s(3366) =< s(3369)*(1/5)+s(3362) s(3367) =< s(3369)*(1/5)+s(3362) s(3365) =< s(3369)*(1/5)+s(3362) s(3370) =< s(3359) s(3371) =< s(3325) s(3371) =< s(3324) s(3371) =< s(3330) s(3372) =< s(3334)*(6/5) s(3373) =< s(3330) s(3374) =< s(3334) s(3375) =< s(3372) s(3376) =< s(3372) s(3374) =< s(3372) s(3376) =< s(3322) s(3374) =< s(3322) s(3374) =< s(3337)*(1/3)+s(3334) s(3375) =< s(3337)*(1/5)+s(3372) s(3376) =< s(3337)*(1/5)+s(3372) s(3374) =< s(3337)*(1/5)+s(3372) s(3377) =< s(3333) s(3378) =< s(3332) s(3379) =< s(3332) s(3377) =< s(3332) s(3379) =< aux(209) s(3377) =< aux(209) s(3377) =< s(3337)*(1/3)+s(3333) s(3378) =< s(3337)*(1/5)+s(3332) s(3379) =< s(3337)*(1/5)+s(3332) s(3377) =< s(3337)*(1/5)+s(3332) s(3380) =< s(3326) s(3381) =< s(3331) s(3382) =< s(3331) s(3380) =< s(3331) s(3382) =< s(3325) s(3380) =< s(3325) s(3383) =< s(3325) s(3383) =< s(3330) s(3380) =< s(3343)*(1/3)+s(3326) s(3381) =< s(3343)*(1/5)+s(3331) s(3382) =< s(3343)*(1/5)+s(3331) s(3380) =< s(3343)*(1/5)+s(3331) s(3384) =< s(3325) s(3385) =< s(3325) s(3384) =< aux(209) s(3385) =< aux(209) s(3386) =< s(3385)*aux(209) s(3387) =< s(3384)*2 s(3388) =< s(3385)*s(3252) s(3389) =< s(3388)*(4/5) s(3390) =< s(3388)*(2/3) s(3391) =< s(3388) s(3392) =< s(3390) s(3393) =< s(3389) s(3394) =< s(3389) s(3392) =< s(3389) s(3394) =< s(3384) s(3392) =< s(3384) s(3395) =< s(3384) s(3396) =< s(3387) s(3392) =< s(3396)*(1/3)+s(3390) s(3393) =< s(3396)*(1/5)+s(3389) s(3394) =< s(3396)*(1/5)+s(3389) s(3392) =< s(3396)*(1/5)+s(3389) s(3397) =< s(3386) s(3398) =< s(3317)*(1/2)+1/2 s(3399) =< s(3358)*s(3317) s(3400) =< s(3358)*s(3398) s(3401) =< s(3400)*(4/5) s(3402) =< s(3400)*(2/3) s(3403) =< s(3400) s(3404) =< s(3402) s(3405) =< s(3401) s(3406) =< s(3401) s(3404) =< s(3401) s(3406) =< s(3357) s(3404) =< s(3357) s(3404) =< s(3369)*(1/3)+s(3402) s(3405) =< s(3369)*(1/5)+s(3401) s(3406) =< s(3369)*(1/5)+s(3401) s(3404) =< s(3369)*(1/5)+s(3401) s(3407) =< s(3399) s(3408) =< s(3329) s(3409) =< s(3323) s(3410) =< s(3328) s(3411) =< s(3328) s(3409) =< s(3328) s(3411) =< s(3325) s(3409) =< s(3325) s(3409) =< s(3343)*(1/3)+s(3323) s(3410) =< s(3343)*(1/5)+s(3328) s(3411) =< s(3343)*(1/5)+s(3328) s(3409) =< s(3343)*(1/5)+s(3328) s(3412) =< aux(211) s(3413) =< aux(209) s(3414) =< aux(209) s(3413) =< aux(211) s(3414) =< aux(211) s(3415) =< s(3413)*(1/2) s(3416) =< s(3413)*2 s(3417) =< s(3414)*aux(221) s(3418) =< s(3414)*s(3316) s(3419) =< s(3414)*s(3317) s(3420) =< s(3414)*s(3318) s(3421) =< s(3414)*s(3319) s(3422) =< s(3417)*(6/5) s(3423) =< s(3414)*s(3252) s(3424) =< s(3418)*(1/2) s(3425) =< s(3420)*(6/5) s(3426) =< s(3418)*(2/5) s(3427) =< s(3418)*(1/3) s(3428) =< s(3421)*(1/3) s(3429) =< s(3418)*2 s(3430) =< s(3419) s(3431) =< s(3413) s(3432) =< s(3416) s(3433) =< s(3419) s(3433) =< s(3418) s(3434) =< s(3418) s(3435) =< s(3418) s(3435) =< s(3416) s(3434) =< s(3413) s(3436) =< s(3416)*(1/2) s(3437) =< s(3421)*(6/5) s(3438) =< s(3418) s(3439) =< s(3421) s(3440) =< s(3437) s(3441) =< s(3437) s(3439) =< s(3437) s(3441) =< s(3416) s(3439) =< s(3416) s(3442) =< s(3416) s(3442) =< s(3436) s(3439) =< s(3432)*(1/3)+s(3421) s(3440) =< s(3432)*(1/5)+s(3437) s(3441) =< s(3432)*(1/5)+s(3437) s(3439) =< s(3432)*(1/5)+s(3437) s(3443) =< s(3413) s(3443) =< s(3416) s(3444) =< s(3413)*(6/5) s(3445) =< s(3415) s(3446) =< s(3413) s(3447) =< s(3444) s(3448) =< s(3444) s(3446) =< s(3444) s(3448) =< s(3416) s(3446) =< s(3416) s(3446) =< s(3432)*(1/3)+s(3413) s(3447) =< s(3432)*(1/5)+s(3444) s(3448) =< s(3432)*(1/5)+s(3444) s(3446) =< s(3432)*(1/5)+s(3444) s(3449) =< s(3418) s(3450) =< s(3429) s(3451) =< s(3429) s(3449) =< s(3429) s(3451) =< s(3413) s(3449) =< s(3413) s(3449) =< s(3432)*(1/3)+s(3418) s(3450) =< s(3432)*(1/5)+s(3429) s(3451) =< s(3432)*(1/5)+s(3429) s(3449) =< s(3432)*(1/5)+s(3429) s(3452) =< s(3419) s(3453) =< s(3419) s(3452) =< s(3429) s(3453) =< s(3429) s(3454) =< s(3453)*aux(209) s(3455) =< s(3452)*2 s(3456) =< s(3453)*s(3252) s(3457) =< s(3456)*(4/5) s(3458) =< s(3456)*(2/3) s(3459) =< s(3456) s(3460) =< s(3458) s(3461) =< s(3457) s(3462) =< s(3457) s(3460) =< s(3457) s(3462) =< s(3452) s(3460) =< s(3452) s(3463) =< s(3452) s(3464) =< s(3455) s(3460) =< s(3464)*(1/3)+s(3458) s(3461) =< s(3464)*(1/5)+s(3457) s(3462) =< s(3464)*(1/5)+s(3457) s(3460) =< s(3464)*(1/5)+s(3457) s(3465) =< s(3454) s(3466) =< s(3419) s(3466) =< s(3418) s(3466) =< s(3424) s(3467) =< s(3428)*(6/5) s(3468) =< s(3424) s(3469) =< s(3428) s(3470) =< s(3467) s(3471) =< s(3467) s(3469) =< s(3467) s(3471) =< s(3416) s(3469) =< s(3416) s(3469) =< s(3432)*(1/3)+s(3428) s(3470) =< s(3432)*(1/5)+s(3467) s(3471) =< s(3432)*(1/5)+s(3467) s(3469) =< s(3432)*(1/5)+s(3467) s(3472) =< s(3427) s(3473) =< s(3426) s(3474) =< s(3426) s(3472) =< s(3426) s(3474) =< s(3413) s(3472) =< s(3413) s(3472) =< s(3432)*(1/3)+s(3427) s(3473) =< s(3432)*(1/5)+s(3426) s(3474) =< s(3432)*(1/5)+s(3426) s(3472) =< s(3432)*(1/5)+s(3426) s(3475) =< s(3420) s(3476) =< s(3425) s(3477) =< s(3425) s(3475) =< s(3425) s(3477) =< s(3419) s(3475) =< s(3419) s(3478) =< s(3419) s(3478) =< s(3424) s(3475) =< s(3438)*(1/3)+s(3420) s(3476) =< s(3438)*(1/5)+s(3425) s(3477) =< s(3438)*(1/5)+s(3425) s(3475) =< s(3438)*(1/5)+s(3425) s(3479) =< s(3419) s(3480) =< s(3419) s(3479) =< s(3413) s(3480) =< s(3413) s(3481) =< s(3480)*aux(209) s(3482) =< s(3479)*2 s(3483) =< s(3480)*s(3252) s(3484) =< s(3483)*(4/5) s(3485) =< s(3483)*(2/3) s(3486) =< s(3483) s(3487) =< s(3485) s(3488) =< s(3484) s(3489) =< s(3484) s(3487) =< s(3484) s(3489) =< s(3479) s(3487) =< s(3479) s(3490) =< s(3479) s(3491) =< s(3482) s(3487) =< s(3491)*(1/3)+s(3485) s(3488) =< s(3491)*(1/5)+s(3484) s(3489) =< s(3491)*(1/5)+s(3484) s(3487) =< s(3491)*(1/5)+s(3484) s(3492) =< s(3481) s(3493) =< s(3453)*s(3317) s(3494) =< s(3453)*s(3398) s(3495) =< s(3494)*(4/5) s(3496) =< s(3494)*(2/3) s(3497) =< s(3494) s(3498) =< s(3496) s(3499) =< s(3495) s(3500) =< s(3495) s(3498) =< s(3495) s(3500) =< s(3452) s(3498) =< s(3452) s(3498) =< s(3464)*(1/3)+s(3496) s(3499) =< s(3464)*(1/5)+s(3495) s(3500) =< s(3464)*(1/5)+s(3495) s(3498) =< s(3464)*(1/5)+s(3495) s(3501) =< s(3493) s(3502) =< s(3423) s(3503) =< s(3417) s(3504) =< s(3422) s(3505) =< s(3422) s(3503) =< s(3422) s(3505) =< s(3419) s(3503) =< s(3419) s(3503) =< s(3438)*(1/3)+s(3417) s(3504) =< s(3438)*(1/5)+s(3422) s(3505) =< s(3438)*(1/5)+s(3422) s(3503) =< s(3438)*(1/5)+s(3422) s(3233) =< aux(210) s(3233) =< aux(206) s(3235) =< aux(212)*(6/5) s(3237) =< aux(212) s(3238) =< s(3235) s(3239) =< s(3235) s(3237) =< s(3235) s(3239) =< aux(206) s(3237) =< aux(206) s(3237) =< s(2129)*(1/3)+aux(212) s(3238) =< s(2129)*(1/5)+s(3235) s(3239) =< s(2129)*(1/5)+s(3235) s(3237) =< s(2129)*(1/5)+s(3235) s(3247) =< aux(210) s(3248) =< aux(218) s(3249) =< aux(218) s(3247) =< aux(218) s(3249) =< aux(205) s(3247) =< aux(205) s(3247) =< s(2129)*(1/3)+aux(210) s(3248) =< s(2129)*(1/5)+aux(218) s(3249) =< s(2129)*(1/5)+aux(218) s(3247) =< s(2129)*(1/5)+aux(218) s(3250) =< aux(227) s(3251) =< aux(227) s(3250) =< aux(209) s(3251) =< aux(209) s(3250) =< aux(218) s(3251) =< aux(218) s(3253) =< s(3251)*aux(209) s(3254) =< s(3250)*2 s(3255) =< s(3251)*s(3252) s(3256) =< s(3255)*(4/5) s(3257) =< s(3255)*(2/3) s(3258) =< s(3255) s(3259) =< s(3257) s(3260) =< s(3256) s(3261) =< s(3256) s(3259) =< s(3256) s(3261) =< s(3250) s(3259) =< s(3250) s(3262) =< s(3250) s(3263) =< s(3254) s(3259) =< s(3263)*(1/3)+s(3257) s(3260) =< s(3263)*(1/5)+s(3256) s(3261) =< s(3263)*(1/5)+s(3256) s(3259) =< s(3263)*(1/5)+s(3256) s(3264) =< s(3253) s(3265) =< aux(209) s(3265) =< aux(210) s(3265) =< aux(220) s(3266) =< aux(222)*(6/5) s(3267) =< aux(220) s(3268) =< aux(222) s(3269) =< s(3266) s(3270) =< s(3266) s(3268) =< s(3266) s(3270) =< aux(206) s(3268) =< aux(206) s(3268) =< s(2129)*(1/3)+aux(222) s(3269) =< s(2129)*(1/5)+s(3266) s(3270) =< s(2129)*(1/5)+s(3266) s(3268) =< s(2129)*(1/5)+s(3266) s(3271) =< aux(223) s(3272) =< aux(226) s(3273) =< aux(226) s(3271) =< aux(226) s(3273) =< aux(205) s(3271) =< aux(205) s(3271) =< s(2129)*(1/3)+aux(223) s(3272) =< s(2129)*(1/5)+aux(226) s(3273) =< s(2129)*(1/5)+aux(226) s(3271) =< s(2129)*(1/5)+aux(226) s(2998) =< aux(205) s(2998) =< aux(207) s(3002) =< s(2988)*(6/5) s(3004) =< s(2988) s(3005) =< s(3002) s(3006) =< s(3002) s(3004) =< s(3002) s(3006) =< aux(205) s(3004) =< aux(205) s(3004) =< s(2128)*(1/3)+s(2988) s(3005) =< s(2128)*(1/5)+s(3002) s(3006) =< s(2128)*(1/5)+s(3002) s(3004) =< s(2128)*(1/5)+s(3002) s(3017) =< aux(206)*(6/5) s(3018) =< aux(206) s(3019) =< s(3017) s(3020) =< s(3017) s(3018) =< s(3017) s(3020) =< aux(205) s(3018) =< aux(205) s(3018) =< s(2128)*(1/3)+aux(206) s(3019) =< s(2128)*(1/5)+s(3017) s(3020) =< s(2128)*(1/5)+s(3017) s(3018) =< s(2128)*(1/5)+s(3017) s(2944) =< s(2926)*(6/5) s(2946) =< s(2926) s(2947) =< s(2944) s(2948) =< s(2944) s(2946) =< s(2944) s(2948) =< aux(206) s(2946) =< aux(206) s(2946) =< s(2129)*(1/3)+s(2926) s(2947) =< s(2129)*(1/5)+s(2944) s(2948) =< s(2129)*(1/5)+s(2944) s(2946) =< s(2129)*(1/5)+s(2944) s(2956) =< aux(205) s(2957) =< aux(206) s(2958) =< aux(206) s(2956) =< aux(206) s(2958) =< aux(205) s(2956) =< s(2129)*(1/3)+aux(205) s(2957) =< s(2129)*(1/5)+aux(206) s(2958) =< s(2129)*(1/5)+aux(206) s(2956) =< s(2129)*(1/5)+aux(206) s(2980) =< s(2930) s(2981) =< s(2931) s(2982) =< s(2931) s(2980) =< s(2931) s(2982) =< aux(205) s(2980) =< aux(205) s(2980) =< s(2129)*(1/3)+s(2930) s(2981) =< s(2129)*(1/5)+s(2931) s(2982) =< s(2129)*(1/5)+s(2931) s(2980) =< s(2129)*(1/5)+s(2931) with precondition: [V1=1,V>=0,V35>=0] * Chain [72]: 5*s(4745)+5*s(4746)+2 Such that:aux(240) =< V aux(241) =< V+1 s(4745) =< aux(240) s(4746) =< aux(241) with precondition: [V1=V,V1>=1] * Chain [71]: 0 with precondition: [V1=1,V=2] * Chain [70]: 1711/10 with precondition: [V1=1,V35=0,V>=1] * Chain [69]: 0 with precondition: [V1=2,V=1] * Chain [68]: 0 with precondition: [V1=2,V=2] * Chain [67]: 39*s(5057)+66*s(5058)+247*s(5059)+7*s(5060)+5*s(5061)+4*s(5062)+30*s(5065)+2*s(5066)+2*s(5067)+2*s(5068)+8*s(5069)+4*s(5070)+4*s(5072)+4*s(5073)+4*s(5074)+4*s(5075)+2*s(5076)+2*s(5077)+2*s(5078)+6*s(5080)+2*s(5087)+2*s(5088)+2*s(5089)+2*s(5090)+2*s(5091)+6*s(5092)+24*s(5093)+4*s(5094)+14*s(5096)+2*s(5097)+2*s(5098)+2*s(5099)+2*s(5100)+2*s(5101)+2*s(5102)+1*s(5118)+1*s(5124)+1*s(5125)+1*s(5126)+1*s(5127)+4*s(5130)+1*s(5138)+1*s(5139)+1*s(5140)+1*s(5141)+4*s(5142)+4*s(5143)+4*s(5144)+384*s(5165)+180*s(5166)+6*s(5167)+12*s(5168)+12*s(5169)+48*s(5172)+6*s(5173)+6*s(5174)+6*s(5175)+24*s(5176)+12*s(5177)+12*s(5179)+12*s(5180)+12*s(5181)+12*s(5182)+6*s(5183)+6*s(5184)+6*s(5185)+18*s(5187)+3*s(5193)+3*s(5194)+3*s(5195)+3*s(5196)+6*s(5197)+18*s(5198)+36*s(5199)+6*s(5200)+18*s(5202)+6*s(5203)+6*s(5204)+6*s(5205)+6*s(5206)+6*s(5207)+6*s(5208)+9*s(5209)+9*s(5210)+9*s(5211)+12*s(5212)+18*s(5214)+6*s(5220)+6*s(5221)+6*s(5222)+6*s(5223)+6*s(5224)+18*s(5225)+72*s(5226)+3*s(5232)+3*s(5233)+3*s(5234)+3*s(5235)+36*s(5236)+6*s(5237)+3*s(5238)+3*s(5239)+3*s(5240)+1*s(5241)+10*s(5243)+128*s(5259)+16*s(5260)+60*s(5261)+2*s(5262)+4*s(5263)+4*s(5264)+16*s(5267)+2*s(5268)+2*s(5269)+2*s(5270)+8*s(5271)+4*s(5272)+4*s(5274)+4*s(5275)+4*s(5276)+4*s(5277)+2*s(5278)+2*s(5279)+2*s(5280)+6*s(5282)+1*s(5288)+1*s(5289)+1*s(5290)+1*s(5291)+2*s(5292)+6*s(5293)+12*s(5294)+2*s(5295)+6*s(5297)+2*s(5298)+2*s(5299)+2*s(5300)+2*s(5301)+2*s(5302)+2*s(5303)+3*s(5304)+3*s(5305)+3*s(5306)+4*s(5307)+6*s(5309)+2*s(5315)+2*s(5316)+2*s(5317)+2*s(5318)+2*s(5319)+6*s(5320)+24*s(5321)+1*s(5326)+1*s(5327)+1*s(5328)+1*s(5329)+12*s(5330)+2*s(5331)+1*s(5332)+1*s(5333)+1*s(5334)+3*s(5402)+1*s(5409)+1*s(5410)+1*s(5411)+1*s(5412)+1*s(5413)+3*s(5414)+12*s(5415)+2*s(5431)+17*s(5433)+1*s(5437)+1*s(5438)+1*s(5439)+1*s(5440)+3*s(5441)+4*s(5442)+4*s(5443)+4*s(5444)+4*s(5445)+84*s(5446)+5*s(5447)+24*s(5448)+1*s(5451)+1*s(5452)+1*s(5453)+1*s(5454)+4*s(5455)+4*s(5456)+4*s(5457)+384*s(5478)+180*s(5479)+6*s(5480)+12*s(5481)+12*s(5482)+48*s(5485)+6*s(5486)+6*s(5487)+6*s(5488)+24*s(5489)+12*s(5490)+12*s(5492)+12*s(5493)+12*s(5494)+12*s(5495)+6*s(5496)+6*s(5497)+6*s(5498)+18*s(5500)+3*s(5506)+3*s(5507)+3*s(5508)+3*s(5509)+6*s(5510)+18*s(5511)+36*s(5512)+6*s(5513)+18*s(5515)+6*s(5516)+6*s(5517)+6*s(5518)+6*s(5519)+6*s(5520)+6*s(5521)+9*s(5522)+9*s(5523)+9*s(5524)+12*s(5525)+18*s(5527)+6*s(5533)+6*s(5534)+6*s(5535)+6*s(5536)+6*s(5537)+18*s(5538)+72*s(5539)+3*s(5545)+3*s(5546)+3*s(5547)+3*s(5548)+36*s(5549)+6*s(5550)+3*s(5551)+3*s(5552)+3*s(5553)+2*s(5554)+20*s(5556)+256*s(5572)+32*s(5573)+120*s(5574)+4*s(5575)+8*s(5576)+8*s(5577)+32*s(5580)+4*s(5581)+4*s(5582)+4*s(5583)+16*s(5584)+8*s(5585)+8*s(5587)+8*s(5588)+8*s(5589)+8*s(5590)+4*s(5591)+4*s(5592)+4*s(5593)+12*s(5595)+2*s(5601)+2*s(5602)+2*s(5603)+2*s(5604)+4*s(5605)+12*s(5606)+24*s(5607)+4*s(5608)+12*s(5610)+4*s(5611)+4*s(5612)+4*s(5613)+4*s(5614)+4*s(5615)+4*s(5616)+6*s(5617)+6*s(5618)+6*s(5619)+8*s(5620)+12*s(5622)+4*s(5628)+4*s(5629)+4*s(5630)+4*s(5631)+4*s(5632)+12*s(5633)+48*s(5634)+2*s(5639)+2*s(5640)+2*s(5641)+2*s(5642)+24*s(5643)+4*s(5644)+2*s(5645)+2*s(5646)+2*s(5647)+3*s(5657)+1*s(5664)+1*s(5665)+1*s(5666)+1*s(5667)+1*s(5668)+3*s(5669)+12*s(5670)+6*s(5680)+2*s(5687)+2*s(5688)+2*s(5689)+2*s(5690)+2*s(5691)+6*s(5692)+24*s(5693)+3*s(5730)+1*s(5737)+1*s(5738)+1*s(5739)+1*s(5740)+1*s(5741)+3*s(5742)+12*s(5743)+5 Such that:aux(252) =< V+1 s(5418) =< V+V35+1 aux(255) =< 2*V+2*V35 s(5114) =< V35+2 s(5106) =< 2*V35 s(5115) =< V35/3 s(5108) =< V35/3+2/3 s(5109) =< 2/5*V35 aux(262) =< 1 aux(263) =< 2 aux(264) =< 1/2 aux(265) =< V aux(266) =< V-V35 aux(267) =< V+V35 aux(268) =< V+V35+2 aux(269) =< V35 aux(270) =< V35+1 aux(271) =< V35+3 aux(272) =< 2*V35+2 aux(273) =< V35/2+1/2 aux(274) =< V35/3+1 aux(275) =< V35/3+1/3 aux(276) =< 2/5*V35+2/5 s(5065) =< aux(270) s(5057) =< aux(262) s(5058) =< aux(263) s(5059) =< aux(269) s(5060) =< aux(269) s(5060) =< aux(270) s(5061) =< aux(270) s(5062) =< aux(270) s(5062) =< aux(263) s(5061) =< aux(262) s(5063) =< aux(263)*(1/2) s(5064) =< aux(271)*(6/5) s(5066) =< aux(271) s(5067) =< s(5064) s(5068) =< s(5064) s(5066) =< s(5064) s(5068) =< aux(263) s(5066) =< aux(263) s(5069) =< aux(263) s(5069) =< s(5063) s(5066) =< s(5058)*(1/3)+aux(271) s(5067) =< s(5058)*(1/5)+s(5064) s(5068) =< s(5058)*(1/5)+s(5064) s(5066) =< s(5058)*(1/5)+s(5064) s(5070) =< aux(262) s(5070) =< aux(263) s(5071) =< aux(262)*(6/5) s(5072) =< aux(264) s(5073) =< aux(262) s(5074) =< s(5071) s(5075) =< s(5071) s(5073) =< s(5071) s(5075) =< aux(263) s(5073) =< aux(263) s(5073) =< s(5058)*(1/3)+aux(262) s(5074) =< s(5058)*(1/5)+s(5071) s(5075) =< s(5058)*(1/5)+s(5071) s(5073) =< s(5058)*(1/5)+s(5071) s(5076) =< aux(270) s(5077) =< aux(272) s(5078) =< aux(272) s(5076) =< aux(272) s(5078) =< aux(262) s(5076) =< aux(262) s(5076) =< s(5058)*(1/3)+aux(270) s(5077) =< s(5058)*(1/5)+aux(272) s(5078) =< s(5058)*(1/5)+aux(272) s(5076) =< s(5058)*(1/5)+aux(272) s(5079) =< aux(265) s(5080) =< aux(265) s(5079) =< aux(269) s(5080) =< aux(269) s(5079) =< aux(272) s(5080) =< aux(272) s(5081) =< aux(269)*(1/2)+1/2 s(5082) =< s(5080)*aux(269) s(5083) =< s(5079)*2 s(5084) =< s(5080)*s(5081) s(5085) =< s(5084)*(4/5) s(5086) =< s(5084)*(2/3) s(5087) =< s(5084) s(5088) =< s(5086) s(5089) =< s(5085) s(5090) =< s(5085) s(5088) =< s(5085) s(5090) =< s(5079) s(5088) =< s(5079) s(5091) =< s(5079) s(5092) =< s(5083) s(5088) =< s(5092)*(1/3)+s(5086) s(5089) =< s(5092)*(1/5)+s(5085) s(5090) =< s(5092)*(1/5)+s(5085) s(5088) =< s(5092)*(1/5)+s(5085) s(5093) =< s(5082) s(5094) =< aux(269) s(5094) =< aux(270) s(5094) =< aux(273) s(5095) =< aux(274)*(6/5) s(5096) =< aux(273) s(5097) =< aux(274) s(5098) =< s(5095) s(5099) =< s(5095) s(5097) =< s(5095) s(5099) =< aux(263) s(5097) =< aux(263) s(5097) =< s(5058)*(1/3)+aux(274) s(5098) =< s(5058)*(1/5)+s(5095) s(5099) =< s(5058)*(1/5)+s(5095) s(5097) =< s(5058)*(1/5)+s(5095) s(5100) =< aux(275) s(5101) =< aux(276) s(5102) =< aux(276) s(5100) =< aux(276) s(5102) =< aux(262) s(5100) =< aux(262) s(5100) =< s(5058)*(1/3)+aux(275) s(5101) =< s(5058)*(1/5)+aux(276) s(5102) =< s(5058)*(1/5)+aux(276) s(5100) =< s(5058)*(1/5)+aux(276) s(5431) =< aux(270) s(5431) =< aux(252) s(5433) =< aux(252) s(5434) =< aux(252)*(1/2) s(5435) =< aux(268)*(6/5) s(5437) =< aux(268) s(5438) =< s(5435) s(5439) =< s(5435) s(5437) =< s(5435) s(5439) =< aux(252) s(5437) =< aux(252) s(5440) =< aux(252) s(5440) =< s(5434) s(5437) =< s(5433)*(1/3)+aux(268) s(5438) =< s(5433)*(1/5)+s(5435) s(5439) =< s(5433)*(1/5)+s(5435) s(5437) =< s(5433)*(1/5)+s(5435) s(5441) =< aux(265) s(5442) =< aux(267) s(5443) =< aux(255) s(5444) =< aux(255) s(5442) =< aux(255) s(5444) =< aux(265) s(5442) =< aux(265) s(5445) =< aux(265) s(5445) =< aux(252) s(5442) =< s(5433)*(1/3)+aux(267) s(5443) =< s(5433)*(1/5)+aux(255) s(5444) =< s(5433)*(1/5)+aux(255) s(5442) =< s(5433)*(1/5)+aux(255) s(5446) =< aux(267) s(5447) =< aux(267) s(5447) =< s(5418) s(5448) =< s(5418) s(5449) =< s(5418)*(1/2) s(5451) =< aux(268) s(5452) =< s(5435) s(5453) =< s(5435) s(5451) =< s(5435) s(5453) =< s(5418) s(5451) =< s(5418) s(5454) =< s(5418) s(5454) =< s(5449) s(5451) =< s(5448)*(1/3)+aux(268) s(5452) =< s(5448)*(1/5)+s(5435) s(5453) =< s(5448)*(1/5)+s(5435) s(5451) =< s(5448)*(1/5)+s(5435) s(5455) =< aux(267) s(5456) =< aux(255) s(5457) =< aux(255) s(5455) =< aux(255) s(5457) =< aux(267) s(5455) =< s(5448)*(1/3)+aux(267) s(5456) =< s(5448)*(1/5)+aux(255) s(5457) =< s(5448)*(1/5)+aux(255) s(5455) =< s(5448)*(1/5)+aux(255) s(5458) =< aux(267)+1 s(5459) =< aux(267) s(5461) =< aux(267)+3 s(5462) =< aux(267)*(1/2)+1/2 s(5463) =< aux(267)*(1/2) s(5464) =< aux(267)*2 s(5465) =< s(5446)*aux(267) s(5466) =< s(5446)*s(5458) s(5467) =< s(5446)*s(5459) s(5469) =< s(5446)*s(5461) s(5470) =< s(5465)*(6/5) s(5471) =< s(5446)*s(5462) s(5472) =< s(5466)*(1/2) s(5473) =< s(5467)*(6/5) s(5474) =< s(5466)*(2/5) s(5475) =< s(5466)*(1/3) s(5476) =< s(5469)*(1/3) s(5477) =< s(5466)*2 s(5478) =< s(5467) s(5479) =< s(5464) s(5480) =< s(5467) s(5480) =< s(5466) s(5481) =< s(5466) s(5482) =< s(5466) s(5482) =< s(5464) s(5481) =< aux(267) s(5483) =< s(5464)*(1/2) s(5484) =< s(5469)*(6/5) s(5485) =< s(5466) s(5486) =< s(5469) s(5487) =< s(5484) s(5488) =< s(5484) s(5486) =< s(5484) s(5488) =< s(5464) s(5486) =< s(5464) s(5489) =< s(5464) s(5489) =< s(5483) s(5486) =< s(5479)*(1/3)+s(5469) s(5487) =< s(5479)*(1/5)+s(5484) s(5488) =< s(5479)*(1/5)+s(5484) s(5486) =< s(5479)*(1/5)+s(5484) s(5490) =< aux(267) s(5490) =< s(5464) s(5491) =< aux(267)*(6/5) s(5492) =< s(5463) s(5493) =< aux(267) s(5494) =< s(5491) s(5495) =< s(5491) s(5493) =< s(5491) s(5495) =< s(5464) s(5493) =< s(5464) s(5493) =< s(5479)*(1/3)+aux(267) s(5494) =< s(5479)*(1/5)+s(5491) s(5495) =< s(5479)*(1/5)+s(5491) s(5493) =< s(5479)*(1/5)+s(5491) s(5496) =< s(5466) s(5497) =< s(5477) s(5498) =< s(5477) s(5496) =< s(5477) s(5498) =< aux(267) s(5496) =< aux(267) s(5496) =< s(5479)*(1/3)+s(5466) s(5497) =< s(5479)*(1/5)+s(5477) s(5498) =< s(5479)*(1/5)+s(5477) s(5496) =< s(5479)*(1/5)+s(5477) s(5499) =< s(5467) s(5500) =< s(5467) s(5499) =< s(5477) s(5500) =< s(5477) s(5501) =< s(5500)*aux(267) s(5502) =< s(5499)*2 s(5503) =< s(5500)*s(5462) s(5504) =< s(5503)*(4/5) s(5505) =< s(5503)*(2/3) s(5506) =< s(5503) s(5507) =< s(5505) s(5508) =< s(5504) s(5509) =< s(5504) s(5507) =< s(5504) s(5509) =< s(5499) s(5507) =< s(5499) s(5510) =< s(5499) s(5511) =< s(5502) s(5507) =< s(5511)*(1/3)+s(5505) s(5508) =< s(5511)*(1/5)+s(5504) s(5509) =< s(5511)*(1/5)+s(5504) s(5507) =< s(5511)*(1/5)+s(5504) s(5512) =< s(5501) s(5513) =< s(5467) s(5513) =< s(5466) s(5513) =< s(5472) s(5514) =< s(5476)*(6/5) s(5515) =< s(5472) s(5516) =< s(5476) s(5517) =< s(5514) s(5518) =< s(5514) s(5516) =< s(5514) s(5518) =< s(5464) s(5516) =< s(5464) s(5516) =< s(5479)*(1/3)+s(5476) s(5517) =< s(5479)*(1/5)+s(5514) s(5518) =< s(5479)*(1/5)+s(5514) s(5516) =< s(5479)*(1/5)+s(5514) s(5519) =< s(5475) s(5520) =< s(5474) s(5521) =< s(5474) s(5519) =< s(5474) s(5521) =< aux(267) s(5519) =< aux(267) s(5519) =< s(5479)*(1/3)+s(5475) s(5520) =< s(5479)*(1/5)+s(5474) s(5521) =< s(5479)*(1/5)+s(5474) s(5519) =< s(5479)*(1/5)+s(5474) s(5522) =< s(5467) s(5523) =< s(5473) s(5524) =< s(5473) s(5522) =< s(5473) s(5524) =< s(5467) s(5525) =< s(5467) s(5525) =< s(5472) s(5522) =< s(5485)*(1/3)+s(5467) s(5523) =< s(5485)*(1/5)+s(5473) s(5524) =< s(5485)*(1/5)+s(5473) s(5522) =< s(5485)*(1/5)+s(5473) s(5526) =< s(5467) s(5527) =< s(5467) s(5526) =< aux(267) s(5527) =< aux(267) s(5528) =< s(5527)*aux(267) s(5529) =< s(5526)*2 s(5530) =< s(5527)*s(5462) s(5531) =< s(5530)*(4/5) s(5532) =< s(5530)*(2/3) s(5533) =< s(5530) s(5534) =< s(5532) s(5535) =< s(5531) s(5536) =< s(5531) s(5534) =< s(5531) s(5536) =< s(5526) s(5534) =< s(5526) s(5537) =< s(5526) s(5538) =< s(5529) s(5534) =< s(5538)*(1/3)+s(5532) s(5535) =< s(5538)*(1/5)+s(5531) s(5536) =< s(5538)*(1/5)+s(5531) s(5534) =< s(5538)*(1/5)+s(5531) s(5539) =< s(5528) s(5540) =< s(5459)*(1/2)+1/2 s(5541) =< s(5500)*s(5459) s(5542) =< s(5500)*s(5540) s(5543) =< s(5542)*(4/5) s(5544) =< s(5542)*(2/3) s(5545) =< s(5542) s(5546) =< s(5544) s(5547) =< s(5543) s(5548) =< s(5543) s(5546) =< s(5543) s(5548) =< s(5499) s(5546) =< s(5499) s(5546) =< s(5511)*(1/3)+s(5544) s(5547) =< s(5511)*(1/5)+s(5543) s(5548) =< s(5511)*(1/5)+s(5543) s(5546) =< s(5511)*(1/5)+s(5543) s(5549) =< s(5541) s(5550) =< s(5471) s(5551) =< s(5465) s(5552) =< s(5470) s(5553) =< s(5470) s(5551) =< s(5470) s(5553) =< s(5467) s(5551) =< s(5467) s(5551) =< s(5485)*(1/3)+s(5465) s(5552) =< s(5485)*(1/5)+s(5470) s(5553) =< s(5485)*(1/5)+s(5470) s(5551) =< s(5485)*(1/5)+s(5470) s(5554) =< aux(268) s(5555) =< aux(267) s(5556) =< aux(267) s(5555) =< aux(268) s(5556) =< aux(268) s(5557) =< s(5555)*(1/2) s(5558) =< s(5555)*2 s(5559) =< s(5556)*aux(267) s(5560) =< s(5556)*s(5458) s(5561) =< s(5556)*s(5459) s(5563) =< s(5556)*s(5461) s(5564) =< s(5559)*(6/5) s(5565) =< s(5556)*s(5462) s(5566) =< s(5560)*(1/2) s(5567) =< s(5561)*(6/5) s(5568) =< s(5560)*(2/5) s(5569) =< s(5560)*(1/3) s(5570) =< s(5563)*(1/3) s(5571) =< s(5560)*2 s(5572) =< s(5561) s(5573) =< s(5555) s(5574) =< s(5558) s(5575) =< s(5561) s(5575) =< s(5560) s(5576) =< s(5560) s(5577) =< s(5560) s(5577) =< s(5558) s(5576) =< s(5555) s(5578) =< s(5558)*(1/2) s(5579) =< s(5563)*(6/5) s(5580) =< s(5560) s(5581) =< s(5563) s(5582) =< s(5579) s(5583) =< s(5579) s(5581) =< s(5579) s(5583) =< s(5558) s(5581) =< s(5558) s(5584) =< s(5558) s(5584) =< s(5578) s(5581) =< s(5574)*(1/3)+s(5563) s(5582) =< s(5574)*(1/5)+s(5579) s(5583) =< s(5574)*(1/5)+s(5579) s(5581) =< s(5574)*(1/5)+s(5579) s(5585) =< s(5555) s(5585) =< s(5558) s(5586) =< s(5555)*(6/5) s(5587) =< s(5557) s(5588) =< s(5555) s(5589) =< s(5586) s(5590) =< s(5586) s(5588) =< s(5586) s(5590) =< s(5558) s(5588) =< s(5558) s(5588) =< s(5574)*(1/3)+s(5555) s(5589) =< s(5574)*(1/5)+s(5586) s(5590) =< s(5574)*(1/5)+s(5586) s(5588) =< s(5574)*(1/5)+s(5586) s(5591) =< s(5560) s(5592) =< s(5571) s(5593) =< s(5571) s(5591) =< s(5571) s(5593) =< s(5555) s(5591) =< s(5555) s(5591) =< s(5574)*(1/3)+s(5560) s(5592) =< s(5574)*(1/5)+s(5571) s(5593) =< s(5574)*(1/5)+s(5571) s(5591) =< s(5574)*(1/5)+s(5571) s(5594) =< s(5561) s(5595) =< s(5561) s(5594) =< s(5571) s(5595) =< s(5571) s(5596) =< s(5595)*aux(267) s(5597) =< s(5594)*2 s(5598) =< s(5595)*s(5462) s(5599) =< s(5598)*(4/5) s(5600) =< s(5598)*(2/3) s(5601) =< s(5598) s(5602) =< s(5600) s(5603) =< s(5599) s(5604) =< s(5599) s(5602) =< s(5599) s(5604) =< s(5594) s(5602) =< s(5594) s(5605) =< s(5594) s(5606) =< s(5597) s(5602) =< s(5606)*(1/3)+s(5600) s(5603) =< s(5606)*(1/5)+s(5599) s(5604) =< s(5606)*(1/5)+s(5599) s(5602) =< s(5606)*(1/5)+s(5599) s(5607) =< s(5596) s(5608) =< s(5561) s(5608) =< s(5560) s(5608) =< s(5566) s(5609) =< s(5570)*(6/5) s(5610) =< s(5566) s(5611) =< s(5570) s(5612) =< s(5609) s(5613) =< s(5609) s(5611) =< s(5609) s(5613) =< s(5558) s(5611) =< s(5558) s(5611) =< s(5574)*(1/3)+s(5570) s(5612) =< s(5574)*(1/5)+s(5609) s(5613) =< s(5574)*(1/5)+s(5609) s(5611) =< s(5574)*(1/5)+s(5609) s(5614) =< s(5569) s(5615) =< s(5568) s(5616) =< s(5568) s(5614) =< s(5568) s(5616) =< s(5555) s(5614) =< s(5555) s(5614) =< s(5574)*(1/3)+s(5569) s(5615) =< s(5574)*(1/5)+s(5568) s(5616) =< s(5574)*(1/5)+s(5568) s(5614) =< s(5574)*(1/5)+s(5568) s(5617) =< s(5561) s(5618) =< s(5567) s(5619) =< s(5567) s(5617) =< s(5567) s(5619) =< s(5561) s(5620) =< s(5561) s(5620) =< s(5566) s(5617) =< s(5580)*(1/3)+s(5561) s(5618) =< s(5580)*(1/5)+s(5567) s(5619) =< s(5580)*(1/5)+s(5567) s(5617) =< s(5580)*(1/5)+s(5567) s(5621) =< s(5561) s(5622) =< s(5561) s(5621) =< s(5555) s(5622) =< s(5555) s(5623) =< s(5622)*aux(267) s(5624) =< s(5621)*2 s(5625) =< s(5622)*s(5462) s(5626) =< s(5625)*(4/5) s(5627) =< s(5625)*(2/3) s(5628) =< s(5625) s(5629) =< s(5627) s(5630) =< s(5626) s(5631) =< s(5626) s(5629) =< s(5626) s(5631) =< s(5621) s(5629) =< s(5621) s(5632) =< s(5621) s(5633) =< s(5624) s(5629) =< s(5633)*(1/3)+s(5627) s(5630) =< s(5633)*(1/5)+s(5626) s(5631) =< s(5633)*(1/5)+s(5626) s(5629) =< s(5633)*(1/5)+s(5626) s(5634) =< s(5623) s(5635) =< s(5595)*s(5459) s(5636) =< s(5595)*s(5540) s(5637) =< s(5636)*(4/5) s(5638) =< s(5636)*(2/3) s(5639) =< s(5636) s(5640) =< s(5638) s(5641) =< s(5637) s(5642) =< s(5637) s(5640) =< s(5637) s(5642) =< s(5594) s(5640) =< s(5594) s(5640) =< s(5606)*(1/3)+s(5638) s(5641) =< s(5606)*(1/5)+s(5637) s(5642) =< s(5606)*(1/5)+s(5637) s(5640) =< s(5606)*(1/5)+s(5637) s(5643) =< s(5635) s(5644) =< s(5565) s(5645) =< s(5559) s(5646) =< s(5564) s(5647) =< s(5564) s(5645) =< s(5564) s(5647) =< s(5561) s(5645) =< s(5561) s(5645) =< s(5580)*(1/3)+s(5559) s(5646) =< s(5580)*(1/5)+s(5564) s(5647) =< s(5580)*(1/5)+s(5564) s(5645) =< s(5580)*(1/5)+s(5564) s(5401) =< aux(265) s(5402) =< aux(265) s(5401) =< aux(267) s(5402) =< aux(267) s(5401) =< aux(269) s(5402) =< aux(269) s(5404) =< s(5402)*aux(269) s(5405) =< s(5401)*2 s(5406) =< s(5402)*s(5081) s(5407) =< s(5406)*(4/5) s(5408) =< s(5406)*(2/3) s(5409) =< s(5406) s(5410) =< s(5408) s(5411) =< s(5407) s(5412) =< s(5407) s(5410) =< s(5407) s(5412) =< s(5401) s(5410) =< s(5401) s(5413) =< s(5401) s(5414) =< s(5405) s(5410) =< s(5414)*(1/3)+s(5408) s(5411) =< s(5414)*(1/5)+s(5407) s(5412) =< s(5414)*(1/5)+s(5407) s(5410) =< s(5414)*(1/5)+s(5407) s(5415) =< s(5404) s(5656) =< aux(265) s(5657) =< aux(265) s(5656) =< aux(269) s(5657) =< aux(269) s(5659) =< s(5657)*aux(269) s(5660) =< s(5656)*2 s(5661) =< s(5657)*s(5081) s(5662) =< s(5661)*(4/5) s(5663) =< s(5661)*(2/3) s(5664) =< s(5661) s(5665) =< s(5663) s(5666) =< s(5662) s(5667) =< s(5662) s(5665) =< s(5662) s(5667) =< s(5656) s(5665) =< s(5656) s(5668) =< s(5656) s(5669) =< s(5660) s(5665) =< s(5669)*(1/3)+s(5663) s(5666) =< s(5669)*(1/5)+s(5662) s(5667) =< s(5669)*(1/5)+s(5662) s(5665) =< s(5669)*(1/5)+s(5662) s(5670) =< s(5659) s(5679) =< aux(265) s(5680) =< aux(265) s(5679) =< aux(266) s(5680) =< aux(266) s(5679) =< aux(269) s(5680) =< aux(269) s(5682) =< s(5680)*aux(269) s(5683) =< s(5679)*2 s(5684) =< s(5680)*s(5081) s(5685) =< s(5684)*(4/5) s(5686) =< s(5684)*(2/3) s(5687) =< s(5684) s(5688) =< s(5686) s(5689) =< s(5685) s(5690) =< s(5685) s(5688) =< s(5685) s(5690) =< s(5679) s(5688) =< s(5679) s(5691) =< s(5679) s(5692) =< s(5683) s(5688) =< s(5692)*(1/3)+s(5686) s(5689) =< s(5692)*(1/5)+s(5685) s(5690) =< s(5692)*(1/5)+s(5685) s(5688) =< s(5692)*(1/5)+s(5685) s(5693) =< s(5682) s(5729) =< aux(265) s(5730) =< aux(265) s(5729) =< aux(268) s(5730) =< aux(268) s(5729) =< aux(269) s(5730) =< aux(269) s(5732) =< s(5730)*aux(269) s(5733) =< s(5729)*2 s(5734) =< s(5730)*s(5081) s(5735) =< s(5734)*(4/5) s(5736) =< s(5734)*(2/3) s(5737) =< s(5734) s(5738) =< s(5736) s(5739) =< s(5735) s(5740) =< s(5735) s(5738) =< s(5735) s(5740) =< s(5729) s(5738) =< s(5729) s(5741) =< s(5729) s(5742) =< s(5733) s(5738) =< s(5742)*(1/3)+s(5736) s(5739) =< s(5742)*(1/5)+s(5735) s(5740) =< s(5742)*(1/5)+s(5735) s(5738) =< s(5742)*(1/5)+s(5735) s(5743) =< s(5732) s(5118) =< aux(270) s(5118) =< aux(264) s(5121) =< aux(262)*(1/2) s(5122) =< s(5108)*(6/5) s(5124) =< s(5108) s(5125) =< s(5122) s(5126) =< s(5122) s(5124) =< s(5122) s(5126) =< aux(262) s(5124) =< aux(262) s(5127) =< aux(262) s(5127) =< s(5121) s(5124) =< s(5057)*(1/3)+s(5108) s(5125) =< s(5057)*(1/5)+s(5122) s(5126) =< s(5057)*(1/5)+s(5122) s(5124) =< s(5057)*(1/5)+s(5122) s(5130) =< s(5109) s(5130) =< s(5057)*(1/5)+s(5109) s(5136) =< aux(270)*(1/2) s(5137) =< s(5114)*(6/5) s(5138) =< s(5114) s(5139) =< s(5137) s(5140) =< s(5137) s(5138) =< s(5137) s(5140) =< aux(270) s(5138) =< aux(270) s(5141) =< aux(270) s(5141) =< s(5136) s(5138) =< s(5065)*(1/3)+s(5114) s(5139) =< s(5065)*(1/5)+s(5137) s(5140) =< s(5065)*(1/5)+s(5137) s(5138) =< s(5065)*(1/5)+s(5137) s(5142) =< aux(269) s(5143) =< s(5106) s(5144) =< s(5106) s(5142) =< s(5106) s(5144) =< aux(269) s(5142) =< s(5065)*(1/3)+aux(269) s(5143) =< s(5065)*(1/5)+s(5106) s(5144) =< s(5065)*(1/5)+s(5106) s(5142) =< s(5065)*(1/5)+s(5106) s(5145) =< aux(269)+1 s(5146) =< aux(269) s(5147) =< s(5115) s(5148) =< aux(269)+3 s(5150) =< aux(269)*(1/2) s(5151) =< aux(269)*2 s(5152) =< s(5059)*s(5115) s(5153) =< s(5059)*s(5145) s(5154) =< s(5059)*s(5146) s(5155) =< s(5059)*s(5147) s(5156) =< s(5059)*s(5148) s(5157) =< s(5152)*(6/5) s(5158) =< s(5059)*s(5081) s(5159) =< s(5153)*(1/2) s(5160) =< s(5155)*(6/5) s(5161) =< s(5153)*(2/5) s(5162) =< s(5153)*(1/3) s(5163) =< s(5156)*(1/3) s(5164) =< s(5153)*2 s(5165) =< s(5154) s(5166) =< s(5151) s(5167) =< s(5154) s(5167) =< s(5153) s(5168) =< s(5153) s(5169) =< s(5153) s(5169) =< s(5151) s(5168) =< aux(269) s(5170) =< s(5151)*(1/2) s(5171) =< s(5156)*(6/5) s(5172) =< s(5153) s(5173) =< s(5156) s(5174) =< s(5171) s(5175) =< s(5171) s(5173) =< s(5171) s(5175) =< s(5151) s(5173) =< s(5151) s(5176) =< s(5151) s(5176) =< s(5170) s(5173) =< s(5166)*(1/3)+s(5156) s(5174) =< s(5166)*(1/5)+s(5171) s(5175) =< s(5166)*(1/5)+s(5171) s(5173) =< s(5166)*(1/5)+s(5171) s(5177) =< aux(269) s(5177) =< s(5151) s(5178) =< aux(269)*(6/5) s(5179) =< s(5150) s(5180) =< aux(269) s(5181) =< s(5178) s(5182) =< s(5178) s(5180) =< s(5178) s(5182) =< s(5151) s(5180) =< s(5151) s(5180) =< s(5166)*(1/3)+aux(269) s(5181) =< s(5166)*(1/5)+s(5178) s(5182) =< s(5166)*(1/5)+s(5178) s(5180) =< s(5166)*(1/5)+s(5178) s(5183) =< s(5153) s(5184) =< s(5164) s(5185) =< s(5164) s(5183) =< s(5164) s(5185) =< aux(269) s(5183) =< aux(269) s(5183) =< s(5166)*(1/3)+s(5153) s(5184) =< s(5166)*(1/5)+s(5164) s(5185) =< s(5166)*(1/5)+s(5164) s(5183) =< s(5166)*(1/5)+s(5164) s(5186) =< s(5154) s(5187) =< s(5154) s(5186) =< s(5164) s(5187) =< s(5164) s(5188) =< s(5187)*aux(269) s(5189) =< s(5186)*2 s(5190) =< s(5187)*s(5081) s(5191) =< s(5190)*(4/5) s(5192) =< s(5190)*(2/3) s(5193) =< s(5190) s(5194) =< s(5192) s(5195) =< s(5191) s(5196) =< s(5191) s(5194) =< s(5191) s(5196) =< s(5186) s(5194) =< s(5186) s(5197) =< s(5186) s(5198) =< s(5189) s(5194) =< s(5198)*(1/3)+s(5192) s(5195) =< s(5198)*(1/5)+s(5191) s(5196) =< s(5198)*(1/5)+s(5191) s(5194) =< s(5198)*(1/5)+s(5191) s(5199) =< s(5188) s(5200) =< s(5154) s(5200) =< s(5153) s(5200) =< s(5159) s(5201) =< s(5163)*(6/5) s(5202) =< s(5159) s(5203) =< s(5163) s(5204) =< s(5201) s(5205) =< s(5201) s(5203) =< s(5201) s(5205) =< s(5151) s(5203) =< s(5151) s(5203) =< s(5166)*(1/3)+s(5163) s(5204) =< s(5166)*(1/5)+s(5201) s(5205) =< s(5166)*(1/5)+s(5201) s(5203) =< s(5166)*(1/5)+s(5201) s(5206) =< s(5162) s(5207) =< s(5161) s(5208) =< s(5161) s(5206) =< s(5161) s(5208) =< aux(269) s(5206) =< aux(269) s(5206) =< s(5166)*(1/3)+s(5162) s(5207) =< s(5166)*(1/5)+s(5161) s(5208) =< s(5166)*(1/5)+s(5161) s(5206) =< s(5166)*(1/5)+s(5161) s(5209) =< s(5155) s(5210) =< s(5160) s(5211) =< s(5160) s(5209) =< s(5160) s(5211) =< s(5154) s(5209) =< s(5154) s(5212) =< s(5154) s(5212) =< s(5159) s(5209) =< s(5172)*(1/3)+s(5155) s(5210) =< s(5172)*(1/5)+s(5160) s(5211) =< s(5172)*(1/5)+s(5160) s(5209) =< s(5172)*(1/5)+s(5160) s(5213) =< s(5154) s(5214) =< s(5154) s(5213) =< aux(269) s(5214) =< aux(269) s(5215) =< s(5214)*aux(269) s(5216) =< s(5213)*2 s(5217) =< s(5214)*s(5081) s(5218) =< s(5217)*(4/5) s(5219) =< s(5217)*(2/3) s(5220) =< s(5217) s(5221) =< s(5219) s(5222) =< s(5218) s(5223) =< s(5218) s(5221) =< s(5218) s(5223) =< s(5213) s(5221) =< s(5213) s(5224) =< s(5213) s(5225) =< s(5216) s(5221) =< s(5225)*(1/3)+s(5219) s(5222) =< s(5225)*(1/5)+s(5218) s(5223) =< s(5225)*(1/5)+s(5218) s(5221) =< s(5225)*(1/5)+s(5218) s(5226) =< s(5215) s(5227) =< s(5146)*(1/2)+1/2 s(5228) =< s(5187)*s(5146) s(5229) =< s(5187)*s(5227) s(5230) =< s(5229)*(4/5) s(5231) =< s(5229)*(2/3) s(5232) =< s(5229) s(5233) =< s(5231) s(5234) =< s(5230) s(5235) =< s(5230) s(5233) =< s(5230) s(5235) =< s(5186) s(5233) =< s(5186) s(5233) =< s(5198)*(1/3)+s(5231) s(5234) =< s(5198)*(1/5)+s(5230) s(5235) =< s(5198)*(1/5)+s(5230) s(5233) =< s(5198)*(1/5)+s(5230) s(5236) =< s(5228) s(5237) =< s(5158) s(5238) =< s(5152) s(5239) =< s(5157) s(5240) =< s(5157) s(5238) =< s(5157) s(5240) =< s(5154) s(5238) =< s(5154) s(5238) =< s(5172)*(1/3)+s(5152) s(5239) =< s(5172)*(1/5)+s(5157) s(5240) =< s(5172)*(1/5)+s(5157) s(5238) =< s(5172)*(1/5)+s(5157) s(5241) =< s(5114) s(5242) =< aux(269) s(5243) =< aux(269) s(5242) =< s(5114) s(5243) =< s(5114) s(5244) =< s(5242)*(1/2) s(5245) =< s(5242)*2 s(5246) =< s(5243)*s(5115) s(5247) =< s(5243)*s(5145) s(5248) =< s(5243)*s(5146) s(5249) =< s(5243)*s(5147) s(5250) =< s(5243)*s(5148) s(5251) =< s(5246)*(6/5) s(5252) =< s(5243)*s(5081) s(5253) =< s(5247)*(1/2) s(5254) =< s(5249)*(6/5) s(5255) =< s(5247)*(2/5) s(5256) =< s(5247)*(1/3) s(5257) =< s(5250)*(1/3) s(5258) =< s(5247)*2 s(5259) =< s(5248) s(5260) =< s(5242) s(5261) =< s(5245) s(5262) =< s(5248) s(5262) =< s(5247) s(5263) =< s(5247) s(5264) =< s(5247) s(5264) =< s(5245) s(5263) =< s(5242) s(5265) =< s(5245)*(1/2) s(5266) =< s(5250)*(6/5) s(5267) =< s(5247) s(5268) =< s(5250) s(5269) =< s(5266) s(5270) =< s(5266) s(5268) =< s(5266) s(5270) =< s(5245) s(5268) =< s(5245) s(5271) =< s(5245) s(5271) =< s(5265) s(5268) =< s(5261)*(1/3)+s(5250) s(5269) =< s(5261)*(1/5)+s(5266) s(5270) =< s(5261)*(1/5)+s(5266) s(5268) =< s(5261)*(1/5)+s(5266) s(5272) =< s(5242) s(5272) =< s(5245) s(5273) =< s(5242)*(6/5) s(5274) =< s(5244) s(5275) =< s(5242) s(5276) =< s(5273) s(5277) =< s(5273) s(5275) =< s(5273) s(5277) =< s(5245) s(5275) =< s(5245) s(5275) =< s(5261)*(1/3)+s(5242) s(5276) =< s(5261)*(1/5)+s(5273) s(5277) =< s(5261)*(1/5)+s(5273) s(5275) =< s(5261)*(1/5)+s(5273) s(5278) =< s(5247) s(5279) =< s(5258) s(5280) =< s(5258) s(5278) =< s(5258) s(5280) =< s(5242) s(5278) =< s(5242) s(5278) =< s(5261)*(1/3)+s(5247) s(5279) =< s(5261)*(1/5)+s(5258) s(5280) =< s(5261)*(1/5)+s(5258) s(5278) =< s(5261)*(1/5)+s(5258) s(5281) =< s(5248) s(5282) =< s(5248) s(5281) =< s(5258) s(5282) =< s(5258) s(5283) =< s(5282)*aux(269) s(5284) =< s(5281)*2 s(5285) =< s(5282)*s(5081) s(5286) =< s(5285)*(4/5) s(5287) =< s(5285)*(2/3) s(5288) =< s(5285) s(5289) =< s(5287) s(5290) =< s(5286) s(5291) =< s(5286) s(5289) =< s(5286) s(5291) =< s(5281) s(5289) =< s(5281) s(5292) =< s(5281) s(5293) =< s(5284) s(5289) =< s(5293)*(1/3)+s(5287) s(5290) =< s(5293)*(1/5)+s(5286) s(5291) =< s(5293)*(1/5)+s(5286) s(5289) =< s(5293)*(1/5)+s(5286) s(5294) =< s(5283) s(5295) =< s(5248) s(5295) =< s(5247) s(5295) =< s(5253) s(5296) =< s(5257)*(6/5) s(5297) =< s(5253) s(5298) =< s(5257) s(5299) =< s(5296) s(5300) =< s(5296) s(5298) =< s(5296) s(5300) =< s(5245) s(5298) =< s(5245) s(5298) =< s(5261)*(1/3)+s(5257) s(5299) =< s(5261)*(1/5)+s(5296) s(5300) =< s(5261)*(1/5)+s(5296) s(5298) =< s(5261)*(1/5)+s(5296) s(5301) =< s(5256) s(5302) =< s(5255) s(5303) =< s(5255) s(5301) =< s(5255) s(5303) =< s(5242) s(5301) =< s(5242) s(5301) =< s(5261)*(1/3)+s(5256) s(5302) =< s(5261)*(1/5)+s(5255) s(5303) =< s(5261)*(1/5)+s(5255) s(5301) =< s(5261)*(1/5)+s(5255) s(5304) =< s(5249) s(5305) =< s(5254) s(5306) =< s(5254) s(5304) =< s(5254) s(5306) =< s(5248) s(5304) =< s(5248) s(5307) =< s(5248) s(5307) =< s(5253) s(5304) =< s(5267)*(1/3)+s(5249) s(5305) =< s(5267)*(1/5)+s(5254) s(5306) =< s(5267)*(1/5)+s(5254) s(5304) =< s(5267)*(1/5)+s(5254) s(5308) =< s(5248) s(5309) =< s(5248) s(5308) =< s(5242) s(5309) =< s(5242) s(5310) =< s(5309)*aux(269) s(5311) =< s(5308)*2 s(5312) =< s(5309)*s(5081) s(5313) =< s(5312)*(4/5) s(5314) =< s(5312)*(2/3) s(5315) =< s(5312) s(5316) =< s(5314) s(5317) =< s(5313) s(5318) =< s(5313) s(5316) =< s(5313) s(5318) =< s(5308) s(5316) =< s(5308) s(5319) =< s(5308) s(5320) =< s(5311) s(5316) =< s(5320)*(1/3)+s(5314) s(5317) =< s(5320)*(1/5)+s(5313) s(5318) =< s(5320)*(1/5)+s(5313) s(5316) =< s(5320)*(1/5)+s(5313) s(5321) =< s(5310) s(5322) =< s(5282)*s(5146) s(5323) =< s(5282)*s(5227) s(5324) =< s(5323)*(4/5) s(5325) =< s(5323)*(2/3) s(5326) =< s(5323) s(5327) =< s(5325) s(5328) =< s(5324) s(5329) =< s(5324) s(5327) =< s(5324) s(5329) =< s(5281) s(5327) =< s(5281) s(5327) =< s(5293)*(1/3)+s(5325) s(5328) =< s(5293)*(1/5)+s(5324) s(5329) =< s(5293)*(1/5)+s(5324) s(5327) =< s(5293)*(1/5)+s(5324) s(5330) =< s(5322) s(5331) =< s(5252) s(5332) =< s(5246) s(5333) =< s(5251) s(5334) =< s(5251) s(5332) =< s(5251) s(5334) =< s(5248) s(5332) =< s(5248) s(5332) =< s(5267)*(1/3)+s(5246) s(5333) =< s(5267)*(1/5)+s(5251) s(5334) =< s(5267)*(1/5)+s(5251) s(5332) =< s(5267)*(1/5)+s(5251) with precondition: [V1=2,V>=0,V35>=0] * Chain [66]: 2 with precondition: [V=0,V1>=1] Closed-form bounds of start(V1,V,V35): ------------------------------------- * Chain [74] with precondition: [V1>=0] - Upper bound: 199/5*V1+534/5+129/5*V1*nat(V)+nat(V)*82+nat(V1+V)*2808+nat(V1+V)*2156*nat(V1+V)+nat(V1+V)*258*nat(V1+V)*nat(V1+V)+nat(V1+V)*136*nat(V1/3+V/3)+(6*V1+6)+nat(V+1)*47+6/5*nat(V+3)+nat(2*V1+2*V)*16+nat(2*V+2)+nat(2/5*V1+2/5*V)*18+nat(2/5*V+2/5)+nat(V1+V+1)*50+54/5*nat(V1+V+2)+51/5*nat(V1/3+V/3+2/3)+(6*V1+6)+nat(V1/3+V/3)*9+nat(V/2+1/2)*2+6/5*nat(V/3+1) - Complexity: n^3 * Chain [73] with precondition: [V1=1,V>=0,V35>=0] - Upper bound: 13221/5*V+3873/5+3527/2*V*V+1032/5*V*V*V+1032/5*V*V35+V/3*(544/5*V)+2941/2*V35+4312/5*V35*V35+516/5*V35*V35*V35+V35/3*(272/5*V35)+32*V+18*V35+32/5*V+2*V35+(4224*V+4224*V35)+(3438*V+3438*V35)*(V+V35)+(V+V35)*((387*V+387*V35)*(V+V35))+(148*V+148)+(44/5*V+88/5)+(12/5*V+36/5)+(47*V35+47)+(28/5*V35+56/5)+(12/5*V35+36/5)+(4*V+4)+(96*V+96*V35)+(4*V35+4)+(4/5*V+4/5)+(4/5*V35+4/5)+(75*V+75*V35+75)+(132/5*V+132/5*V35+264/5)+(2*V+2)+(4/5*V+12/5)+(34/15*V+68/15)+(7*V35+7)+(4/5*V35+12/5)+(4/5*V35+8/5)+8/3*V+V35 - Complexity: n^3 * Chain [72] with precondition: [V1=V,V1>=1] - Upper bound: 10*V+7 - Complexity: n * Chain [71] with precondition: [V1=1,V=2] - Upper bound: 0 - Complexity: constant * Chain [70] with precondition: [V1=1,V35=0,V>=1] - Upper bound: 1711/10 - Complexity: constant * Chain [69] with precondition: [V1=2,V=1] - Upper bound: 0 - Complexity: constant * Chain [68] with precondition: [V1=2,V=2] - Upper bound: 0 - Complexity: constant * Chain [67] with precondition: [V1=2,V>=0,V35>=0] - Upper bound: 973/10*V+2521/10+903/10*V*V35+6476/5*V35+4312/5*V35*V35+516/5*V35*V35*V35+V35/3*(272/5*V35)+16*V35+8/5*V35+(1408*V+1408*V35)+(1146*V+1146*V35)*(V+V35)+(V+V35)*((129*V+129*V35)*(V+V35))+(18*V+18)+(33*V35+33)+(22/5*V35+44/5)+(12/5*V35+36/5)+(32*V+32*V35)+(4*V35+4)+(4/5*V35+4/5)+(25*V+25*V35+25)+(44/5*V+44/5*V35+88/5)+(7*V35+7)+(4/5*V35+12/5)+(2/5*V35+4/5) - Complexity: n^3 * Chain [66] with precondition: [V=0,V1>=1] - Upper bound: 2 - Complexity: constant ### Maximum cost of start(V1,V,V35): max([1711/10,524/5+nat(V)*77+nat(V+1)*13+max([199/5*V1+129/5*V1*nat(V)+nat(V1+V)*2808+nat(V1+V)*2156*nat(V1+V)+nat(V1+V)*258*nat(V1+V)*nat(V1+V)+nat(V1+V)*136*nat(V1/3+V/3)+(6*V1+6)+nat(V+1)*29+6/5*nat(V+3)+nat(2*V1+2*V)*16+nat(2*V+2)+nat(2/5*V1+2/5*V)*18+nat(2/5*V+2/5)+nat(V1+V+1)*50+54/5*nat(V1+V+2)+51/5*nat(V1/3+V/3+2/3)+(6*V1+6)+nat(V1/3+V/3)*9+nat(V/2+1/2)*2+6/5*nat(V/3+1),1453/10+153/10*nat(V)+903/10*nat(V)*nat(V35)+6476/5*nat(V35)+4312/5*nat(V35)*nat(V35)+516/5*nat(V35)*nat(V35)*nat(V35)+272/5*nat(V35)*nat(V35/3)+nat(2*V35)*8+nat(2/5*V35)*4+nat(V+V35)*1408+nat(V+V35)*1146*nat(V+V35)+nat(V+V35)*129*nat(V+V35)*nat(V+V35)+nat(V35+1)*33+22/5*nat(V35+2)+12/5*nat(V35+3)+nat(2*V+2*V35)*16+nat(2*V35+2)*2+nat(2/5*V35+2/5)*2+nat(V+V35+1)*25+44/5*nat(V+V35+2)+nat(V35/2+1/2)*14+12/5*nat(V35/3+1)+6/5*nat(V35/3+2/3)+(1045/2+25469/10*nat(V)+3527/2*nat(V)*nat(V)+1032/5*nat(V)*nat(V)*nat(V)+1161/10*nat(V)*nat(V35)+544/5*nat(V)*nat(V/3)+1753/10*nat(V35)+nat(2*V)*16+nat(2*V35)+nat(2/5*V)*16+nat(2/5*V35)+nat(V+V35)*2816+nat(V+V35)*2292*nat(V+V35)+nat(V+V35)*258*nat(V+V35)*nat(V+V35)+nat(V+1)*130+44/5*nat(V+2)+12/5*nat(V+3)+nat(V35+1)*14+6/5*nat(V35+2)+nat(2*V+2)*2+nat(2*V+2*V35)*32+nat(2/5*V+2/5)*2+nat(V+V35+1)*50+88/5*nat(V+V35+2)+nat(V/2+1/2)*4+12/5*nat(V/3+1)+34/5*nat(V/3+2/3)+6/5*nat(V35/3+2/3)+nat(V/3)*8+nat(V35/2)*2)])+(nat(V)*5+2+nat(V+1)*5)]) Asymptotic class: n^3 * Total analysis performed in 92862 ms. ---------------------------------------- (12) BOUNDS(1, n^3) ---------------------------------------- (13) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (14) Obligation: The Runtime Complexity (innermost) of the given CpxRelTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) @(Nil, ys) -> ys gt0(Cons(x, xs), Nil) -> True gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) gcd(Nil, Nil) -> Nil gcd(Nil, Cons(x, xs)) -> Nil gcd(Cons(x, xs), Nil) -> Nil gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) eqList(Cons(x, xs), Nil) -> False eqList(Nil, Cons(y, ys)) -> False eqList(Nil, Nil) -> True lgth(Nil) -> Nil gt0(Nil, y) -> False monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) goal(x, y) -> gcd(x, y) The (relative) TRS S consists of the following rules: and(False, False) -> False and(True, False) -> False and(False, True) -> False and(True, True) -> True monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) monus[Ite](True, Cons(x, xs), y) -> xs gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) gcd[Ite](True, x, y) -> x gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x) gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y)) Rewrite Strategy: INNERMOST ---------------------------------------- (15) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (16) Obligation: Innermost TRS: Rules: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) @(Nil, ys) -> ys gt0(Cons(x, xs), Nil) -> True gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) gcd(Nil, Nil) -> Nil gcd(Nil, Cons(x, xs)) -> Nil gcd(Cons(x, xs), Nil) -> Nil gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) eqList(Cons(x, xs), Nil) -> False eqList(Nil, Cons(y, ys)) -> False eqList(Nil, Nil) -> True lgth(Nil) -> Nil gt0(Nil, y) -> False monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) goal(x, y) -> gcd(x, y) and(False, False) -> False and(True, False) -> False and(False, True) -> False and(True, True) -> True monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) monus[Ite](True, Cons(x, xs), y) -> xs gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) gcd[Ite](True, x, y) -> x gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x) gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y)) Types: @ :: Cons:Nil -> Cons:Nil -> Cons:Nil Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil Nil :: Cons:Nil gt0 :: Cons:Nil -> Cons:Nil -> True:False True :: True:False gcd :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil eqList :: Cons:Nil -> Cons:Nil -> True:False lgth :: Cons:Nil -> Cons:Nil and :: True:False -> True:False -> True:False False :: True:False monus :: Cons:Nil -> Cons:Nil -> Cons:Nil monus[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil goal :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[False][Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil hole_Cons:Nil1_1 :: Cons:Nil hole_True:False2_1 :: True:False gen_Cons:Nil3_1 :: Nat -> Cons:Nil ---------------------------------------- (17) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: @, gt0, gcd, eqList, lgth, monus They will be analysed ascendingly in the following order: @ < lgth gt0 < gcd eqList < gcd monus < gcd eqList < monus lgth < monus ---------------------------------------- (18) Obligation: Innermost TRS: Rules: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) @(Nil, ys) -> ys gt0(Cons(x, xs), Nil) -> True gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) gcd(Nil, Nil) -> Nil gcd(Nil, Cons(x, xs)) -> Nil gcd(Cons(x, xs), Nil) -> Nil gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) eqList(Cons(x, xs), Nil) -> False eqList(Nil, Cons(y, ys)) -> False eqList(Nil, Nil) -> True lgth(Nil) -> Nil gt0(Nil, y) -> False monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) goal(x, y) -> gcd(x, y) and(False, False) -> False and(True, False) -> False and(False, True) -> False and(True, True) -> True monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) monus[Ite](True, Cons(x, xs), y) -> xs gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) gcd[Ite](True, x, y) -> x gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x) gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y)) Types: @ :: Cons:Nil -> Cons:Nil -> Cons:Nil Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil Nil :: Cons:Nil gt0 :: Cons:Nil -> Cons:Nil -> True:False True :: True:False gcd :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil eqList :: Cons:Nil -> Cons:Nil -> True:False lgth :: Cons:Nil -> Cons:Nil and :: True:False -> True:False -> True:False False :: True:False monus :: Cons:Nil -> Cons:Nil -> Cons:Nil monus[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil goal :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[False][Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil hole_Cons:Nil1_1 :: Cons:Nil hole_True:False2_1 :: True:False gen_Cons:Nil3_1 :: Nat -> Cons:Nil Generator Equations: gen_Cons:Nil3_1(0) <=> Nil gen_Cons:Nil3_1(+(x, 1)) <=> Cons(Nil, gen_Cons:Nil3_1(x)) The following defined symbols remain to be analysed: @, gt0, gcd, eqList, lgth, monus They will be analysed ascendingly in the following order: @ < lgth gt0 < gcd eqList < gcd monus < gcd eqList < monus lgth < monus ---------------------------------------- (19) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: @(gen_Cons:Nil3_1(n5_1), gen_Cons:Nil3_1(b)) -> gen_Cons:Nil3_1(+(n5_1, b)), rt in Omega(1 + n5_1) Induction Base: @(gen_Cons:Nil3_1(0), gen_Cons:Nil3_1(b)) ->_R^Omega(1) gen_Cons:Nil3_1(b) Induction Step: @(gen_Cons:Nil3_1(+(n5_1, 1)), gen_Cons:Nil3_1(b)) ->_R^Omega(1) Cons(Nil, @(gen_Cons:Nil3_1(n5_1), gen_Cons:Nil3_1(b))) ->_IH Cons(Nil, gen_Cons:Nil3_1(+(b, c6_1))) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (20) Complex Obligation (BEST) ---------------------------------------- (21) Obligation: Proved the lower bound n^1 for the following obligation: Innermost TRS: Rules: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) @(Nil, ys) -> ys gt0(Cons(x, xs), Nil) -> True gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) gcd(Nil, Nil) -> Nil gcd(Nil, Cons(x, xs)) -> Nil gcd(Cons(x, xs), Nil) -> Nil gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) eqList(Cons(x, xs), Nil) -> False eqList(Nil, Cons(y, ys)) -> False eqList(Nil, Nil) -> True lgth(Nil) -> Nil gt0(Nil, y) -> False monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) goal(x, y) -> gcd(x, y) and(False, False) -> False and(True, False) -> False and(False, True) -> False and(True, True) -> True monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) monus[Ite](True, Cons(x, xs), y) -> xs gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) gcd[Ite](True, x, y) -> x gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x) gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y)) Types: @ :: Cons:Nil -> Cons:Nil -> Cons:Nil Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil Nil :: Cons:Nil gt0 :: Cons:Nil -> Cons:Nil -> True:False True :: True:False gcd :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil eqList :: Cons:Nil -> Cons:Nil -> True:False lgth :: Cons:Nil -> Cons:Nil and :: True:False -> True:False -> True:False False :: True:False monus :: Cons:Nil -> Cons:Nil -> Cons:Nil monus[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil goal :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[False][Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil hole_Cons:Nil1_1 :: Cons:Nil hole_True:False2_1 :: True:False gen_Cons:Nil3_1 :: Nat -> Cons:Nil Generator Equations: gen_Cons:Nil3_1(0) <=> Nil gen_Cons:Nil3_1(+(x, 1)) <=> Cons(Nil, gen_Cons:Nil3_1(x)) The following defined symbols remain to be analysed: @, gt0, gcd, eqList, lgth, monus They will be analysed ascendingly in the following order: @ < lgth gt0 < gcd eqList < gcd monus < gcd eqList < monus lgth < monus ---------------------------------------- (22) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (23) BOUNDS(n^1, INF) ---------------------------------------- (24) Obligation: Innermost TRS: Rules: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) @(Nil, ys) -> ys gt0(Cons(x, xs), Nil) -> True gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) gcd(Nil, Nil) -> Nil gcd(Nil, Cons(x, xs)) -> Nil gcd(Cons(x, xs), Nil) -> Nil gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) eqList(Cons(x, xs), Nil) -> False eqList(Nil, Cons(y, ys)) -> False eqList(Nil, Nil) -> True lgth(Nil) -> Nil gt0(Nil, y) -> False monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) goal(x, y) -> gcd(x, y) and(False, False) -> False and(True, False) -> False and(False, True) -> False and(True, True) -> True monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) monus[Ite](True, Cons(x, xs), y) -> xs gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) gcd[Ite](True, x, y) -> x gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x) gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y)) Types: @ :: Cons:Nil -> Cons:Nil -> Cons:Nil Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil Nil :: Cons:Nil gt0 :: Cons:Nil -> Cons:Nil -> True:False True :: True:False gcd :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil eqList :: Cons:Nil -> Cons:Nil -> True:False lgth :: Cons:Nil -> Cons:Nil and :: True:False -> True:False -> True:False False :: True:False monus :: Cons:Nil -> Cons:Nil -> Cons:Nil monus[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil goal :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[False][Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil hole_Cons:Nil1_1 :: Cons:Nil hole_True:False2_1 :: True:False gen_Cons:Nil3_1 :: Nat -> Cons:Nil Lemmas: @(gen_Cons:Nil3_1(n5_1), gen_Cons:Nil3_1(b)) -> gen_Cons:Nil3_1(+(n5_1, b)), rt in Omega(1 + n5_1) Generator Equations: gen_Cons:Nil3_1(0) <=> Nil gen_Cons:Nil3_1(+(x, 1)) <=> Cons(Nil, gen_Cons:Nil3_1(x)) The following defined symbols remain to be analysed: gt0, gcd, eqList, lgth, monus They will be analysed ascendingly in the following order: gt0 < gcd eqList < gcd monus < gcd eqList < monus lgth < monus ---------------------------------------- (25) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: gt0(gen_Cons:Nil3_1(+(1, n946_1)), gen_Cons:Nil3_1(n946_1)) -> True, rt in Omega(1 + n946_1) Induction Base: gt0(gen_Cons:Nil3_1(+(1, 0)), gen_Cons:Nil3_1(0)) ->_R^Omega(1) True Induction Step: gt0(gen_Cons:Nil3_1(+(1, +(n946_1, 1))), gen_Cons:Nil3_1(+(n946_1, 1))) ->_R^Omega(1) gt0(gen_Cons:Nil3_1(+(1, n946_1)), gen_Cons:Nil3_1(n946_1)) ->_IH True We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (26) Obligation: Innermost TRS: Rules: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) @(Nil, ys) -> ys gt0(Cons(x, xs), Nil) -> True gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) gcd(Nil, Nil) -> Nil gcd(Nil, Cons(x, xs)) -> Nil gcd(Cons(x, xs), Nil) -> Nil gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) eqList(Cons(x, xs), Nil) -> False eqList(Nil, Cons(y, ys)) -> False eqList(Nil, Nil) -> True lgth(Nil) -> Nil gt0(Nil, y) -> False monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) goal(x, y) -> gcd(x, y) and(False, False) -> False and(True, False) -> False and(False, True) -> False and(True, True) -> True monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) monus[Ite](True, Cons(x, xs), y) -> xs gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) gcd[Ite](True, x, y) -> x gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x) gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y)) Types: @ :: Cons:Nil -> Cons:Nil -> Cons:Nil Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil Nil :: Cons:Nil gt0 :: Cons:Nil -> Cons:Nil -> True:False True :: True:False gcd :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil eqList :: Cons:Nil -> Cons:Nil -> True:False lgth :: Cons:Nil -> Cons:Nil and :: True:False -> True:False -> True:False False :: True:False monus :: Cons:Nil -> Cons:Nil -> Cons:Nil monus[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil goal :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[False][Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil hole_Cons:Nil1_1 :: Cons:Nil hole_True:False2_1 :: True:False gen_Cons:Nil3_1 :: Nat -> Cons:Nil Lemmas: @(gen_Cons:Nil3_1(n5_1), gen_Cons:Nil3_1(b)) -> gen_Cons:Nil3_1(+(n5_1, b)), rt in Omega(1 + n5_1) gt0(gen_Cons:Nil3_1(+(1, n946_1)), gen_Cons:Nil3_1(n946_1)) -> True, rt in Omega(1 + n946_1) Generator Equations: gen_Cons:Nil3_1(0) <=> Nil gen_Cons:Nil3_1(+(x, 1)) <=> Cons(Nil, gen_Cons:Nil3_1(x)) The following defined symbols remain to be analysed: eqList, gcd, lgth, monus They will be analysed ascendingly in the following order: eqList < gcd monus < gcd eqList < monus lgth < monus ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: eqList(gen_Cons:Nil3_1(+(1, n1415_1)), gen_Cons:Nil3_1(n1415_1)) -> False, rt in Omega(1 + n1415_1) Induction Base: eqList(gen_Cons:Nil3_1(+(1, 0)), gen_Cons:Nil3_1(0)) ->_R^Omega(1) False Induction Step: eqList(gen_Cons:Nil3_1(+(1, +(n1415_1, 1))), gen_Cons:Nil3_1(+(n1415_1, 1))) ->_R^Omega(1) and(eqList(Nil, Nil), eqList(gen_Cons:Nil3_1(+(1, n1415_1)), gen_Cons:Nil3_1(n1415_1))) ->_R^Omega(1) and(True, eqList(gen_Cons:Nil3_1(+(1, n1415_1)), gen_Cons:Nil3_1(n1415_1))) ->_IH and(True, False) ->_R^Omega(0) False We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (28) Obligation: Innermost TRS: Rules: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) @(Nil, ys) -> ys gt0(Cons(x, xs), Nil) -> True gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) gcd(Nil, Nil) -> Nil gcd(Nil, Cons(x, xs)) -> Nil gcd(Cons(x, xs), Nil) -> Nil gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) eqList(Cons(x, xs), Nil) -> False eqList(Nil, Cons(y, ys)) -> False eqList(Nil, Nil) -> True lgth(Nil) -> Nil gt0(Nil, y) -> False monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) goal(x, y) -> gcd(x, y) and(False, False) -> False and(True, False) -> False and(False, True) -> False and(True, True) -> True monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) monus[Ite](True, Cons(x, xs), y) -> xs gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) gcd[Ite](True, x, y) -> x gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x) gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y)) Types: @ :: Cons:Nil -> Cons:Nil -> Cons:Nil Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil Nil :: Cons:Nil gt0 :: Cons:Nil -> Cons:Nil -> True:False True :: True:False gcd :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil eqList :: Cons:Nil -> Cons:Nil -> True:False lgth :: Cons:Nil -> Cons:Nil and :: True:False -> True:False -> True:False False :: True:False monus :: Cons:Nil -> Cons:Nil -> Cons:Nil monus[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil goal :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[False][Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil hole_Cons:Nil1_1 :: Cons:Nil hole_True:False2_1 :: True:False gen_Cons:Nil3_1 :: Nat -> Cons:Nil Lemmas: @(gen_Cons:Nil3_1(n5_1), gen_Cons:Nil3_1(b)) -> gen_Cons:Nil3_1(+(n5_1, b)), rt in Omega(1 + n5_1) gt0(gen_Cons:Nil3_1(+(1, n946_1)), gen_Cons:Nil3_1(n946_1)) -> True, rt in Omega(1 + n946_1) eqList(gen_Cons:Nil3_1(+(1, n1415_1)), gen_Cons:Nil3_1(n1415_1)) -> False, rt in Omega(1 + n1415_1) Generator Equations: gen_Cons:Nil3_1(0) <=> Nil gen_Cons:Nil3_1(+(x, 1)) <=> Cons(Nil, gen_Cons:Nil3_1(x)) The following defined symbols remain to be analysed: lgth, gcd, monus They will be analysed ascendingly in the following order: monus < gcd lgth < monus ---------------------------------------- (29) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: lgth(gen_Cons:Nil3_1(n2029_1)) -> gen_Cons:Nil3_1(n2029_1), rt in Omega(1 + n2029_1) Induction Base: lgth(gen_Cons:Nil3_1(0)) ->_R^Omega(1) Nil Induction Step: lgth(gen_Cons:Nil3_1(+(n2029_1, 1))) ->_R^Omega(1) @(Cons(Nil, Nil), lgth(gen_Cons:Nil3_1(n2029_1))) ->_IH @(Cons(Nil, Nil), gen_Cons:Nil3_1(c2030_1)) ->_L^Omega(2) gen_Cons:Nil3_1(+(+(0, 1), n2029_1)) We have rt in Omega(n^1) and sz in O(n). Thus, we have irc_R in Omega(n). ---------------------------------------- (30) Obligation: Innermost TRS: Rules: @(Cons(x, xs), ys) -> Cons(x, @(xs, ys)) @(Nil, ys) -> ys gt0(Cons(x, xs), Nil) -> True gt0(Cons(x', xs'), Cons(x, xs)) -> gt0(xs', xs) gcd(Nil, Nil) -> Nil gcd(Nil, Cons(x, xs)) -> Nil gcd(Cons(x, xs), Nil) -> Nil gcd(Cons(x', xs'), Cons(x, xs)) -> gcd[Ite](eqList(Cons(x', xs'), Cons(x, xs)), Cons(x', xs'), Cons(x, xs)) lgth(Cons(x, xs)) -> @(Cons(Nil, Nil), lgth(xs)) eqList(Cons(x, xs), Cons(y, ys)) -> and(eqList(x, y), eqList(xs, ys)) eqList(Cons(x, xs), Nil) -> False eqList(Nil, Cons(y, ys)) -> False eqList(Nil, Nil) -> True lgth(Nil) -> Nil gt0(Nil, y) -> False monus(x, y) -> monus[Ite](eqList(lgth(y), Cons(Nil, Nil)), x, y) goal(x, y) -> gcd(x, y) and(False, False) -> False and(True, False) -> False and(False, True) -> False and(True, True) -> True monus[Ite](False, Cons(x', xs'), Cons(x, xs)) -> monus(xs', xs) monus[Ite](True, Cons(x, xs), y) -> xs gcd[Ite](False, x, y) -> gcd[False][Ite](gt0(x, y), x, y) gcd[Ite](True, x, y) -> x gcd[False][Ite](False, x, y) -> gcd(monus(y, x), x) gcd[False][Ite](True, x, y) -> gcd(y, monus(x, y)) Types: @ :: Cons:Nil -> Cons:Nil -> Cons:Nil Cons :: Cons:Nil -> Cons:Nil -> Cons:Nil Nil :: Cons:Nil gt0 :: Cons:Nil -> Cons:Nil -> True:False True :: True:False gcd :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil eqList :: Cons:Nil -> Cons:Nil -> True:False lgth :: Cons:Nil -> Cons:Nil and :: True:False -> True:False -> True:False False :: True:False monus :: Cons:Nil -> Cons:Nil -> Cons:Nil monus[Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil goal :: Cons:Nil -> Cons:Nil -> Cons:Nil gcd[False][Ite] :: True:False -> Cons:Nil -> Cons:Nil -> Cons:Nil hole_Cons:Nil1_1 :: Cons:Nil hole_True:False2_1 :: True:False gen_Cons:Nil3_1 :: Nat -> Cons:Nil Lemmas: @(gen_Cons:Nil3_1(n5_1), gen_Cons:Nil3_1(b)) -> gen_Cons:Nil3_1(+(n5_1, b)), rt in Omega(1 + n5_1) gt0(gen_Cons:Nil3_1(+(1, n946_1)), gen_Cons:Nil3_1(n946_1)) -> True, rt in Omega(1 + n946_1) eqList(gen_Cons:Nil3_1(+(1, n1415_1)), gen_Cons:Nil3_1(n1415_1)) -> False, rt in Omega(1 + n1415_1) lgth(gen_Cons:Nil3_1(n2029_1)) -> gen_Cons:Nil3_1(n2029_1), rt in Omega(1 + n2029_1) Generator Equations: gen_Cons:Nil3_1(0) <=> Nil gen_Cons:Nil3_1(+(x, 1)) <=> Cons(Nil, gen_Cons:Nil3_1(x)) The following defined symbols remain to be analysed: monus, gcd They will be analysed ascendingly in the following order: monus < gcd