/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^2)) proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). (0) CpxTRS (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] (2) CpxWeightedTrs (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] (4) CpxTypedWeightedTrs (5) CompletionProof [UPPER BOUND(ID), 0 ms] (6) CpxTypedWeightedCompleteTrs (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] (8) CpxRNTS (9) CompleteCoflocoProof [FINISHED, 7741 ms] (10) BOUNDS(1, n^2) (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] (12) TRS for Loop Detection (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] (14) BEST (15) proven lower bound (16) LowerBoundPropagationProof [FINISHED, 0 ms] (17) BOUNDS(n^1, INF) (18) TRS for Loop Detection ---------------------------------------- (0) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) plus(x, 0) -> x plus(x, s(y)) -> s(plus(x, y)) length(nil) -> 0 length(cons(x, y)) -> s(length(y)) helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) ge(x, 0) -> true ge(0, s(x)) -> false ge(s(x), s(y)) -> ge(x, y) if(true, c, l, ys, zs) -> nil if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) helpc(true, ys, zs) -> ys helpc(false, ys, zs) -> zs helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) Transformed relative TRS to weighted TRS ---------------------------------------- (2) Obligation: The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). The TRS R consists of the following rules: app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) [1] plus(x, 0) -> x [1] plus(x, s(y)) -> s(plus(x, y)) [1] length(nil) -> 0 [1] length(cons(x, y)) -> s(length(y)) [1] helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) [1] ge(x, 0) -> true [1] ge(0, s(x)) -> false [1] ge(s(x), s(y)) -> ge(x, y) [1] if(true, c, l, ys, zs) -> nil [1] if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) [1] greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) [1] smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) [1] helpc(true, ys, zs) -> ys [1] helpc(false, ys, zs) -> zs [1] helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (4) Obligation: Runtime Complexity Weighted TRS with Types. The TRS R consists of the following rules: app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) [1] plus(x, 0) -> x [1] plus(x, s(y)) -> s(plus(x, y)) [1] length(nil) -> 0 [1] length(cons(x, y)) -> s(length(y)) [1] helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) [1] ge(x, 0) -> true [1] ge(0, s(x)) -> false [1] ge(s(x), s(y)) -> ge(x, y) [1] if(true, c, l, ys, zs) -> nil [1] if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) [1] greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) [1] smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) [1] helpc(true, ys, zs) -> ys [1] helpc(false, ys, zs) -> zs [1] helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) [1] The TRS has the following type information: app :: nil:cons -> nil:cons -> nil:cons helpa :: 0:s -> 0:s -> nil:cons -> nil:cons -> nil:cons 0 :: 0:s plus :: 0:s -> 0:s -> 0:s length :: nil:cons -> 0:s s :: 0:s -> 0:s nil :: nil:cons cons :: a -> nil:cons -> nil:cons if :: true:false -> 0:s -> 0:s -> nil:cons -> nil:cons -> nil:cons ge :: 0:s -> 0:s -> true:false true :: true:false false :: true:false helpb :: 0:s -> 0:s -> nil:cons -> nil:cons -> nil:cons greater :: nil:cons -> nil:cons -> nil:cons smaller :: nil:cons -> nil:cons -> nil:cons helpc :: true:false -> nil:cons -> nil:cons -> nil:cons Rewrite Strategy: INNERMOST ---------------------------------------- (5) 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: helpb(v0, v1, v2, v3) -> null_helpb [0] length(v0) -> null_length [0] plus(v0, v1) -> null_plus [0] ge(v0, v1) -> null_ge [0] if(v0, v1, v2, v3, v4) -> null_if [0] helpc(v0, v1, v2) -> null_helpc [0] And the following fresh constants: null_helpb, null_length, null_plus, null_ge, null_if, null_helpc, const ---------------------------------------- (6) 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: app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) [1] plus(x, 0) -> x [1] plus(x, s(y)) -> s(plus(x, y)) [1] length(nil) -> 0 [1] length(cons(x, y)) -> s(length(y)) [1] helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) [1] ge(x, 0) -> true [1] ge(0, s(x)) -> false [1] ge(s(x), s(y)) -> ge(x, y) [1] if(true, c, l, ys, zs) -> nil [1] if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) [1] greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) [1] smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) [1] helpc(true, ys, zs) -> ys [1] helpc(false, ys, zs) -> zs [1] helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) [1] helpb(v0, v1, v2, v3) -> null_helpb [0] length(v0) -> null_length [0] plus(v0, v1) -> null_plus [0] ge(v0, v1) -> null_ge [0] if(v0, v1, v2, v3, v4) -> null_if [0] helpc(v0, v1, v2) -> null_helpc [0] The TRS has the following type information: app :: nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc helpa :: 0:s:null_length:null_plus -> 0:s:null_length:null_plus -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc 0 :: 0:s:null_length:null_plus plus :: 0:s:null_length:null_plus -> 0:s:null_length:null_plus -> 0:s:null_length:null_plus length :: nil:cons:null_helpb:null_if:null_helpc -> 0:s:null_length:null_plus s :: 0:s:null_length:null_plus -> 0:s:null_length:null_plus nil :: nil:cons:null_helpb:null_if:null_helpc cons :: a -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc if :: true:false:null_ge -> 0:s:null_length:null_plus -> 0:s:null_length:null_plus -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc ge :: 0:s:null_length:null_plus -> 0:s:null_length:null_plus -> true:false:null_ge true :: true:false:null_ge false :: true:false:null_ge helpb :: 0:s:null_length:null_plus -> 0:s:null_length:null_plus -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc greater :: nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc smaller :: nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc helpc :: true:false:null_ge -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc -> nil:cons:null_helpb:null_if:null_helpc null_helpb :: nil:cons:null_helpb:null_if:null_helpc null_length :: 0:s:null_length:null_plus null_plus :: 0:s:null_length:null_plus null_ge :: true:false:null_ge null_if :: nil:cons:null_helpb:null_if:null_helpc null_helpc :: nil:cons:null_helpb:null_if:null_helpc const :: a Rewrite Strategy: INNERMOST ---------------------------------------- (7) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. The constant constructors are abstracted as follows: 0 => 0 nil => 0 true => 2 false => 1 null_helpb => 0 null_length => 0 null_plus => 0 null_ge => 0 null_if => 0 null_helpc => 0 const => 0 ---------------------------------------- (8) Obligation: Complexity RNTS consisting of the following rules: app(z, z') -{ 1 }-> helpa(0, plus(length(x), length(y)), x, y) :|: x >= 0, y >= 0, z = x, z' = y ge(z, z') -{ 1 }-> ge(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x ge(z, z') -{ 1 }-> 2 :|: x >= 0, z = x, z' = 0 ge(z, z') -{ 1 }-> 1 :|: z' = 1 + x, x >= 0, z = 0 ge(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 greater(z, z') -{ 1 }-> helpc(ge(length(ys), length(zs)), ys, zs) :|: z = ys, z' = zs, ys >= 0, zs >= 0 helpa(z, z', z'', z1) -{ 1 }-> if(ge(c, l), c, l, ys, zs) :|: z' = l, c >= 0, ys >= 0, zs >= 0, z'' = ys, z = c, l >= 0, z1 = zs helpb(z, z', z'', z1) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0, v3 >= 0 helpb(z, z', z'', z1) -{ 1 }-> 1 + y + helpa(1 + c, l, ys, zs) :|: z' = l, z'' = 1 + y + ys, c >= 0, ys >= 0, zs >= 0, y >= 0, z = c, l >= 0, z1 = zs helpc(z, z', z'') -{ 1 }-> ys :|: z = 2, z' = ys, ys >= 0, zs >= 0, z'' = zs helpc(z, z', z'') -{ 1 }-> zs :|: z' = ys, z = 1, ys >= 0, zs >= 0, z'' = zs helpc(z, z', z'') -{ 0 }-> 0 :|: v0 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, v2 >= 0 if(z, z', z'', z1, z2) -{ 1 }-> helpb(c, l, greater(ys, zs), smaller(ys, zs)) :|: z2 = zs, c >= 0, z = 1, ys >= 0, zs >= 0, l >= 0, z' = c, z'' = l, z1 = ys if(z, z', z'', z1, z2) -{ 1 }-> 0 :|: z = 2, z2 = zs, c >= 0, ys >= 0, zs >= 0, l >= 0, z' = c, z'' = l, z1 = ys if(z, z', z'', z1, z2) -{ 0 }-> 0 :|: z1 = v3, v0 >= 0, v4 >= 0, z'' = v2, v1 >= 0, z = v0, z' = v1, z2 = v4, v2 >= 0, v3 >= 0 length(z) -{ 1 }-> 0 :|: z = 0 length(z) -{ 0 }-> 0 :|: v0 >= 0, z = v0 length(z) -{ 1 }-> 1 + length(y) :|: z = 1 + x + y, x >= 0, y >= 0 plus(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0 plus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 plus(z, z') -{ 1 }-> 1 + plus(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = x smaller(z, z') -{ 1 }-> helpc(ge(length(ys), length(zs)), zs, ys) :|: z = ys, z' = zs, ys >= 0, zs >= 0 Only complete derivations are relevant for the runtime complexity. ---------------------------------------- (9) CompleteCoflocoProof (FINISHED) Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: eq(start(V1, V, V9, V14, V22),0,[app(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V9, V14, V22),0,[plus(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V9, V14, V22),0,[length(V1, Out)],[V1 >= 0]). eq(start(V1, V, V9, V14, V22),0,[helpa(V1, V, V9, V14, Out)],[V1 >= 0,V >= 0,V9 >= 0,V14 >= 0]). eq(start(V1, V, V9, V14, V22),0,[ge(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V9, V14, V22),0,[if(V1, V, V9, V14, V22, Out)],[V1 >= 0,V >= 0,V9 >= 0,V14 >= 0,V22 >= 0]). eq(start(V1, V, V9, V14, V22),0,[greater(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V9, V14, V22),0,[smaller(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V, V9, V14, V22),0,[helpc(V1, V, V9, Out)],[V1 >= 0,V >= 0,V9 >= 0]). eq(start(V1, V, V9, V14, V22),0,[helpb(V1, V, V9, V14, Out)],[V1 >= 0,V >= 0,V9 >= 0,V14 >= 0]). eq(app(V1, V, Out),1,[length(V3, Ret10),length(V2, Ret11),plus(Ret10, Ret11, Ret1),helpa(0, Ret1, V3, V2, Ret)],[Out = Ret,V3 >= 0,V2 >= 0,V1 = V3,V = V2]). eq(plus(V1, V, Out),1,[],[Out = V4,V4 >= 0,V1 = V4,V = 0]). eq(plus(V1, V, Out),1,[plus(V5, V6, Ret12)],[Out = 1 + Ret12,V = 1 + V6,V5 >= 0,V6 >= 0,V1 = V5]). eq(length(V1, Out),1,[],[Out = 0,V1 = 0]). eq(length(V1, Out),1,[length(V8, Ret13)],[Out = 1 + Ret13,V1 = 1 + V7 + V8,V7 >= 0,V8 >= 0]). eq(helpa(V1, V, V9, V14, Out),1,[ge(V10, V11, Ret0),if(Ret0, V10, V11, V12, V13, Ret2)],[Out = Ret2,V = V11,V10 >= 0,V12 >= 0,V13 >= 0,V9 = V12,V1 = V10,V11 >= 0,V14 = V13]). eq(ge(V1, V, Out),1,[],[Out = 2,V15 >= 0,V1 = V15,V = 0]). eq(ge(V1, V, Out),1,[],[Out = 1,V = 1 + V16,V16 >= 0,V1 = 0]). eq(ge(V1, V, Out),1,[ge(V18, V17, Ret3)],[Out = Ret3,V = 1 + V17,V18 >= 0,V17 >= 0,V1 = 1 + V18]). eq(if(V1, V, V9, V14, V22, Out),1,[],[Out = 0,V1 = 2,V22 = V21,V19 >= 0,V20 >= 0,V21 >= 0,V23 >= 0,V = V19,V9 = V23,V14 = V20]). eq(if(V1, V, V9, V14, V22, Out),1,[greater(V26, V25, Ret21),smaller(V26, V25, Ret31),helpb(V24, V27, Ret21, Ret31, Ret4)],[Out = Ret4,V22 = V25,V24 >= 0,V1 = 1,V26 >= 0,V25 >= 0,V27 >= 0,V = V24,V9 = V27,V14 = V26]). eq(greater(V1, V, Out),1,[length(V28, Ret00),length(V29, Ret01),ge(Ret00, Ret01, Ret02),helpc(Ret02, V28, V29, Ret5)],[Out = Ret5,V1 = V28,V = V29,V28 >= 0,V29 >= 0]). eq(smaller(V1, V, Out),1,[length(V30, Ret001),length(V31, Ret011),ge(Ret001, Ret011, Ret03),helpc(Ret03, V31, V30, Ret6)],[Out = Ret6,V1 = V30,V = V31,V30 >= 0,V31 >= 0]). eq(helpc(V1, V, V9, Out),1,[],[Out = V32,V1 = 2,V = V32,V32 >= 0,V33 >= 0,V9 = V33]). eq(helpc(V1, V, V9, Out),1,[],[Out = V34,V = V35,V1 = 1,V35 >= 0,V34 >= 0,V9 = V34]). eq(helpb(V1, V, V9, V14, Out),1,[helpa(1 + V39, V40, V37, V38, Ret14)],[Out = 1 + Ret14 + V36,V = V40,V9 = 1 + V36 + V37,V39 >= 0,V37 >= 0,V38 >= 0,V36 >= 0,V1 = V39,V40 >= 0,V14 = V38]). eq(helpb(V1, V, V9, V14, Out),0,[],[Out = 0,V14 = V43,V42 >= 0,V9 = V44,V41 >= 0,V1 = V42,V = V41,V44 >= 0,V43 >= 0]). eq(length(V1, Out),0,[],[Out = 0,V45 >= 0,V1 = V45]). eq(plus(V1, V, Out),0,[],[Out = 0,V47 >= 0,V46 >= 0,V1 = V47,V = V46]). eq(ge(V1, V, Out),0,[],[Out = 0,V48 >= 0,V49 >= 0,V1 = V48,V = V49]). eq(if(V1, V, V9, V14, V22, Out),0,[],[Out = 0,V14 = V54,V50 >= 0,V53 >= 0,V9 = V51,V52 >= 0,V1 = V50,V = V52,V22 = V53,V51 >= 0,V54 >= 0]). eq(helpc(V1, V, V9, Out),0,[],[Out = 0,V56 >= 0,V9 = V57,V55 >= 0,V1 = V56,V = V55,V57 >= 0]). input_output_vars(app(V1,V,Out),[V1,V],[Out]). input_output_vars(plus(V1,V,Out),[V1,V],[Out]). input_output_vars(length(V1,Out),[V1],[Out]). input_output_vars(helpa(V1,V,V9,V14,Out),[V1,V,V9,V14],[Out]). input_output_vars(ge(V1,V,Out),[V1,V],[Out]). input_output_vars(if(V1,V,V9,V14,V22,Out),[V1,V,V9,V14,V22],[Out]). input_output_vars(greater(V1,V,Out),[V1,V],[Out]). input_output_vars(smaller(V1,V,Out),[V1,V],[Out]). input_output_vars(helpc(V1,V,V9,Out),[V1,V,V9],[Out]). input_output_vars(helpb(V1,V,V9,V14,Out),[V1,V,V9,V14],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [ge/3] 1. non_recursive : [helpc/4] 2. recursive : [length/2] 3. non_recursive : [greater/3] 4. non_recursive : [smaller/3] 5. recursive : [helpa/5,helpb/5,if/6] 6. recursive : [plus/3] 7. non_recursive : [app/3] 8. non_recursive : [start/5] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into ge/3 1. SCC is partially evaluated into helpc/4 2. SCC is partially evaluated into length/2 3. SCC is partially evaluated into greater/3 4. SCC is partially evaluated into smaller/3 5. SCC is partially evaluated into helpa/5 6. SCC is partially evaluated into plus/3 7. SCC is partially evaluated into app/3 8. SCC is partially evaluated into start/5 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations ge/3 * CE 30 is refined into CE [34] * CE 27 is refined into CE [35] * CE 28 is refined into CE [36] * CE 29 is refined into CE [37] ### Cost equations --> "Loop" of ge/3 * CEs [37] --> Loop 20 * CEs [34] --> Loop 21 * CEs [35] --> Loop 22 * CEs [36] --> Loop 23 ### Ranking functions of CR ge(V1,V,Out) * RF of phase [20]: [V,V1] #### Partial ranking functions of CR ge(V1,V,Out) * Partial RF of phase [20]: - RF of loop [20:1]: V V1 ### Specialization of cost equations helpc/4 * CE 33 is refined into CE [38] * CE 31 is refined into CE [39] * CE 32 is refined into CE [40] ### Cost equations --> "Loop" of helpc/4 * CEs [38] --> Loop 24 * CEs [39] --> Loop 25 * CEs [40] --> Loop 26 ### Ranking functions of CR helpc(V1,V,V9,Out) #### Partial ranking functions of CR helpc(V1,V,V9,Out) ### Specialization of cost equations length/2 * CE 24 is refined into CE [41] * CE 26 is refined into CE [42] * CE 25 is refined into CE [43] ### Cost equations --> "Loop" of length/2 * CEs [43] --> Loop 27 * CEs [41,42] --> Loop 28 ### Ranking functions of CR length(V1,Out) * RF of phase [27]: [V1] #### Partial ranking functions of CR length(V1,Out) * Partial RF of phase [27]: - RF of loop [27:1]: V1 ### Specialization of cost equations greater/3 * CE 14 is refined into CE [44,45,46,47,48,49,50,51,52,53,54,55,56,57] ### Cost equations --> "Loop" of greater/3 * CEs [47,54] --> Loop 29 * CEs [44,50,56] --> Loop 30 * CEs [45,46,48,49,51,52,53,55,57] --> Loop 31 ### Ranking functions of CR greater(V1,V,Out) #### Partial ranking functions of CR greater(V1,V,Out) ### Specialization of cost equations smaller/3 * CE 15 is refined into CE [58,59,60,61,62,63,64,65,66,67,68,69,70,71] ### Cost equations --> "Loop" of smaller/3 * CEs [58,64,70] --> Loop 32 * CEs [61,68] --> Loop 33 * CEs [59,60,62,63,65,66,67,69,71] --> Loop 34 ### Ranking functions of CR smaller(V1,V,Out) #### Partial ranking functions of CR smaller(V1,V,Out) ### Specialization of cost equations helpa/5 * CE 16 is refined into CE [72,73,74,75,76] * CE 17 is refined into CE [77,78] * CE 19 is refined into CE [79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96] * CE 18 is refined into CE [97,98,99,100,101,102,103,104,105,106,107,108] ### Cost equations --> "Loop" of helpa/5 * CEs [108] --> Loop 35 * CEs [105] --> Loop 36 * CEs [107] --> Loop 37 * CEs [104] --> Loop 38 * CEs [106] --> Loop 39 * CEs [103] --> Loop 40 * CEs [102] --> Loop 41 * CEs [99] --> Loop 42 * CEs [101] --> Loop 43 * CEs [98] --> Loop 44 * CEs [100] --> Loop 45 * CEs [97] --> Loop 46 * CEs [73,77] --> Loop 47 * CEs [72,74,75,76,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96] --> Loop 48 ### Ranking functions of CR helpa(V1,V,V9,V14,Out) * RF of phase [35,36,37,38,39,40]: [-V1+V] #### Partial ranking functions of CR helpa(V1,V,V9,V14,Out) * Partial RF of phase [35,36,37,38,39,40]: - RF of loop [35:1,36:1,37:1,38:1,39:1,40:1]: -V1+V - RF of loop [36:1,38:1,40:1]: V9 depends on loops [35:1,37:1,39:1] - RF of loop [37:1,39:1]: V9+V14 depends on loops [35:1,38:1] - RF of loop [39:1]: V14 depends on loops [37:1,38:1] ### Specialization of cost equations plus/3 * CE 23 is refined into CE [109] * CE 21 is refined into CE [110] * CE 22 is refined into CE [111] ### Cost equations --> "Loop" of plus/3 * CEs [111] --> Loop 49 * CEs [109] --> Loop 50 * CEs [110] --> Loop 51 ### Ranking functions of CR plus(V1,V,Out) * RF of phase [49]: [V] #### Partial ranking functions of CR plus(V1,V,Out) * Partial RF of phase [49]: - RF of loop [49:1]: V ### Specialization of cost equations app/3 * CE 20 is refined into CE [112,113,114,115,116,117,118,119,120,121,122,123,124,125,126,127,128,129,130,131,132,133,134,135,136,137,138,139,140,141] ### Cost equations --> "Loop" of app/3 * CEs [116,121,126,133,138] --> Loop 52 * CEs [128] --> Loop 53 * CEs [127,134,135] --> Loop 54 * CEs [115,120,125,132,137] --> Loop 55 * CEs [117,118,122,123,139,140] --> Loop 56 * CEs [112,113,114,119,124,129,130,131,136,141] --> Loop 57 ### Ranking functions of CR app(V1,V,Out) #### Partial ranking functions of CR app(V1,V,Out) ### Specialization of cost equations start/5 * CE 2 is refined into CE [142] * CE 1 is refined into CE [143] * CE 3 is refined into CE [144,145,146,147,148,149,150,151,152,153,154,155] * CE 4 is refined into CE [156,157,158,159,160,161,162,163,164] * CE 5 is refined into CE [165,166] * CE 6 is refined into CE [167,168,169,170,171,172] * CE 7 is refined into CE [173,174,175,176] * CE 8 is refined into CE [177,178] * CE 9 is refined into CE [179,180,181,182,183,184] * CE 10 is refined into CE [185,186,187,188,189] * CE 11 is refined into CE [190,191,192] * CE 12 is refined into CE [193,194,195] * CE 13 is refined into CE [196,197,198] ### Cost equations --> "Loop" of start/5 * CEs [173,186] --> Loop 58 * CEs [142,197] --> Loop 59 * CEs [144,145,146,147,148,149,150,151,152,153,154,155,156,157,158,159,160,161,162,163,164,196] --> Loop 60 * CEs [143,165,166,167,168,169,170,171,172,174,175,176,177,178,179,180,181,182,183,184,185,187,188,189,190,191,192,193,194,195,198] --> Loop 61 ### Ranking functions of CR start(V1,V,V9,V14,V22) #### Partial ranking functions of CR start(V1,V,V9,V14,V22) Computing Bounds ===================================== #### Cost of chains of ge(V1,V,Out): * Chain [[20],23]: 1*it(20)+1 Such that:it(20) =< V1 with precondition: [Out=1,V1>=1,V>=V1+1] * Chain [[20],22]: 1*it(20)+1 Such that:it(20) =< V with precondition: [Out=2,V>=1,V1>=V] * Chain [[20],21]: 1*it(20)+0 Such that:it(20) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [23]: 1 with precondition: [V1=0,Out=1,V>=1] * Chain [22]: 1 with precondition: [V=0,Out=2,V1>=0] * Chain [21]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of helpc(V1,V,V9,Out): * Chain [26]: 1 with precondition: [V1=1,V9=Out,V>=0,V9>=0] * Chain [25]: 1 with precondition: [V1=2,V=Out,V>=0,V9>=0] * Chain [24]: 0 with precondition: [Out=0,V1>=0,V>=0,V9>=0] #### Cost of chains of length(V1,Out): * Chain [[27],28]: 1*it(27)+1 Such that:it(27) =< V1 with precondition: [Out>=1,V1>=Out] * Chain [28]: 1 with precondition: [Out=0,V1>=0] #### Cost of chains of greater(V1,V,Out): * Chain [31]: 9*s(3)+5*s(6)+4 Such that:aux(5) =< V1 aux(6) =< V s(6) =< aux(5) s(3) =< aux(6) with precondition: [Out=0,V1>=0,V>=0] * Chain [30]: 2*s(18)+2*s(20)+5 Such that:aux(7) =< V aux(8) =< V1 s(18) =< aux(8) s(20) =< aux(7) with precondition: [V1=Out,V1>=0,V>=0] * Chain [29]: 3*s(22)+1*s(23)+5 Such that:s(23) =< V1 aux(10) =< V s(22) =< aux(10) with precondition: [V=Out,V1>=0,V>=1] #### Cost of chains of smaller(V1,V,Out): * Chain [34]: 9*s(27)+5*s(30)+4 Such that:aux(15) =< V1 aux(16) =< V s(30) =< aux(15) s(27) =< aux(16) with precondition: [Out=0,V1>=0,V>=0] * Chain [33]: 3*s(42)+1*s(43)+5 Such that:s(43) =< V1 aux(18) =< V s(42) =< aux(18) with precondition: [V1=Out,V1>=0,V>=1] * Chain [32]: 2*s(46)+2*s(48)+5 Such that:aux(19) =< V aux(20) =< V1 s(46) =< aux(20) s(48) =< aux(19) with precondition: [V=Out,V1>=0,V>=0] #### Cost of chains of helpa(V1,V,V9,V14,Out): * Chain [[35,36,37,38,39,40],48]: 69*it(35)+13*it(39)+13*s(50)+264*s(56)+1*s(274)+8*s(275)+4*s(279)+31*s(280)+1*s(294)+6*s(295)+12*s(296)+11*s(301)+13 Such that:aux(118) =< V1+V9+V14 aux(143) =< V+2*V9+2*V14 aux(149) =< -V1+V aux(150) =< V aux(151) =< V9+V14 aux(152) =< V14 s(50) =< aux(150) s(56) =< aux(151) it(35) =< aux(149) it(39) =< aux(149) aux(87) =< aux(151) aux(86) =< aux(150) aux(113) =< aux(151)-1 aux(116) =< it(35)*aux(143) aux(77) =< it(35)*aux(151) s(274) =< it(35)*aux(150) aux(126) =< it(35)*aux(87) s(279) =< it(35)*aux(86) aux(105) =< it(35)*aux(113) s(297) =< aux(105)+aux(77)+aux(152) s(302) =< aux(105)+aux(77)+aux(152) s(298) =< aux(116)+aux(116)+aux(118) s(302) =< aux(116)+aux(116)+aux(118) it(39) =< aux(105)+aux(77)+aux(152) s(297) =< it(39)*aux(87) s(298) =< it(39)*aux(87) s(294) =< it(39)*aux(86) s(280) =< aux(126) s(301) =< s(302) s(295) =< s(298) s(296) =< s(297) s(275) =< aux(77) with precondition: [V1>=1,V9>=0,V14>=0,Out>=1,V>=V1+1,V9+V14>=1] * Chain [48]: 3*s(50)+10*s(51)+96*s(56)+168*s(57)+13 Such that:aux(57) =< V1 aux(58) =< V aux(59) =< V9 aux(60) =< V14 s(51) =< aux(57) s(50) =< aux(58) s(56) =< aux(59) s(57) =< aux(60) with precondition: [Out=0,V1>=0,V>=0,V9>=0,V14>=0] * Chain [47]: 3 with precondition: [V=0,Out=0,V1>=0,V9>=0,V14>=0] * Chain [46,[35,36,37,38,39,40],48]: 82*it(35)+13*it(39)+271*s(56)+1*s(274)+8*s(275)+4*s(279)+31*s(280)+1*s(294)+6*s(295)+12*s(296)+11*s(301)+11*s(307)+26 Such that:aux(143) =< V+2*V9 aux(154) =< V14 aux(155) =< V aux(156) =< V9 it(35) =< aux(155) s(56) =< aux(156) it(39) =< aux(155) aux(87) =< aux(156) aux(86) =< aux(155) aux(113) =< aux(156)-1 aux(116) =< it(35)*aux(143) aux(77) =< it(35)*aux(156) s(274) =< it(35)*aux(155) aux(126) =< it(35)*aux(87) s(279) =< it(35)*aux(86) aux(105) =< it(35)*aux(113) s(297) =< aux(105)+aux(77) s(302) =< aux(105)+aux(77) s(298) =< aux(116)+aux(116)+aux(156) s(302) =< aux(116)+aux(116)+aux(156) it(39) =< aux(105)+aux(77) s(297) =< it(39)*aux(87) s(298) =< it(39)*aux(87) s(294) =< it(39)*aux(86) s(280) =< aux(126) s(301) =< s(302) s(295) =< s(298) s(296) =< s(297) s(275) =< aux(77) s(307) =< aux(154) with precondition: [V1=0,V>=2,V9>=2,V14>=0,Out>=2] * Chain [46,48]: 3*s(50)+10*s(51)+96*s(56)+7*s(306)+11*s(307)+26 Such that:aux(57) =< 1 aux(58) =< V aux(153) =< V9 aux(59) =< V9-Out aux(154) =< V14 s(51) =< aux(57) s(50) =< aux(58) s(56) =< aux(59) s(306) =< aux(153) s(307) =< aux(154) with precondition: [V1=0,V>=1,V14>=0,Out>=1,V9>=Out] * Chain [45,[35,36,37,38,39,40],48]: 82*it(35)+13*it(39)+276*s(56)+1*s(274)+8*s(275)+4*s(279)+31*s(280)+1*s(294)+6*s(295)+12*s(296)+11*s(301)+6*s(312)+26 Such that:aux(143) =< V+2*V14 aux(157) =< V9 aux(159) =< V aux(160) =< V14 it(35) =< aux(159) s(56) =< aux(160) it(39) =< aux(159) aux(87) =< aux(160) aux(86) =< aux(159) aux(113) =< aux(160)-1 aux(116) =< it(35)*aux(143) aux(77) =< it(35)*aux(160) s(274) =< it(35)*aux(159) aux(126) =< it(35)*aux(87) s(279) =< it(35)*aux(86) aux(105) =< it(35)*aux(113) s(297) =< aux(105)+aux(77) s(302) =< aux(105)+aux(77) s(298) =< aux(116)+aux(116)+aux(160) s(302) =< aux(116)+aux(116)+aux(160) it(39) =< aux(105)+aux(77) s(297) =< it(39)*aux(87) s(298) =< it(39)*aux(87) s(294) =< it(39)*aux(86) s(280) =< aux(126) s(301) =< s(302) s(295) =< s(298) s(296) =< s(297) s(275) =< aux(77) s(312) =< aux(157) with precondition: [V1=0,V>=2,V9>=0,V14>=2,Out>=2] * Chain [45,48]: 3*s(50)+10*s(51)+96*s(56)+6*s(312)+12*s(314)+26 Such that:aux(57) =< 1 aux(58) =< V aux(157) =< V9 aux(158) =< V14 aux(59) =< V14-Out s(51) =< aux(57) s(50) =< aux(58) s(56) =< aux(59) s(312) =< aux(157) s(314) =< aux(158) with precondition: [V1=0,V>=1,V9>=0,Out>=1,V14>=Out] * Chain [44,[35,36,37,38,39,40],48]: 82*it(35)+13*it(39)+264*s(56)+1*s(274)+8*s(275)+4*s(279)+31*s(280)+1*s(294)+6*s(295)+12*s(296)+11*s(301)+3*s(321)+5*s(322)+27 Such that:aux(143) =< V+4*V9 aux(161) =< V14 aux(163) =< V aux(164) =< V9 aux(165) =< 2*V9 it(35) =< aux(163) s(56) =< aux(165) it(39) =< aux(163) aux(87) =< aux(165) aux(86) =< aux(163) aux(113) =< aux(165)-1 aux(116) =< it(35)*aux(143) aux(77) =< it(35)*aux(165) s(274) =< it(35)*aux(163) aux(126) =< it(35)*aux(87) s(279) =< it(35)*aux(86) aux(105) =< it(35)*aux(113) s(297) =< aux(105)+aux(77)+aux(164) s(302) =< aux(105)+aux(77)+aux(164) s(298) =< aux(116)+aux(116)+aux(165) s(302) =< aux(116)+aux(116)+aux(165) it(39) =< aux(105)+aux(77)+aux(164) s(297) =< it(39)*aux(87) s(298) =< it(39)*aux(87) s(294) =< it(39)*aux(86) s(280) =< aux(126) s(301) =< s(302) s(295) =< s(298) s(296) =< s(297) s(275) =< aux(77) s(321) =< aux(164) s(322) =< aux(161) with precondition: [V1=0,V>=2,V9>=1,V14>=1,Out>=2] * Chain [44,48]: 3*s(50)+10*s(51)+96*s(56)+171*s(57)+5*s(322)+27 Such that:aux(57) =< 1 aux(58) =< V aux(59) =< V9-Out aux(161) =< V14 aux(166) =< V9 s(51) =< aux(57) s(50) =< aux(58) s(56) =< aux(59) s(57) =< aux(166) s(322) =< aux(161) with precondition: [V1=0,V>=1,V14>=1,Out>=1,V9>=Out] * Chain [43,[35,36,37,38,39,40],48]: 82*it(35)+13*it(39)+264*s(56)+1*s(274)+8*s(275)+4*s(279)+31*s(280)+1*s(294)+6*s(295)+12*s(296)+11*s(301)+2*s(326)+6*s(328)+27 Such that:aux(143) =< V+2*V9+2*V14 aux(167) =< V14 aux(169) =< V aux(170) =< V9 aux(171) =< V9+V14 it(35) =< aux(169) s(56) =< aux(171) it(39) =< aux(169) aux(87) =< aux(171) aux(86) =< aux(169) aux(113) =< aux(171)-1 aux(116) =< it(35)*aux(143) aux(77) =< it(35)*aux(171) s(274) =< it(35)*aux(169) aux(126) =< it(35)*aux(87) s(279) =< it(35)*aux(86) aux(105) =< it(35)*aux(113) s(297) =< aux(105)+aux(77)+aux(170) s(302) =< aux(105)+aux(77)+aux(170) s(298) =< aux(116)+aux(116)+aux(171) s(302) =< aux(116)+aux(116)+aux(171) it(39) =< aux(105)+aux(77)+aux(170) s(297) =< it(39)*aux(87) s(298) =< it(39)*aux(87) s(294) =< it(39)*aux(86) s(280) =< aux(126) s(301) =< s(302) s(295) =< s(298) s(296) =< s(297) s(275) =< aux(77) s(326) =< aux(170) s(328) =< aux(167) with precondition: [V1=0,V>=2,V9>=0,V14>=1,Out>=2,V9+V14>=2] * Chain [43,48]: 3*s(50)+10*s(51)+96*s(56)+170*s(57)+6*s(328)+27 Such that:aux(57) =< 1 aux(58) =< V aux(167) =< V14 aux(59) =< V14-Out aux(172) =< V9 s(51) =< aux(57) s(50) =< aux(58) s(56) =< aux(59) s(57) =< aux(172) s(328) =< aux(167) with precondition: [V1=0,V>=1,V9>=0,Out>=1,V14>=Out] * Chain [42,[35,36,37,38,39,40],48]: 82*it(35)+13*it(39)+264*s(56)+1*s(274)+8*s(275)+4*s(279)+31*s(280)+1*s(294)+6*s(295)+12*s(296)+11*s(301)+4*s(334)+4*s(335)+27 Such that:aux(143) =< V+2*V9+2*V14 aux(173) =< V9 aux(175) =< V aux(176) =< V9+V14 aux(177) =< V14 it(35) =< aux(175) s(56) =< aux(176) it(39) =< aux(175) aux(87) =< aux(176) aux(86) =< aux(175) aux(113) =< aux(176)-1 aux(116) =< it(35)*aux(143) aux(77) =< it(35)*aux(176) s(274) =< it(35)*aux(175) aux(126) =< it(35)*aux(87) s(279) =< it(35)*aux(86) aux(105) =< it(35)*aux(113) s(297) =< aux(105)+aux(77)+aux(177) s(302) =< aux(105)+aux(77)+aux(177) s(298) =< aux(116)+aux(116)+aux(176) s(302) =< aux(116)+aux(116)+aux(176) it(39) =< aux(105)+aux(77)+aux(177) s(297) =< it(39)*aux(87) s(298) =< it(39)*aux(87) s(294) =< it(39)*aux(86) s(280) =< aux(126) s(301) =< s(302) s(295) =< s(298) s(296) =< s(297) s(275) =< aux(77) s(334) =< aux(173) s(335) =< aux(177) with precondition: [V1=0,V>=2,V9>=1,V14>=0,Out>=2,V9+V14>=2] * Chain [42,48]: 3*s(50)+10*s(51)+96*s(56)+172*s(57)+4*s(334)+27 Such that:aux(57) =< 1 aux(58) =< V aux(173) =< V9 aux(59) =< V9-Out aux(178) =< V14 s(51) =< aux(57) s(50) =< aux(58) s(56) =< aux(59) s(57) =< aux(178) s(334) =< aux(173) with precondition: [V1=0,V>=1,V14>=0,Out>=1,V9>=Out] * Chain [41,[35,36,37,38,39,40],48]: 82*it(35)+13*it(39)+264*s(56)+1*s(274)+8*s(275)+4*s(279)+31*s(280)+1*s(294)+6*s(295)+12*s(296)+11*s(301)+3*s(340)+5*s(342)+27 Such that:aux(143) =< V+4*V14 aux(179) =< V9 aux(181) =< V aux(182) =< V14 aux(183) =< 2*V14 it(35) =< aux(181) s(56) =< aux(183) it(39) =< aux(181) aux(87) =< aux(183) aux(86) =< aux(181) aux(113) =< aux(183)-1 aux(116) =< it(35)*aux(143) aux(77) =< it(35)*aux(183) s(274) =< it(35)*aux(181) aux(126) =< it(35)*aux(87) s(279) =< it(35)*aux(86) aux(105) =< it(35)*aux(113) s(297) =< aux(105)+aux(77)+aux(182) s(302) =< aux(105)+aux(77)+aux(182) s(298) =< aux(116)+aux(116)+aux(183) s(302) =< aux(116)+aux(116)+aux(183) it(39) =< aux(105)+aux(77)+aux(182) s(297) =< it(39)*aux(87) s(298) =< it(39)*aux(87) s(294) =< it(39)*aux(86) s(280) =< aux(126) s(301) =< s(302) s(295) =< s(298) s(296) =< s(297) s(275) =< aux(77) s(340) =< aux(179) s(342) =< aux(182) with precondition: [V1=0,V>=2,V9>=0,V14>=1,Out>=2] * Chain [41,48]: 3*s(50)+10*s(51)+96*s(56)+173*s(57)+3*s(340)+27 Such that:aux(57) =< 1 aux(58) =< V aux(179) =< V9 aux(59) =< V14-Out aux(184) =< V14 s(51) =< aux(57) s(50) =< aux(58) s(56) =< aux(59) s(57) =< aux(184) s(340) =< aux(179) with precondition: [V1=0,V>=1,V9>=0,Out>=1,V14>=Out] #### Cost of chains of plus(V1,V,Out): * Chain [[49],51]: 1*it(49)+1 Such that:it(49) =< V with precondition: [V+V1=Out,V1>=0,V>=1] * Chain [[49],50]: 1*it(49)+0 Such that:it(49) =< Out with precondition: [V1>=0,Out>=1,V>=Out] * Chain [51]: 1 with precondition: [V=0,V1=Out,V1>=0] * Chain [50]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of app(V1,V,Out): * Chain [57]: 968*s(585)+1699*s(586)+3*s(660)+17 Such that:s(656) =< V1+V aux(217) =< V1 aux(218) =< V s(585) =< aux(217) s(586) =< aux(218) s(660) =< s(656) with precondition: [Out=0,V1>=0,V>=0] * Chain [56]: 2409*s(674)+1584*s(687)+39*s(688)+18*s(694)+72*s(696)+3*s(701)+186*s(702)+33*s(703)+18*s(704)+36*s(705)+48*s(706)+869*s(707)+792*s(709)+39*s(710)+3*s(720)+93*s(721)+33*s(722)+18*s(723)+36*s(724)+24*s(725)+39*s(726)+3*s(736)+93*s(737)+33*s(738)+18*s(739)+36*s(740)+24*s(741)+792*s(742)+39*s(743)+3*s(753)+93*s(754)+33*s(755)+18*s(756)+36*s(757)+24*s(758)+39*s(769)+3*s(782)+93*s(783)+33*s(784)+18*s(785)+36*s(786)+24*s(787)+39*s(790)+3*s(800)+33*s(802)+18*s(803)+36*s(804)+31 Such that:aux(227) =< V1 aux(228) =< V1+V aux(229) =< 2*V1 aux(230) =< 2*V1+V aux(231) =< 2*V1+3*V aux(232) =< 4*V1+V aux(233) =< V aux(234) =< 2*V aux(235) =< 3*V aux(236) =< 5*V s(674) =< aux(233) s(687) =< aux(228) s(688) =< aux(233) s(689) =< aux(228) s(690) =< aux(233) s(691) =< aux(228)-1 s(692) =< s(674)*aux(231) s(693) =< s(674)*aux(228) s(694) =< s(674)*aux(233) s(695) =< s(674)*s(689) s(696) =< s(674)*s(690) s(697) =< s(674)*s(691) s(698) =< s(697)+s(693)+aux(227) s(699) =< s(697)+s(693)+aux(227) s(700) =< s(692)+s(692)+aux(228) s(699) =< s(692)+s(692)+aux(228) s(688) =< s(697)+s(693)+aux(227) s(698) =< s(688)*s(689) s(700) =< s(688)*s(689) s(701) =< s(688)*s(690) s(702) =< s(695) s(703) =< s(699) s(704) =< s(700) s(705) =< s(698) s(706) =< s(693) s(707) =< aux(227) s(709) =< aux(229) s(710) =< aux(233) s(711) =< aux(229) s(712) =< aux(229)-1 s(713) =< s(674)*aux(232) s(714) =< s(674)*aux(229) s(715) =< s(674)*s(711) s(716) =< s(674)*s(712) s(717) =< s(716)+s(714)+aux(227) s(718) =< s(716)+s(714)+aux(227) s(719) =< s(713)+s(713)+aux(229) s(718) =< s(713)+s(713)+aux(229) s(710) =< s(716)+s(714)+aux(227) s(717) =< s(710)*s(711) s(719) =< s(710)*s(711) s(720) =< s(710)*s(690) s(721) =< s(715) s(722) =< s(718) s(723) =< s(719) s(724) =< s(717) s(725) =< s(714) s(726) =< aux(233) s(728) =< aux(233)-1 s(729) =< s(674)*aux(235) s(730) =< s(674)*aux(233) s(731) =< s(674)*s(690) s(732) =< s(674)*s(728) s(733) =< s(732)+s(730) s(734) =< s(732)+s(730) s(735) =< s(729)+s(729)+aux(233) s(734) =< s(729)+s(729)+aux(233) s(726) =< s(732)+s(730) s(733) =< s(726)*s(690) s(735) =< s(726)*s(690) s(736) =< s(726)*s(690) s(737) =< s(731) s(738) =< s(734) s(739) =< s(735) s(740) =< s(733) s(741) =< s(730) s(742) =< aux(234) s(743) =< aux(233) s(744) =< aux(234) s(745) =< aux(234)-1 s(746) =< s(674)*aux(236) s(747) =< s(674)*aux(234) s(748) =< s(674)*s(744) s(749) =< s(674)*s(745) s(750) =< s(749)+s(747)+aux(233) s(751) =< s(749)+s(747)+aux(233) s(752) =< s(746)+s(746)+aux(234) s(751) =< s(746)+s(746)+aux(234) s(743) =< s(749)+s(747)+aux(233) s(750) =< s(743)*s(744) s(752) =< s(743)*s(744) s(753) =< s(743)*s(690) s(754) =< s(748) s(755) =< s(751) s(756) =< s(752) s(757) =< s(750) s(758) =< s(747) s(769) =< aux(233) s(770) =< aux(227) s(772) =< aux(227)-1 s(773) =< s(674)*aux(230) s(774) =< s(674)*aux(227) s(776) =< s(674)*s(770) s(778) =< s(674)*s(772) s(779) =< s(778)+s(774) s(780) =< s(778)+s(774) s(781) =< s(773)+s(773)+aux(227) s(780) =< s(773)+s(773)+aux(227) s(769) =< s(778)+s(774) s(779) =< s(769)*s(770) s(781) =< s(769)*s(770) s(782) =< s(769)*s(690) s(783) =< s(776) s(784) =< s(780) s(785) =< s(781) s(786) =< s(779) s(787) =< s(774) s(790) =< aux(233) s(797) =< s(697)+s(693)+aux(233) s(798) =< s(697)+s(693)+aux(233) s(799) =< s(692)+s(692)+aux(228) s(798) =< s(692)+s(692)+aux(228) s(790) =< s(697)+s(693)+aux(233) s(797) =< s(790)*s(689) s(799) =< s(790)*s(689) s(800) =< s(790)*s(690) s(802) =< s(798) s(803) =< s(799) s(804) =< s(797) with precondition: [V1>=0,V>=2,Out>=2] * Chain [55]: 2430*s(1072)+150*s(1079)+907*s(1083)+9*s(1116)+31 Such that:s(1111) =< V1+V aux(245) =< 1 aux(246) =< V1 aux(247) =< V s(1072) =< aux(247) s(1079) =< aux(245) s(1083) =< aux(246) s(1116) =< s(1111) with precondition: [V1>=0,Out>=1,V>=Out] * Chain [54]: 634*s(1133)+1284*s(1145)+13*s(1146)+4*s(1152)+16*s(1154)+1*s(1159)+31*s(1160)+11*s(1161)+6*s(1162)+12*s(1163)+8*s(1164)+603*s(1166)+528*s(1167)+13*s(1168)+1*s(1178)+31*s(1179)+11*s(1180)+6*s(1181)+12*s(1182)+8*s(1183)+13*s(1184)+1*s(1194)+31*s(1195)+11*s(1196)+6*s(1197)+12*s(1198)+8*s(1199)+528*s(1200)+13*s(1201)+1*s(1211)+31*s(1212)+11*s(1213)+6*s(1214)+12*s(1215)+8*s(1216)+13*s(1232)+6*s(1238)+24*s(1240)+1*s(1245)+62*s(1246)+11*s(1247)+6*s(1248)+12*s(1249)+16*s(1250)+13*s(1254)+1*s(1264)+31*s(1265)+11*s(1266)+6*s(1267)+12*s(1268)+8*s(1269)+13*s(1270)+1*s(1280)+31*s(1281)+11*s(1282)+6*s(1283)+12*s(1284)+8*s(1285)+13*s(1287)+1*s(1297)+31*s(1298)+11*s(1299)+6*s(1300)+12*s(1301)+8*s(1302)+13*s(1314)+1*s(1327)+31*s(1328)+11*s(1329)+6*s(1330)+12*s(1331)+8*s(1332)+13*s(1335)+1*s(1345)+11*s(1347)+6*s(1348)+12*s(1349)+31 Such that:s(1136) =< V1+2*V s(1222) =< V1+3*V s(1137) =< V1+4*V s(1223) =< V1+5*V s(1306) =< 3*V1+V s(1134) =< 3*V1+2*V s(1135) =< 5*V1 s(1221) =< 5*V1+V aux(255) =< V1 aux(256) =< V1+V aux(257) =< 2*V1 aux(258) =< 3*V1+3*V aux(259) =< V aux(260) =< 2*V s(1133) =< aux(255) s(1145) =< aux(256) s(1146) =< aux(255) s(1147) =< aux(256) s(1148) =< aux(255) s(1149) =< aux(256)-1 s(1150) =< s(1133)*s(1134) s(1151) =< s(1133)*aux(256) s(1152) =< s(1133)*aux(255) s(1153) =< s(1133)*s(1147) s(1154) =< s(1133)*s(1148) s(1155) =< s(1133)*s(1149) s(1156) =< s(1155)+s(1151)+aux(255) s(1157) =< s(1155)+s(1151)+aux(255) s(1158) =< s(1150)+s(1150)+aux(256) s(1157) =< s(1150)+s(1150)+aux(256) s(1146) =< s(1155)+s(1151)+aux(255) s(1156) =< s(1146)*s(1147) s(1158) =< s(1146)*s(1147) s(1159) =< s(1146)*s(1148) s(1160) =< s(1153) s(1161) =< s(1157) s(1162) =< s(1158) s(1163) =< s(1156) s(1164) =< s(1151) s(1166) =< aux(259) s(1167) =< aux(257) s(1168) =< aux(255) s(1169) =< aux(257) s(1170) =< aux(257)-1 s(1171) =< s(1133)*s(1135) s(1172) =< s(1133)*aux(257) s(1173) =< s(1133)*s(1169) s(1174) =< s(1133)*s(1170) s(1175) =< s(1174)+s(1172)+aux(255) s(1176) =< s(1174)+s(1172)+aux(255) s(1177) =< s(1171)+s(1171)+aux(257) s(1176) =< s(1171)+s(1171)+aux(257) s(1168) =< s(1174)+s(1172)+aux(255) s(1175) =< s(1168)*s(1169) s(1177) =< s(1168)*s(1169) s(1178) =< s(1168)*s(1148) s(1179) =< s(1173) s(1180) =< s(1176) s(1181) =< s(1177) s(1182) =< s(1175) s(1183) =< s(1172) s(1184) =< aux(255) s(1185) =< aux(259) s(1186) =< aux(259)-1 s(1187) =< s(1133)*s(1136) s(1188) =< s(1133)*aux(259) s(1189) =< s(1133)*s(1185) s(1190) =< s(1133)*s(1186) s(1191) =< s(1190)+s(1188) s(1192) =< s(1190)+s(1188) s(1193) =< s(1187)+s(1187)+aux(259) s(1192) =< s(1187)+s(1187)+aux(259) s(1184) =< s(1190)+s(1188) s(1191) =< s(1184)*s(1185) s(1193) =< s(1184)*s(1185) s(1194) =< s(1184)*s(1148) s(1195) =< s(1189) s(1196) =< s(1192) s(1197) =< s(1193) s(1198) =< s(1191) s(1199) =< s(1188) s(1200) =< aux(260) s(1201) =< aux(255) s(1202) =< aux(260) s(1203) =< aux(260)-1 s(1204) =< s(1133)*s(1137) s(1205) =< s(1133)*aux(260) s(1206) =< s(1133)*s(1202) s(1207) =< s(1133)*s(1203) s(1208) =< s(1207)+s(1205)+aux(259) s(1209) =< s(1207)+s(1205)+aux(259) s(1210) =< s(1204)+s(1204)+aux(260) s(1209) =< s(1204)+s(1204)+aux(260) s(1201) =< s(1207)+s(1205)+aux(259) s(1208) =< s(1201)*s(1202) s(1210) =< s(1201)*s(1202) s(1211) =< s(1201)*s(1148) s(1212) =< s(1206) s(1213) =< s(1209) s(1214) =< s(1210) s(1215) =< s(1208) s(1216) =< s(1205) s(1232) =< aux(256) s(1236) =< s(1145)*aux(258) s(1237) =< s(1145)*aux(256) s(1238) =< s(1145)*aux(256) s(1239) =< s(1145)*s(1147) s(1240) =< s(1145)*s(1147) s(1241) =< s(1145)*s(1149) s(1242) =< s(1241)+s(1237)+aux(255) s(1243) =< s(1241)+s(1237)+aux(255) s(1244) =< s(1236)+s(1236)+aux(256) s(1243) =< s(1236)+s(1236)+aux(256) s(1232) =< s(1241)+s(1237)+aux(255) s(1242) =< s(1232)*s(1147) s(1244) =< s(1232)*s(1147) s(1245) =< s(1232)*s(1147) s(1246) =< s(1239) s(1247) =< s(1243) s(1248) =< s(1244) s(1249) =< s(1242) s(1250) =< s(1237) s(1254) =< aux(256) s(1257) =< s(1145)*s(1221) s(1258) =< s(1145)*aux(257) s(1259) =< s(1145)*s(1169) s(1260) =< s(1145)*s(1170) s(1261) =< s(1260)+s(1258)+aux(255) s(1262) =< s(1260)+s(1258)+aux(255) s(1263) =< s(1257)+s(1257)+aux(257) s(1262) =< s(1257)+s(1257)+aux(257) s(1254) =< s(1260)+s(1258)+aux(255) s(1261) =< s(1254)*s(1169) s(1263) =< s(1254)*s(1169) s(1264) =< s(1254)*s(1147) s(1265) =< s(1259) s(1266) =< s(1262) s(1267) =< s(1263) s(1268) =< s(1261) s(1269) =< s(1258) s(1270) =< aux(256) s(1273) =< s(1145)*s(1222) s(1274) =< s(1145)*aux(259) s(1275) =< s(1145)*s(1185) s(1276) =< s(1145)*s(1186) s(1277) =< s(1276)+s(1274) s(1278) =< s(1276)+s(1274) s(1279) =< s(1273)+s(1273)+aux(259) s(1278) =< s(1273)+s(1273)+aux(259) s(1270) =< s(1276)+s(1274) s(1277) =< s(1270)*s(1185) s(1279) =< s(1270)*s(1185) s(1280) =< s(1270)*s(1147) s(1281) =< s(1275) s(1282) =< s(1278) s(1283) =< s(1279) s(1284) =< s(1277) s(1285) =< s(1274) s(1287) =< aux(256) s(1290) =< s(1145)*s(1223) s(1291) =< s(1145)*aux(260) s(1292) =< s(1145)*s(1202) s(1293) =< s(1145)*s(1203) s(1294) =< s(1293)+s(1291)+aux(259) s(1295) =< s(1293)+s(1291)+aux(259) s(1296) =< s(1290)+s(1290)+aux(260) s(1295) =< s(1290)+s(1290)+aux(260) s(1287) =< s(1293)+s(1291)+aux(259) s(1294) =< s(1287)*s(1202) s(1296) =< s(1287)*s(1202) s(1297) =< s(1287)*s(1147) s(1298) =< s(1292) s(1299) =< s(1295) s(1300) =< s(1296) s(1301) =< s(1294) s(1302) =< s(1291) s(1314) =< aux(256) s(1317) =< aux(255)-1 s(1318) =< s(1145)*s(1306) s(1319) =< s(1145)*aux(255) s(1321) =< s(1145)*s(1148) s(1323) =< s(1145)*s(1317) s(1324) =< s(1323)+s(1319) s(1325) =< s(1323)+s(1319) s(1326) =< s(1318)+s(1318)+aux(255) s(1325) =< s(1318)+s(1318)+aux(255) s(1314) =< s(1323)+s(1319) s(1324) =< s(1314)*s(1148) s(1326) =< s(1314)*s(1148) s(1327) =< s(1314)*s(1147) s(1328) =< s(1321) s(1329) =< s(1325) s(1330) =< s(1326) s(1331) =< s(1324) s(1332) =< s(1319) s(1335) =< aux(256) s(1342) =< s(1241)+s(1237)+aux(259) s(1343) =< s(1241)+s(1237)+aux(259) s(1344) =< s(1236)+s(1236)+aux(256) s(1343) =< s(1236)+s(1236)+aux(256) s(1335) =< s(1241)+s(1237)+aux(259) s(1342) =< s(1335)*s(1147) s(1344) =< s(1335)*s(1147) s(1345) =< s(1335)*s(1147) s(1347) =< s(1343) s(1348) =< s(1344) s(1349) =< s(1342) with precondition: [V1>=1,V>=1,Out>=2] * Chain [53]: 440*s(1351)+13*s(1360)+2*s(1366)+8*s(1368)+1*s(1373)+31*s(1374)+11*s(1375)+6*s(1376)+12*s(1377)+8*s(1378)+15*s(1379)+264*s(1380)+13*s(1381)+1*s(1391)+31*s(1392)+11*s(1393)+6*s(1394)+12*s(1395)+8*s(1396)+31 Such that:s(1354) =< V1+V s(1352) =< 3*V1 s(1353) =< 3*V1+2*V s(1357) =< V aux(261) =< V1 s(1351) =< aux(261) s(1360) =< aux(261) s(1361) =< aux(261) s(1363) =< aux(261)-1 s(1364) =< s(1351)*s(1352) s(1365) =< s(1351)*aux(261) s(1366) =< s(1351)*aux(261) s(1367) =< s(1351)*s(1361) s(1368) =< s(1351)*s(1361) s(1369) =< s(1351)*s(1363) s(1370) =< s(1369)+s(1365) s(1371) =< s(1369)+s(1365) s(1372) =< s(1364)+s(1364)+aux(261) s(1371) =< s(1364)+s(1364)+aux(261) s(1360) =< s(1369)+s(1365) s(1370) =< s(1360)*s(1361) s(1372) =< s(1360)*s(1361) s(1373) =< s(1360)*s(1361) s(1374) =< s(1367) s(1375) =< s(1371) s(1376) =< s(1372) s(1377) =< s(1370) s(1378) =< s(1365) s(1379) =< s(1357) s(1380) =< s(1354) s(1381) =< aux(261) s(1382) =< s(1354) s(1383) =< s(1354)-1 s(1384) =< s(1351)*s(1353) s(1385) =< s(1351)*s(1354) s(1386) =< s(1351)*s(1382) s(1387) =< s(1351)*s(1383) s(1388) =< s(1387)+s(1385)+s(1357) s(1389) =< s(1387)+s(1385)+s(1357) s(1390) =< s(1384)+s(1384)+s(1354) s(1389) =< s(1384)+s(1384)+s(1354) s(1381) =< s(1387)+s(1385)+s(1357) s(1388) =< s(1381)*s(1382) s(1390) =< s(1381)*s(1382) s(1391) =< s(1381)*s(1361) s(1392) =< s(1386) s(1393) =< s(1389) s(1394) =< s(1390) s(1395) =< s(1388) s(1396) =< s(1385) with precondition: [V1>=2,V>=0,Out>=2] * Chain [52]: 975*s(1397)+150*s(1404)+2362*s(1406)+9*s(1441)+31 Such that:s(1436) =< V1+V aux(271) =< 1 aux(272) =< V1 aux(273) =< V s(1397) =< aux(273) s(1404) =< aux(271) s(1406) =< aux(272) s(1441) =< s(1436) with precondition: [V>=0,Out>=1,V1>=Out] #### Cost of chains of start(V1,V,V9,V14,V22): * Chain [61]: 10*s(1462)+8705*s(1463)+1130*s(1464)+1310*s(1465)+1056*s(1473)+138*s(1474)+26*s(1475)+2*s(1481)+8*s(1483)+2*s(1488)+62*s(1489)+22*s(1490)+12*s(1491)+24*s(1492)+16*s(1493)+6208*s(1497)+3153*s(1499)+39*s(1512)+24*s(1518)+96*s(1520)+3*s(1525)+186*s(1526)+33*s(1527)+18*s(1528)+36*s(1529)+48*s(1530)+1320*s(1532)+39*s(1533)+3*s(1543)+93*s(1544)+33*s(1545)+18*s(1546)+36*s(1547)+24*s(1548)+39*s(1549)+3*s(1558)+93*s(1559)+33*s(1560)+18*s(1561)+36*s(1562)+24*s(1563)+1320*s(1564)+39*s(1565)+3*s(1575)+93*s(1576)+33*s(1577)+18*s(1578)+36*s(1579)+24*s(1580)+39*s(1581)+3*s(1591)+93*s(1592)+33*s(1593)+18*s(1594)+36*s(1595)+24*s(1596)+39*s(1597)+3*s(1601)+33*s(1602)+18*s(1603)+36*s(1604)+360*s(1610)+13*s(1629)+6*s(1635)+24*s(1637)+1*s(1642)+62*s(1643)+11*s(1644)+6*s(1645)+12*s(1646)+16*s(1647)+13*s(1650)+1*s(1660)+31*s(1661)+11*s(1662)+6*s(1663)+12*s(1664)+8*s(1665)+13*s(1666)+1*s(1676)+31*s(1677)+11*s(1678)+6*s(1679)+12*s(1680)+8*s(1681)+13*s(1683)+1*s(1693)+31*s(1694)+11*s(1695)+6*s(1696)+12*s(1697)+8*s(1698)+13*s(1699)+6*s(1702)+24*s(1704)+1*s(1709)+62*s(1710)+11*s(1711)+6*s(1712)+12*s(1713)+16*s(1714)+13*s(1715)+1*s(1723)+31*s(1724)+11*s(1725)+6*s(1726)+12*s(1727)+8*s(1728)+13*s(1729)+1*s(1737)+31*s(1738)+11*s(1739)+6*s(1740)+12*s(1741)+8*s(1742)+13*s(1743)+1*s(1751)+31*s(1752)+11*s(1753)+6*s(1754)+12*s(1755)+8*s(1756)+13*s(1757)+1*s(1766)+31*s(1767)+11*s(1768)+6*s(1769)+12*s(1770)+8*s(1771)+13*s(1772)+1*s(1776)+11*s(1777)+6*s(1778)+12*s(1779)+13*s(1786)+1*s(1798)+31*s(1799)+11*s(1800)+6*s(1801)+12*s(1802)+8*s(1803)+13*s(1806)+1*s(1816)+11*s(1818)+6*s(1819)+12*s(1820)+13*s(1865)+1*s(1878)+62*s(1879)+11*s(1880)+6*s(1881)+12*s(1882)+16*s(1883)+264*s(1886)+13*s(1887)+1*s(1897)+31*s(1898)+11*s(1899)+6*s(1900)+12*s(1901)+8*s(1902)+13*s(1903)+1*s(1913)+31*s(1914)+11*s(1915)+6*s(1916)+12*s(1917)+8*s(1918)+264*s(1919)+13*s(1920)+1*s(1930)+31*s(1931)+11*s(1932)+6*s(1933)+12*s(1934)+8*s(1935)+13*s(1944)+1*s(1957)+31*s(1958)+11*s(1959)+6*s(1960)+12*s(1961)+8*s(1962)+13*s(1965)+1*s(1975)+11*s(1977)+6*s(1978)+12*s(1979)+31 Such that:s(1458) =< V1+1 s(1613) =< V1+2*V s(1614) =< V1+3*V s(1615) =< V1+4*V s(1616) =< V1+5*V s(1503) =< 2*V1+V s(1504) =< 2*V1+3*V s(1781) =< 3*V1 s(1617) =< 3*V1+V s(1624) =< 3*V1+3*V s(1505) =< 4*V1+V s(1619) =< 5*V1 s(1620) =< 5*V1+V s(1936) =< V+2*V9 s(1854) =< V+4*V9 s(1855) =< V+2*V14 s(1856) =< V+4*V14 s(1508) =< 3*V s(1509) =< 5*V s(1858) =< 2*V9 s(1859) =< 2*V14 aux(276) =< 1 aux(277) =< -V1+V aux(278) =< V1 aux(279) =< V1+V aux(280) =< V1+V9+V14 aux(281) =< 2*V1 aux(282) =< 3*V1+2*V aux(283) =< V aux(284) =< V+2*V9+2*V14 aux(285) =< 2*V aux(286) =< V9 aux(287) =< V9+V14 aux(288) =< V14 s(1497) =< aux(278) s(1463) =< aux(283) s(1610) =< aux(276) s(1499) =< aux(279) s(1465) =< aux(288) s(1464) =< aux(286) s(1473) =< aux(287) s(1474) =< aux(277) s(1475) =< aux(277) s(1476) =< aux(287) s(1477) =< aux(283) s(1478) =< aux(287)-1 s(1479) =< s(1474)*aux(284) s(1480) =< s(1474)*aux(287) s(1481) =< s(1474)*aux(283) s(1482) =< s(1474)*s(1476) s(1483) =< s(1474)*s(1477) s(1484) =< s(1474)*s(1478) s(1485) =< s(1484)+s(1480)+aux(288) s(1486) =< s(1484)+s(1480)+aux(288) s(1487) =< s(1479)+s(1479)+aux(280) s(1486) =< s(1479)+s(1479)+aux(280) s(1475) =< s(1484)+s(1480)+aux(288) s(1485) =< s(1475)*s(1476) s(1487) =< s(1475)*s(1476) s(1488) =< s(1475)*s(1477) s(1489) =< s(1482) s(1490) =< s(1486) s(1491) =< s(1487) s(1492) =< s(1485) s(1493) =< s(1480) s(1512) =< aux(283) s(1513) =< aux(279) s(1515) =< aux(279)-1 s(1516) =< s(1463)*s(1504) s(1517) =< s(1463)*aux(279) s(1518) =< s(1463)*aux(283) s(1519) =< s(1463)*s(1513) s(1520) =< s(1463)*s(1477) s(1521) =< s(1463)*s(1515) s(1522) =< s(1521)+s(1517)+aux(278) s(1523) =< s(1521)+s(1517)+aux(278) s(1524) =< s(1516)+s(1516)+aux(279) s(1523) =< s(1516)+s(1516)+aux(279) s(1512) =< s(1521)+s(1517)+aux(278) s(1522) =< s(1512)*s(1513) s(1524) =< s(1512)*s(1513) s(1525) =< s(1512)*s(1477) s(1526) =< s(1519) s(1527) =< s(1523) s(1528) =< s(1524) s(1529) =< s(1522) s(1530) =< s(1517) s(1532) =< aux(281) s(1533) =< aux(283) s(1534) =< aux(281) s(1535) =< aux(281)-1 s(1536) =< s(1463)*s(1505) s(1537) =< s(1463)*aux(281) s(1538) =< s(1463)*s(1534) s(1539) =< s(1463)*s(1535) s(1540) =< s(1539)+s(1537)+aux(278) s(1541) =< s(1539)+s(1537)+aux(278) s(1542) =< s(1536)+s(1536)+aux(281) s(1541) =< s(1536)+s(1536)+aux(281) s(1533) =< s(1539)+s(1537)+aux(278) s(1540) =< s(1533)*s(1534) s(1542) =< s(1533)*s(1534) s(1543) =< s(1533)*s(1477) s(1544) =< s(1538) s(1545) =< s(1541) s(1546) =< s(1542) s(1547) =< s(1540) s(1548) =< s(1537) s(1549) =< aux(283) s(1550) =< aux(283)-1 s(1551) =< s(1463)*s(1508) s(1552) =< s(1463)*aux(283) s(1553) =< s(1463)*s(1477) s(1554) =< s(1463)*s(1550) s(1555) =< s(1554)+s(1552) s(1556) =< s(1554)+s(1552) s(1557) =< s(1551)+s(1551)+aux(283) s(1556) =< s(1551)+s(1551)+aux(283) s(1549) =< s(1554)+s(1552) s(1555) =< s(1549)*s(1477) s(1557) =< s(1549)*s(1477) s(1558) =< s(1549)*s(1477) s(1559) =< s(1553) s(1560) =< s(1556) s(1561) =< s(1557) s(1562) =< s(1555) s(1563) =< s(1552) s(1564) =< aux(285) s(1565) =< aux(283) s(1566) =< aux(285) s(1567) =< aux(285)-1 s(1568) =< s(1463)*s(1509) s(1569) =< s(1463)*aux(285) s(1570) =< s(1463)*s(1566) s(1571) =< s(1463)*s(1567) s(1572) =< s(1571)+s(1569)+aux(283) s(1573) =< s(1571)+s(1569)+aux(283) s(1574) =< s(1568)+s(1568)+aux(285) s(1573) =< s(1568)+s(1568)+aux(285) s(1565) =< s(1571)+s(1569)+aux(283) s(1572) =< s(1565)*s(1566) s(1574) =< s(1565)*s(1566) s(1575) =< s(1565)*s(1477) s(1576) =< s(1570) s(1577) =< s(1573) s(1578) =< s(1574) s(1579) =< s(1572) s(1580) =< s(1569) s(1581) =< aux(283) s(1582) =< aux(278) s(1583) =< aux(278)-1 s(1584) =< s(1463)*s(1503) s(1585) =< s(1463)*aux(278) s(1586) =< s(1463)*s(1582) s(1587) =< s(1463)*s(1583) s(1588) =< s(1587)+s(1585) s(1589) =< s(1587)+s(1585) s(1590) =< s(1584)+s(1584)+aux(278) s(1589) =< s(1584)+s(1584)+aux(278) s(1581) =< s(1587)+s(1585) s(1588) =< s(1581)*s(1582) s(1590) =< s(1581)*s(1582) s(1591) =< s(1581)*s(1477) s(1592) =< s(1586) s(1593) =< s(1589) s(1594) =< s(1590) s(1595) =< s(1588) s(1596) =< s(1585) s(1597) =< aux(283) s(1598) =< s(1521)+s(1517)+aux(283) s(1599) =< s(1521)+s(1517)+aux(283) s(1600) =< s(1516)+s(1516)+aux(279) s(1599) =< s(1516)+s(1516)+aux(279) s(1597) =< s(1521)+s(1517)+aux(283) s(1598) =< s(1597)*s(1513) s(1600) =< s(1597)*s(1513) s(1601) =< s(1597)*s(1477) s(1602) =< s(1599) s(1603) =< s(1600) s(1604) =< s(1598) s(1629) =< aux(278) s(1633) =< s(1497)*aux(282) s(1634) =< s(1497)*aux(279) s(1635) =< s(1497)*aux(278) s(1636) =< s(1497)*s(1513) s(1637) =< s(1497)*s(1582) s(1638) =< s(1497)*s(1515) s(1639) =< s(1638)+s(1634)+aux(278) s(1640) =< s(1638)+s(1634)+aux(278) s(1641) =< s(1633)+s(1633)+aux(279) s(1640) =< s(1633)+s(1633)+aux(279) s(1629) =< s(1638)+s(1634)+aux(278) s(1639) =< s(1629)*s(1513) s(1641) =< s(1629)*s(1513) s(1642) =< s(1629)*s(1582) s(1643) =< s(1636) s(1644) =< s(1640) s(1645) =< s(1641) s(1646) =< s(1639) s(1647) =< s(1634) s(1650) =< aux(278) s(1653) =< s(1497)*s(1619) s(1654) =< s(1497)*aux(281) s(1655) =< s(1497)*s(1534) s(1656) =< s(1497)*s(1535) s(1657) =< s(1656)+s(1654)+aux(278) s(1658) =< s(1656)+s(1654)+aux(278) s(1659) =< s(1653)+s(1653)+aux(281) s(1658) =< s(1653)+s(1653)+aux(281) s(1650) =< s(1656)+s(1654)+aux(278) s(1657) =< s(1650)*s(1534) s(1659) =< s(1650)*s(1534) s(1660) =< s(1650)*s(1582) s(1661) =< s(1655) s(1662) =< s(1658) s(1663) =< s(1659) s(1664) =< s(1657) s(1665) =< s(1654) s(1666) =< aux(278) s(1669) =< s(1497)*s(1613) s(1670) =< s(1497)*aux(283) s(1671) =< s(1497)*s(1477) s(1672) =< s(1497)*s(1550) s(1673) =< s(1672)+s(1670) s(1674) =< s(1672)+s(1670) s(1675) =< s(1669)+s(1669)+aux(283) s(1674) =< s(1669)+s(1669)+aux(283) s(1666) =< s(1672)+s(1670) s(1673) =< s(1666)*s(1477) s(1675) =< s(1666)*s(1477) s(1676) =< s(1666)*s(1582) s(1677) =< s(1671) s(1678) =< s(1674) s(1679) =< s(1675) s(1680) =< s(1673) s(1681) =< s(1670) s(1683) =< aux(278) s(1686) =< s(1497)*s(1615) s(1687) =< s(1497)*aux(285) s(1688) =< s(1497)*s(1566) s(1689) =< s(1497)*s(1567) s(1690) =< s(1689)+s(1687)+aux(283) s(1691) =< s(1689)+s(1687)+aux(283) s(1692) =< s(1686)+s(1686)+aux(285) s(1691) =< s(1686)+s(1686)+aux(285) s(1683) =< s(1689)+s(1687)+aux(283) s(1690) =< s(1683)*s(1566) s(1692) =< s(1683)*s(1566) s(1693) =< s(1683)*s(1582) s(1694) =< s(1688) s(1695) =< s(1691) s(1696) =< s(1692) s(1697) =< s(1690) s(1698) =< s(1687) s(1699) =< aux(279) s(1700) =< s(1499)*s(1624) s(1701) =< s(1499)*aux(279) s(1702) =< s(1499)*aux(279) s(1703) =< s(1499)*s(1513) s(1704) =< s(1499)*s(1513) s(1705) =< s(1499)*s(1515) s(1706) =< s(1705)+s(1701)+aux(278) s(1707) =< s(1705)+s(1701)+aux(278) s(1708) =< s(1700)+s(1700)+aux(279) s(1707) =< s(1700)+s(1700)+aux(279) s(1699) =< s(1705)+s(1701)+aux(278) s(1706) =< s(1699)*s(1513) s(1708) =< s(1699)*s(1513) s(1709) =< s(1699)*s(1513) s(1710) =< s(1703) s(1711) =< s(1707) s(1712) =< s(1708) s(1713) =< s(1706) s(1714) =< s(1701) s(1715) =< aux(279) s(1716) =< s(1499)*s(1620) s(1717) =< s(1499)*aux(281) s(1718) =< s(1499)*s(1534) s(1719) =< s(1499)*s(1535) s(1720) =< s(1719)+s(1717)+aux(278) s(1721) =< s(1719)+s(1717)+aux(278) s(1722) =< s(1716)+s(1716)+aux(281) s(1721) =< s(1716)+s(1716)+aux(281) s(1715) =< s(1719)+s(1717)+aux(278) s(1720) =< s(1715)*s(1534) s(1722) =< s(1715)*s(1534) s(1723) =< s(1715)*s(1513) s(1724) =< s(1718) s(1725) =< s(1721) s(1726) =< s(1722) s(1727) =< s(1720) s(1728) =< s(1717) s(1729) =< aux(279) s(1730) =< s(1499)*s(1614) s(1731) =< s(1499)*aux(283) s(1732) =< s(1499)*s(1477) s(1733) =< s(1499)*s(1550) s(1734) =< s(1733)+s(1731) s(1735) =< s(1733)+s(1731) s(1736) =< s(1730)+s(1730)+aux(283) s(1735) =< s(1730)+s(1730)+aux(283) s(1729) =< s(1733)+s(1731) s(1734) =< s(1729)*s(1477) s(1736) =< s(1729)*s(1477) s(1737) =< s(1729)*s(1513) s(1738) =< s(1732) s(1739) =< s(1735) s(1740) =< s(1736) s(1741) =< s(1734) s(1742) =< s(1731) s(1743) =< aux(279) s(1744) =< s(1499)*s(1616) s(1745) =< s(1499)*aux(285) s(1746) =< s(1499)*s(1566) s(1747) =< s(1499)*s(1567) s(1748) =< s(1747)+s(1745)+aux(283) s(1749) =< s(1747)+s(1745)+aux(283) s(1750) =< s(1744)+s(1744)+aux(285) s(1749) =< s(1744)+s(1744)+aux(285) s(1743) =< s(1747)+s(1745)+aux(283) s(1748) =< s(1743)*s(1566) s(1750) =< s(1743)*s(1566) s(1751) =< s(1743)*s(1513) s(1752) =< s(1746) s(1753) =< s(1749) s(1754) =< s(1750) s(1755) =< s(1748) s(1756) =< s(1745) s(1757) =< aux(279) s(1759) =< s(1499)*s(1617) s(1760) =< s(1499)*aux(278) s(1761) =< s(1499)*s(1582) s(1762) =< s(1499)*s(1583) s(1763) =< s(1762)+s(1760) s(1764) =< s(1762)+s(1760) s(1765) =< s(1759)+s(1759)+aux(278) s(1764) =< s(1759)+s(1759)+aux(278) s(1757) =< s(1762)+s(1760) s(1763) =< s(1757)*s(1582) s(1765) =< s(1757)*s(1582) s(1766) =< s(1757)*s(1513) s(1767) =< s(1761) s(1768) =< s(1764) s(1769) =< s(1765) s(1770) =< s(1763) s(1771) =< s(1760) s(1772) =< aux(279) s(1773) =< s(1705)+s(1701)+aux(283) s(1774) =< s(1705)+s(1701)+aux(283) s(1775) =< s(1700)+s(1700)+aux(279) s(1774) =< s(1700)+s(1700)+aux(279) s(1772) =< s(1705)+s(1701)+aux(283) s(1773) =< s(1772)*s(1513) s(1775) =< s(1772)*s(1513) s(1776) =< s(1772)*s(1513) s(1777) =< s(1774) s(1778) =< s(1775) s(1779) =< s(1773) s(1786) =< aux(278) s(1789) =< s(1497)*s(1781) s(1790) =< s(1497)*aux(278) s(1792) =< s(1497)*s(1582) s(1794) =< s(1497)*s(1583) s(1795) =< s(1794)+s(1790) s(1796) =< s(1794)+s(1790) s(1797) =< s(1789)+s(1789)+aux(278) s(1796) =< s(1789)+s(1789)+aux(278) s(1786) =< s(1794)+s(1790) s(1795) =< s(1786)*s(1582) s(1797) =< s(1786)*s(1582) s(1798) =< s(1786)*s(1582) s(1799) =< s(1792) s(1800) =< s(1796) s(1801) =< s(1797) s(1802) =< s(1795) s(1803) =< s(1790) s(1806) =< aux(278) s(1813) =< s(1638)+s(1634)+aux(283) s(1814) =< s(1638)+s(1634)+aux(283) s(1815) =< s(1633)+s(1633)+aux(279) s(1814) =< s(1633)+s(1633)+aux(279) s(1806) =< s(1638)+s(1634)+aux(283) s(1813) =< s(1806)*s(1513) s(1815) =< s(1806)*s(1513) s(1816) =< s(1806)*s(1582) s(1818) =< s(1814) s(1819) =< s(1815) s(1820) =< s(1813) s(1462) =< s(1458) s(1865) =< aux(283) s(1869) =< s(1463)*aux(284) s(1870) =< s(1463)*aux(287) s(1872) =< s(1463)*s(1476) s(1874) =< s(1463)*s(1478) s(1875) =< s(1874)+s(1870)+aux(286) s(1876) =< s(1874)+s(1870)+aux(286) s(1877) =< s(1869)+s(1869)+aux(287) s(1876) =< s(1869)+s(1869)+aux(287) s(1865) =< s(1874)+s(1870)+aux(286) s(1875) =< s(1865)*s(1476) s(1877) =< s(1865)*s(1476) s(1878) =< s(1865)*s(1477) s(1879) =< s(1872) s(1880) =< s(1876) s(1881) =< s(1877) s(1882) =< s(1875) s(1883) =< s(1870) s(1886) =< s(1858) s(1887) =< aux(283) s(1888) =< s(1858) s(1889) =< s(1858)-1 s(1890) =< s(1463)*s(1854) s(1891) =< s(1463)*s(1858) s(1892) =< s(1463)*s(1888) s(1893) =< s(1463)*s(1889) s(1894) =< s(1893)+s(1891)+aux(286) s(1895) =< s(1893)+s(1891)+aux(286) s(1896) =< s(1890)+s(1890)+s(1858) s(1895) =< s(1890)+s(1890)+s(1858) s(1887) =< s(1893)+s(1891)+aux(286) s(1894) =< s(1887)*s(1888) s(1896) =< s(1887)*s(1888) s(1897) =< s(1887)*s(1477) s(1898) =< s(1892) s(1899) =< s(1895) s(1900) =< s(1896) s(1901) =< s(1894) s(1902) =< s(1891) s(1903) =< aux(283) s(1904) =< aux(288) s(1905) =< aux(288)-1 s(1906) =< s(1463)*s(1855) s(1907) =< s(1463)*aux(288) s(1908) =< s(1463)*s(1904) s(1909) =< s(1463)*s(1905) s(1910) =< s(1909)+s(1907) s(1911) =< s(1909)+s(1907) s(1912) =< s(1906)+s(1906)+aux(288) s(1911) =< s(1906)+s(1906)+aux(288) s(1903) =< s(1909)+s(1907) s(1910) =< s(1903)*s(1904) s(1912) =< s(1903)*s(1904) s(1913) =< s(1903)*s(1477) s(1914) =< s(1908) s(1915) =< s(1911) s(1916) =< s(1912) s(1917) =< s(1910) s(1918) =< s(1907) s(1919) =< s(1859) s(1920) =< aux(283) s(1921) =< s(1859) s(1922) =< s(1859)-1 s(1923) =< s(1463)*s(1856) s(1924) =< s(1463)*s(1859) s(1925) =< s(1463)*s(1921) s(1926) =< s(1463)*s(1922) s(1927) =< s(1926)+s(1924)+aux(288) s(1928) =< s(1926)+s(1924)+aux(288) s(1929) =< s(1923)+s(1923)+s(1859) s(1928) =< s(1923)+s(1923)+s(1859) s(1920) =< s(1926)+s(1924)+aux(288) s(1927) =< s(1920)*s(1921) s(1929) =< s(1920)*s(1921) s(1930) =< s(1920)*s(1477) s(1931) =< s(1925) s(1932) =< s(1928) s(1933) =< s(1929) s(1934) =< s(1927) s(1935) =< s(1924) s(1944) =< aux(283) s(1945) =< aux(286) s(1947) =< aux(286)-1 s(1948) =< s(1463)*s(1936) s(1949) =< s(1463)*aux(286) s(1951) =< s(1463)*s(1945) s(1953) =< s(1463)*s(1947) s(1954) =< s(1953)+s(1949) s(1955) =< s(1953)+s(1949) s(1956) =< s(1948)+s(1948)+aux(286) s(1955) =< s(1948)+s(1948)+aux(286) s(1944) =< s(1953)+s(1949) s(1954) =< s(1944)*s(1945) s(1956) =< s(1944)*s(1945) s(1957) =< s(1944)*s(1477) s(1958) =< s(1951) s(1959) =< s(1955) s(1960) =< s(1956) s(1961) =< s(1954) s(1962) =< s(1949) s(1965) =< aux(283) s(1972) =< s(1874)+s(1870)+aux(288) s(1973) =< s(1874)+s(1870)+aux(288) s(1974) =< s(1869)+s(1869)+aux(287) s(1973) =< s(1869)+s(1869)+aux(287) s(1965) =< s(1874)+s(1870)+aux(288) s(1972) =< s(1965)*s(1476) s(1974) =< s(1965)*s(1476) s(1975) =< s(1965)*s(1477) s(1977) =< s(1973) s(1978) =< s(1974) s(1979) =< s(1972) with precondition: [V1>=0] * Chain [60]: 986*s(2044)+1058*s(2045)+60*s(2054)+96*s(2055)+414*s(2074)+13*s(2075)+6*s(2081)+24*s(2083)+1*s(2088)+31*s(2089)+11*s(2090)+6*s(2091)+12*s(2092)+8*s(2093)+264*s(2123)+13*s(2125)+1*s(2138)+31*s(2139)+11*s(2140)+6*s(2141)+12*s(2142)+8*s(2143)+528*s(2175)+13*s(2177)+1*s(2190)+62*s(2191)+11*s(2192)+6*s(2193)+12*s(2194)+16*s(2195)+13*s(2227)+1*s(2240)+31*s(2241)+11*s(2242)+6*s(2243)+12*s(2244)+8*s(2245)+13*s(2275)+1*s(2288)+11*s(2290)+6*s(2291)+12*s(2292)+264*s(2323)+13*s(2325)+1*s(2338)+31*s(2339)+11*s(2340)+6*s(2341)+12*s(2342)+8*s(2343)+25 Such that:s(2066) =< V+V14 s(2116) =< V+2*V14 s(2218) =< V+V22 s(2316) =< V+2*V22 s(2067) =< V9+2*V14 s(2117) =< V9+4*V14 s(2219) =< V9+2*V22 s(2317) =< V9+4*V22 s(2120) =< 2*V14 s(2320) =< 2*V22 aux(331) =< -V+V9 aux(332) =< V+1 aux(333) =< V+V14+V22 aux(334) =< V9 aux(335) =< V9+2*V14+2*V22 aux(336) =< V14 aux(337) =< V14+V22 aux(338) =< V22 s(2055) =< aux(334) s(2044) =< aux(336) s(2074) =< aux(331) s(2075) =< aux(331) s(2076) =< aux(336) s(2077) =< aux(334) s(2078) =< aux(336)-1 s(2079) =< s(2074)*s(2067) s(2080) =< s(2074)*aux(336) s(2081) =< s(2074)*aux(334) s(2082) =< s(2074)*s(2076) s(2083) =< s(2074)*s(2077) s(2084) =< s(2074)*s(2078) s(2085) =< s(2084)+s(2080) s(2086) =< s(2084)+s(2080) s(2087) =< s(2079)+s(2079)+s(2066) s(2086) =< s(2079)+s(2079)+s(2066) s(2075) =< s(2084)+s(2080) s(2085) =< s(2075)*s(2076) s(2087) =< s(2075)*s(2076) s(2088) =< s(2075)*s(2077) s(2089) =< s(2082) s(2090) =< s(2086) s(2091) =< s(2087) s(2092) =< s(2085) s(2093) =< s(2080) s(2045) =< aux(338) s(2123) =< s(2120) s(2125) =< aux(331) s(2126) =< s(2120) s(2128) =< s(2120)-1 s(2129) =< s(2074)*s(2117) s(2130) =< s(2074)*s(2120) s(2132) =< s(2074)*s(2126) s(2134) =< s(2074)*s(2128) s(2135) =< s(2134)+s(2130)+aux(336) s(2136) =< s(2134)+s(2130)+aux(336) s(2137) =< s(2129)+s(2129)+s(2116) s(2136) =< s(2129)+s(2129)+s(2116) s(2125) =< s(2134)+s(2130)+aux(336) s(2135) =< s(2125)*s(2126) s(2137) =< s(2125)*s(2126) s(2138) =< s(2125)*s(2077) s(2139) =< s(2132) s(2140) =< s(2136) s(2141) =< s(2137) s(2142) =< s(2135) s(2143) =< s(2130) s(2175) =< aux(337) s(2177) =< aux(331) s(2178) =< aux(337) s(2180) =< aux(337)-1 s(2181) =< s(2074)*aux(335) s(2182) =< s(2074)*aux(337) s(2184) =< s(2074)*s(2178) s(2186) =< s(2074)*s(2180) s(2187) =< s(2186)+s(2182)+aux(338) s(2188) =< s(2186)+s(2182)+aux(338) s(2189) =< s(2181)+s(2181)+aux(333) s(2188) =< s(2181)+s(2181)+aux(333) s(2177) =< s(2186)+s(2182)+aux(338) s(2187) =< s(2177)*s(2178) s(2189) =< s(2177)*s(2178) s(2190) =< s(2177)*s(2077) s(2191) =< s(2184) s(2192) =< s(2188) s(2193) =< s(2189) s(2194) =< s(2187) s(2195) =< s(2182) s(2227) =< aux(331) s(2228) =< aux(338) s(2230) =< aux(338)-1 s(2231) =< s(2074)*s(2219) s(2232) =< s(2074)*aux(338) s(2234) =< s(2074)*s(2228) s(2236) =< s(2074)*s(2230) s(2237) =< s(2236)+s(2232) s(2238) =< s(2236)+s(2232) s(2239) =< s(2231)+s(2231)+s(2218) s(2238) =< s(2231)+s(2231)+s(2218) s(2227) =< s(2236)+s(2232) s(2237) =< s(2227)*s(2228) s(2239) =< s(2227)*s(2228) s(2240) =< s(2227)*s(2077) s(2241) =< s(2234) s(2242) =< s(2238) s(2243) =< s(2239) s(2244) =< s(2237) s(2245) =< s(2232) s(2275) =< aux(331) s(2285) =< s(2186)+s(2182)+aux(336) s(2286) =< s(2186)+s(2182)+aux(336) s(2287) =< s(2181)+s(2181)+aux(333) s(2286) =< s(2181)+s(2181)+aux(333) s(2275) =< s(2186)+s(2182)+aux(336) s(2285) =< s(2275)*s(2178) s(2287) =< s(2275)*s(2178) s(2288) =< s(2275)*s(2077) s(2290) =< s(2286) s(2291) =< s(2287) s(2292) =< s(2285) s(2323) =< s(2320) s(2325) =< aux(331) s(2326) =< s(2320) s(2328) =< s(2320)-1 s(2329) =< s(2074)*s(2317) s(2330) =< s(2074)*s(2320) s(2332) =< s(2074)*s(2326) s(2334) =< s(2074)*s(2328) s(2335) =< s(2334)+s(2330)+aux(338) s(2336) =< s(2334)+s(2330)+aux(338) s(2337) =< s(2329)+s(2329)+s(2316) s(2336) =< s(2329)+s(2329)+s(2316) s(2325) =< s(2334)+s(2330)+aux(338) s(2335) =< s(2325)*s(2326) s(2337) =< s(2325)*s(2326) s(2338) =< s(2325)*s(2077) s(2339) =< s(2332) s(2340) =< s(2336) s(2341) =< s(2337) s(2342) =< s(2335) s(2343) =< s(2330) s(2054) =< aux(332) with precondition: [V1=1,V>=0,V9>=0] * Chain [59]: 1 with precondition: [V1=2,V>=0,V9>=0] * Chain [58]: 1 with precondition: [V=0,V1>=0] Closed-form bounds of start(V1,V,V9,V14,V22): ------------------------------------- * Chain [61] with precondition: [V1>=0] - Upper bound: 6546*V1+391+98*V1*V1+248*V1*nat(V)+23*V1*nat(V1-1)+23*V1*nat(nat(V)+ -1)+23*V1*nat(2*V1-1)+23*V1*nat(nat(2*V)+ -1)+46*V1*nat(nat(V1+V)+ -1)+62*V1*(2*V1)+62*V1*nat(2*V)+12*V1*(3*V1)+12*V1*(5*V1)+186*V1*nat(V1+V)+12*V1*nat(V1+2*V)+12*V1*nat(V1+4*V)+24*V1*nat(3*V1+2*V)+nat(V)*9277+nat(V)*330*nat(V)+nat(V)*62*nat(V9)+nat(V)*62*nat(V14)+nat(V)*69*nat(V1-1)+nat(V)*69*nat(nat(V)+ -1)+nat(V)*23*nat(nat(V9)+ -1)+nat(V)*23*nat(nat(V14)+ -1)+nat(V)*69*nat(2*V1-1)+nat(V)*69*nat(nat(2*V)+ -1)+nat(V)*23*nat(nat(2*V9)+ -1)+nat(V)*23*nat(nat(2*V14)+ -1)+nat(V)*138*nat(nat(V1+V)+ -1)+nat(V)*46*nat(nat(V9+V14)+ -1)+nat(V)*186*(2*V1)+nat(V)*186*nat(2*V)+nat(V)*62*nat(2*V9)+nat(V)*62*nat(2*V14)+nat(V)*36*nat(3*V)+nat(V)*36*nat(5*V)+nat(V)*434*nat(V1+V)+nat(V)*12*nat(V+2*V9)+nat(V)*12*nat(V+2*V14)+nat(V)*12*nat(V+4*V9)+nat(V)*12*nat(V+4*V14)+nat(V)*124*nat(V9+V14)+nat(V)*12*nat(-V1+V)+nat(V)*36*nat(2*V1+V)+nat(V)*72*nat(2*V1+3*V)+nat(V)*36*nat(4*V1+V)+nat(V)*24*nat(V+2*V9+2*V14)+nat(V9)*1182+nat(V14)*1408+nat(V1-1)*23*nat(V1+V)+nat(nat(V)+ -1)*23*nat(V1+V)+nat(2*V1-1)*23*nat(V1+V)+nat(nat(2*V)+ -1)*23*nat(V1+V)+nat(nat(V1+V)+ -1)*46*nat(V1+V)+nat(nat(V9+V14)+ -1)*46*nat(-V1+V)+2700*V1+124*V1*nat(V1+V)+nat(2*V)*1350+nat(2*V)*62*nat(V1+V)+nat(2*V9)*270+nat(2*V14)*270+nat(V1+V)*3291+nat(V1+V)*160*nat(V1+V)+nat(V1+V)*12*nat(V1+3*V)+nat(V1+V)*12*nat(V1+5*V)+nat(V1+V)*12*nat(3*V1+V)+nat(V1+V)*24*nat(3*V1+3*V)+nat(V1+V)*12*nat(5*V1+V)+(10*V1+10)+nat(V9+V14)*1068+nat(V9+V14)*124*nat(-V1+V)+nat(-V1+V)*164+nat(-V1+V)*24*nat(V+2*V9+2*V14)+nat(V1+V9+V14)*12 - Complexity: n^2 * Chain [60] with precondition: [V1=1,V>=0,V9>=0] - Upper bound: 96*V9+25+36*V9*nat(-V+V9)+nat(V14)*1032+nat(V14)*62*nat(-V+V9)+nat(V22)*1104+nat(V22)*62*nat(-V+V9)+nat(nat(V14)+ -1)*23*nat(-V+V9)+nat(nat(V22)+ -1)*23*nat(-V+V9)+nat(nat(2*V14)+ -1)*23*nat(-V+V9)+nat(nat(2*V22)+ -1)*23*nat(-V+V9)+nat(nat(V14+V22)+ -1)*46*nat(-V+V9)+nat(2*V14)*264+nat(2*V14)*62*nat(-V+V9)+nat(2*V22)*264+nat(2*V22)*62*nat(-V+V9)+nat(V+V14)*6+nat(V+V22)*6+(60*V+60)+nat(V+2*V14)*6+nat(V+2*V22)*6+nat(V9+2*V14)*12*nat(-V+V9)+nat(V9+2*V22)*12*nat(-V+V9)+nat(V9+4*V14)*12*nat(-V+V9)+nat(V9+4*V22)*12*nat(-V+V9)+nat(V14+V22)*528+nat(V14+V22)*124*nat(-V+V9)+nat(-V+V9)*492+nat(-V+V9)*24*nat(V9+2*V14+2*V22)+nat(V+V14+V22)*12 - Complexity: n^2 * Chain [59] with precondition: [V1=2,V>=0,V9>=0] - Upper bound: 1 - Complexity: constant * Chain [58] with precondition: [V=0,V1>=0] - Upper bound: 1 - Complexity: constant ### Maximum cost of start(V1,V,V9,V14,V22): nat(V9)*96+24+nat(V14)*1032+nat(2*V14)*264+max([nat(V14)*62*nat(-V+V9)+nat(V9)*36*nat(-V+V9)+nat(V22)*1104+nat(V22)*62*nat(-V+V9)+nat(nat(V14)+ -1)*23*nat(-V+V9)+nat(nat(V22)+ -1)*23*nat(-V+V9)+nat(nat(2*V14)+ -1)*23*nat(-V+V9)+nat(nat(2*V22)+ -1)*23*nat(-V+V9)+nat(nat(V14+V22)+ -1)*46*nat(-V+V9)+nat(2*V14)*62*nat(-V+V9)+nat(2*V22)*264+nat(2*V22)*62*nat(-V+V9)+nat(V+V14)*6+nat(V+V22)*6+nat(V+1)*60+nat(V+2*V14)*6+nat(V+2*V22)*6+nat(V9+2*V14)*12*nat(-V+V9)+nat(V9+2*V22)*12*nat(-V+V9)+nat(V9+4*V14)*12*nat(-V+V9)+nat(V9+4*V22)*12*nat(-V+V9)+nat(V14+V22)*528+nat(V14+V22)*124*nat(-V+V9)+nat(-V+V9)*492+nat(-V+V9)*24*nat(V9+2*V14+2*V22)+nat(V+V14+V22)*12,6546*V1+366+98*V1*V1+248*V1*nat(V)+23*V1*nat(V1-1)+23*V1*nat(nat(V)+ -1)+23*V1*nat(2*V1-1)+23*V1*nat(nat(2*V)+ -1)+46*V1*nat(nat(V1+V)+ -1)+62*V1*(2*V1)+62*V1*nat(2*V)+12*V1*(3*V1)+12*V1*(5*V1)+186*V1*nat(V1+V)+12*V1*nat(V1+2*V)+12*V1*nat(V1+4*V)+24*V1*nat(3*V1+2*V)+nat(V)*9277+nat(V)*330*nat(V)+nat(V)*62*nat(V9)+nat(V)*62*nat(V14)+nat(V)*69*nat(V1-1)+nat(V)*69*nat(nat(V)+ -1)+nat(V)*23*nat(nat(V9)+ -1)+nat(V)*23*nat(nat(V14)+ -1)+nat(V)*69*nat(2*V1-1)+nat(V)*69*nat(nat(2*V)+ -1)+nat(V)*23*nat(nat(2*V9)+ -1)+nat(V)*23*nat(nat(2*V14)+ -1)+nat(V)*138*nat(nat(V1+V)+ -1)+nat(V)*46*nat(nat(V9+V14)+ -1)+nat(V)*186*(2*V1)+nat(V)*186*nat(2*V)+nat(V)*62*nat(2*V9)+nat(V)*62*nat(2*V14)+nat(V)*36*nat(3*V)+nat(V)*36*nat(5*V)+nat(V)*434*nat(V1+V)+nat(V)*12*nat(V+2*V9)+nat(V)*12*nat(V+2*V14)+nat(V)*12*nat(V+4*V9)+nat(V)*12*nat(V+4*V14)+nat(V)*124*nat(V9+V14)+nat(V)*12*nat(-V1+V)+nat(V)*36*nat(2*V1+V)+nat(V)*72*nat(2*V1+3*V)+nat(V)*36*nat(4*V1+V)+nat(V)*24*nat(V+2*V9+2*V14)+nat(V9)*1086+nat(V14)*376+nat(V1-1)*23*nat(V1+V)+nat(nat(V)+ -1)*23*nat(V1+V)+nat(2*V1-1)*23*nat(V1+V)+nat(nat(2*V)+ -1)*23*nat(V1+V)+nat(nat(V1+V)+ -1)*46*nat(V1+V)+nat(nat(V9+V14)+ -1)*46*nat(-V1+V)+2700*V1+124*V1*nat(V1+V)+nat(2*V)*1350+nat(2*V)*62*nat(V1+V)+nat(2*V9)*270+nat(2*V14)*6+nat(V1+V)*3291+nat(V1+V)*160*nat(V1+V)+nat(V1+V)*12*nat(V1+3*V)+nat(V1+V)*12*nat(V1+5*V)+nat(V1+V)*12*nat(3*V1+V)+nat(V1+V)*24*nat(3*V1+3*V)+nat(V1+V)*12*nat(5*V1+V)+(10*V1+10)+nat(V9+V14)*1068+nat(V9+V14)*124*nat(-V1+V)+nat(-V1+V)*164+nat(-V1+V)*24*nat(V+2*V9+2*V14)+nat(V1+V9+V14)*12])+1 Asymptotic class: n^2 * Total analysis performed in 6693 ms. ---------------------------------------- (10) BOUNDS(1, n^2) ---------------------------------------- (11) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) Transformed a relative TRS into a decreasing-loop problem. ---------------------------------------- (12) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) plus(x, 0) -> x plus(x, s(y)) -> s(plus(x, y)) length(nil) -> 0 length(cons(x, y)) -> s(length(y)) helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) ge(x, 0) -> true ge(0, s(x)) -> false ge(s(x), s(y)) -> ge(x, y) if(true, c, l, ys, zs) -> nil if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) helpc(true, ys, zs) -> ys helpc(false, ys, zs) -> zs helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (13) DecreasingLoopProof (LOWER BOUND(ID)) The following loop(s) give(s) rise to the lower bound Omega(n^1): The rewrite sequence plus(x, s(y)) ->^+ s(plus(x, y)) gives rise to a decreasing loop by considering the right hand sides subterm at position [0]. The pumping substitution is [y / s(y)]. The result substitution is [ ]. ---------------------------------------- (14) Complex Obligation (BEST) ---------------------------------------- (15) Obligation: Proved the lower bound n^1 for the following obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) plus(x, 0) -> x plus(x, s(y)) -> s(plus(x, y)) length(nil) -> 0 length(cons(x, y)) -> s(length(y)) helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) ge(x, 0) -> true ge(0, s(x)) -> false ge(s(x), s(y)) -> ge(x, y) if(true, c, l, ys, zs) -> nil if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) helpc(true, ys, zs) -> ys helpc(false, ys, zs) -> zs helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (16) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (17) BOUNDS(n^1, INF) ---------------------------------------- (18) Obligation: Analyzing the following TRS for decreasing loops: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). The TRS R consists of the following rules: app(x, y) -> helpa(0, plus(length(x), length(y)), x, y) plus(x, 0) -> x plus(x, s(y)) -> s(plus(x, y)) length(nil) -> 0 length(cons(x, y)) -> s(length(y)) helpa(c, l, ys, zs) -> if(ge(c, l), c, l, ys, zs) ge(x, 0) -> true ge(0, s(x)) -> false ge(s(x), s(y)) -> ge(x, y) if(true, c, l, ys, zs) -> nil if(false, c, l, ys, zs) -> helpb(c, l, greater(ys, zs), smaller(ys, zs)) greater(ys, zs) -> helpc(ge(length(ys), length(zs)), ys, zs) smaller(ys, zs) -> helpc(ge(length(ys), length(zs)), zs, ys) helpc(true, ys, zs) -> ys helpc(false, ys, zs) -> zs helpb(c, l, cons(y, ys), zs) -> cons(y, helpa(s(c), l, ys, zs)) S is empty. Rewrite Strategy: INNERMOST