/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2).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) CpxWeightedTrsRenamingProof [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, 7561 ms] (12) BOUNDS(1, n^2) (13) RenamingProof [BOTH BOUNDS(ID, ID), 0 ms] (14) CpxTRS (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), 280 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), 55 ms] (26) typed CpxTrs (27) RewriteLemmaProof [LOWER BOUND(ID), 58 ms] (28) typed CpxTrs ---------------------------------------- (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: min(x, 0) -> 0 min(0, y) -> 0 min(s(x), s(y)) -> s(min(x, y)) max(x, 0) -> x max(0, y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0) -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) 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: min(x, 0) -> 0 [1] min(0, y) -> 0 [1] min(s(x), s(y)) -> s(min(x, y)) [1] max(x, 0) -> x [1] max(0, y) -> y [1] max(s(x), s(y)) -> s(max(x, y)) [1] -(x, 0) -> x [1] -(s(x), s(y)) -> -(x, y) [1] gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) [1] Rewrite Strategy: INNERMOST ---------------------------------------- (3) CpxWeightedTrsRenamingProof (BOTH BOUNDS(ID, ID)) Renamed defined symbols to avoid conflicts with arithmetic symbols: - => minus ---------------------------------------- (4) 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: min(x, 0) -> 0 [1] min(0, y) -> 0 [1] min(s(x), s(y)) -> s(min(x, y)) [1] max(x, 0) -> x [1] max(0, y) -> y [1] max(s(x), s(y)) -> s(max(x, y)) [1] minus(x, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] gcd(s(x), s(y)) -> gcd(minus(s(max(x, y)), s(min(x, y))), s(min(x, y))) [1] 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: min(x, 0) -> 0 [1] min(0, y) -> 0 [1] min(s(x), s(y)) -> s(min(x, y)) [1] max(x, 0) -> x [1] max(0, y) -> y [1] max(s(x), s(y)) -> s(max(x, y)) [1] minus(x, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] gcd(s(x), s(y)) -> gcd(minus(s(max(x, y)), s(min(x, y))), s(min(x, y))) [1] The TRS has the following type information: min :: 0:s -> 0:s -> 0:s 0 :: 0:s s :: 0:s -> 0:s max :: 0:s -> 0:s -> 0:s minus :: 0:s -> 0:s -> 0:s gcd :: 0:s -> 0:s -> gcd 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: minus(v0, v1) -> null_minus [0] gcd(v0, v1) -> null_gcd [0] min(v0, v1) -> null_min [0] max(v0, v1) -> null_max [0] And the following fresh constants: null_minus, null_gcd, null_min, null_max ---------------------------------------- (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: min(x, 0) -> 0 [1] min(0, y) -> 0 [1] min(s(x), s(y)) -> s(min(x, y)) [1] max(x, 0) -> x [1] max(0, y) -> y [1] max(s(x), s(y)) -> s(max(x, y)) [1] minus(x, 0) -> x [1] minus(s(x), s(y)) -> minus(x, y) [1] gcd(s(x), s(y)) -> gcd(minus(s(max(x, y)), s(min(x, y))), s(min(x, y))) [1] minus(v0, v1) -> null_minus [0] gcd(v0, v1) -> null_gcd [0] min(v0, v1) -> null_min [0] max(v0, v1) -> null_max [0] The TRS has the following type information: min :: 0:s:null_minus:null_min:null_max -> 0:s:null_minus:null_min:null_max -> 0:s:null_minus:null_min:null_max 0 :: 0:s:null_minus:null_min:null_max s :: 0:s:null_minus:null_min:null_max -> 0:s:null_minus:null_min:null_max max :: 0:s:null_minus:null_min:null_max -> 0:s:null_minus:null_min:null_max -> 0:s:null_minus:null_min:null_max minus :: 0:s:null_minus:null_min:null_max -> 0:s:null_minus:null_min:null_max -> 0:s:null_minus:null_min:null_max gcd :: 0:s:null_minus:null_min:null_max -> 0:s:null_minus:null_min:null_max -> null_gcd null_minus :: 0:s:null_minus:null_min:null_max null_gcd :: null_gcd null_min :: 0:s:null_minus:null_min:null_max null_max :: 0:s:null_minus:null_min:null_max 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: 0 => 0 null_minus => 0 null_gcd => 0 null_min => 0 null_max => 0 ---------------------------------------- (10) Obligation: Complexity RNTS consisting of the following rules: gcd(z, z') -{ 1 }-> gcd(minus(1 + max(x, y), 1 + min(x, y)), 1 + min(x, y)) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x gcd(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 max(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0 max(z, z') -{ 1 }-> y :|: y >= 0, z = 0, z' = y max(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 max(z, z') -{ 1 }-> 1 + max(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x min(z, z') -{ 1 }-> 0 :|: x >= 0, z = x, z' = 0 min(z, z') -{ 1 }-> 0 :|: y >= 0, z = 0, z' = y min(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 min(z, z') -{ 1 }-> 1 + min(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x minus(z, z') -{ 1 }-> x :|: x >= 0, z = x, z' = 0 minus(z, z') -{ 1 }-> minus(x, y) :|: z' = 1 + y, x >= 0, y >= 0, z = 1 + x minus(z, z') -{ 0 }-> 0 :|: v0 >= 0, v1 >= 0, z = v0, z' = v1 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),0,[min(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V),0,[max(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V),0,[minus(V1, V, Out)],[V1 >= 0,V >= 0]). eq(start(V1, V),0,[gcd(V1, V, Out)],[V1 >= 0,V >= 0]). eq(min(V1, V, Out),1,[],[Out = 0,V2 >= 0,V1 = V2,V = 0]). eq(min(V1, V, Out),1,[],[Out = 0,V3 >= 0,V1 = 0,V = V3]). eq(min(V1, V, Out),1,[min(V4, V5, Ret1)],[Out = 1 + Ret1,V = 1 + V5,V4 >= 0,V5 >= 0,V1 = 1 + V4]). eq(max(V1, V, Out),1,[],[Out = V6,V6 >= 0,V1 = V6,V = 0]). eq(max(V1, V, Out),1,[],[Out = V7,V7 >= 0,V1 = 0,V = V7]). eq(max(V1, V, Out),1,[max(V8, V9, Ret11)],[Out = 1 + Ret11,V = 1 + V9,V8 >= 0,V9 >= 0,V1 = 1 + V8]). eq(minus(V1, V, Out),1,[],[Out = V10,V10 >= 0,V1 = V10,V = 0]). eq(minus(V1, V, Out),1,[minus(V12, V11, Ret)],[Out = Ret,V = 1 + V11,V12 >= 0,V11 >= 0,V1 = 1 + V12]). eq(gcd(V1, V, Out),1,[max(V14, V13, Ret001),min(V14, V13, Ret011),minus(1 + Ret001, 1 + Ret011, Ret0),min(V14, V13, Ret111),gcd(Ret0, 1 + Ret111, Ret2)],[Out = Ret2,V = 1 + V13,V14 >= 0,V13 >= 0,V1 = 1 + V14]). eq(minus(V1, V, Out),0,[],[Out = 0,V16 >= 0,V15 >= 0,V1 = V16,V = V15]). eq(gcd(V1, V, Out),0,[],[Out = 0,V18 >= 0,V17 >= 0,V1 = V18,V = V17]). eq(min(V1, V, Out),0,[],[Out = 0,V20 >= 0,V19 >= 0,V1 = V20,V = V19]). eq(max(V1, V, Out),0,[],[Out = 0,V21 >= 0,V22 >= 0,V1 = V21,V = V22]). input_output_vars(min(V1,V,Out),[V1,V],[Out]). input_output_vars(max(V1,V,Out),[V1,V],[Out]). input_output_vars(minus(V1,V,Out),[V1,V],[Out]). input_output_vars(gcd(V1,V,Out),[V1,V],[Out]). CoFloCo proof output: Preprocessing Cost Relations ===================================== #### Computed strongly connected components 0. recursive : [max/3] 1. recursive : [min/3] 2. recursive : [minus/3] 3. recursive : [gcd/3] 4. non_recursive : [start/2] #### Obtained direct recursion through partial evaluation 0. SCC is partially evaluated into max/3 1. SCC is partially evaluated into min/3 2. SCC is partially evaluated into minus/3 3. SCC is partially evaluated into gcd/3 4. SCC is partially evaluated into start/2 Control-Flow Refinement of Cost Relations ===================================== ### Specialization of cost equations max/3 * CE 12 is refined into CE [18] * CE 9 is refined into CE [19] * CE 10 is refined into CE [20] * CE 11 is refined into CE [21] ### Cost equations --> "Loop" of max/3 * CEs [21] --> Loop 14 * CEs [18] --> Loop 15 * CEs [19] --> Loop 16 * CEs [20] --> Loop 17 ### Ranking functions of CR max(V1,V,Out) * RF of phase [14]: [V,V1] #### Partial ranking functions of CR max(V1,V,Out) * Partial RF of phase [14]: - RF of loop [14:1]: V V1 ### Specialization of cost equations min/3 * CE 5 is refined into CE [22] * CE 6 is refined into CE [23] * CE 8 is refined into CE [24] * CE 7 is refined into CE [25] ### Cost equations --> "Loop" of min/3 * CEs [25] --> Loop 18 * CEs [22] --> Loop 19 * CEs [23,24] --> Loop 20 ### Ranking functions of CR min(V1,V,Out) * RF of phase [18]: [V,V1] #### Partial ranking functions of CR min(V1,V,Out) * Partial RF of phase [18]: - RF of loop [18:1]: V V1 ### Specialization of cost equations minus/3 * CE 15 is refined into CE [26] * CE 13 is refined into CE [27] * CE 14 is refined into CE [28] ### Cost equations --> "Loop" of minus/3 * CEs [28] --> Loop 21 * CEs [26] --> Loop 22 * CEs [27] --> Loop 23 ### Ranking functions of CR minus(V1,V,Out) * RF of phase [21]: [V,V1] #### Partial ranking functions of CR minus(V1,V,Out) * Partial RF of phase [21]: - RF of loop [21:1]: V V1 ### Specialization of cost equations gcd/3 * CE 17 is refined into CE [29] * CE 16 is refined into CE [30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63] ### Cost equations --> "Loop" of gcd/3 * CEs [47] --> Loop 24 * CEs [55] --> Loop 25 * CEs [59] --> Loop 26 * CEs [51] --> Loop 27 * CEs [43] --> Loop 28 * CEs [46] --> Loop 29 * CEs [54] --> Loop 30 * CEs [58] --> Loop 31 * CEs [62] --> Loop 32 * CEs [50] --> Loop 33 * CEs [42] --> Loop 34 * CEs [41,45] --> Loop 35 * CEs [35,37,39,49,53,57,61,63] --> Loop 36 * CEs [33] --> Loop 37 * CEs [32] --> Loop 38 * CEs [31] --> Loop 39 * CEs [30,34,36,38,40,44,48,52,56,60] --> Loop 40 * CEs [29] --> Loop 41 ### Ranking functions of CR gcd(V1,V,Out) * RF of phase [24,25,26,27,28,36]: [V1+V-3] * RF of phase [37,39]: [V1+V-1] #### Partial ranking functions of CR gcd(V1,V,Out) * Partial RF of phase [24,25,26,27,28,36]: - RF of loop [24:1,26:1,28:1,36:1]: V1-1 depends on loops [25:1,27:1] - RF of loop [25:1,26:1,27:1,36:1]: V1+V-3 * Partial RF of phase [37,39]: - RF of loop [37:1]: V1 depends on loops [39:1] - RF of loop [39:1]: V1+V-1 ### Specialization of cost equations start/2 * CE 1 is refined into CE [64,65] * CE 2 is refined into CE [66,67,68,69,70,71] * CE 3 is refined into CE [72,73,74] * CE 4 is refined into CE [75] ### Cost equations --> "Loop" of start/2 * CEs [67,72] --> Loop 42 * CEs [64,65,66,68,69,70,71,73,74,75] --> Loop 43 ### Ranking functions of CR start(V1,V) #### Partial ranking functions of CR start(V1,V) Computing Bounds ===================================== #### Cost of chains of max(V1,V,Out): * Chain [[14],17]: 1*it(14)+1 Such that:it(14) =< V1 with precondition: [V=Out,V1>=1,V>=V1] * Chain [[14],16]: 1*it(14)+1 Such that:it(14) =< V with precondition: [V1=Out,V>=1,V1>=V] * Chain [[14],15]: 1*it(14)+0 Such that:it(14) =< Out with precondition: [Out>=1,V1>=Out,V>=Out] * Chain [17]: 1 with precondition: [V1=0,V=Out,V>=0] * Chain [16]: 1 with precondition: [V=0,V1=Out,V1>=0] * Chain [15]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of min(V1,V,Out): * Chain [[18],20]: 1*it(18)+1 Such that:it(18) =< Out with precondition: [Out>=1,V1>=Out,V>=Out] * Chain [[18],19]: 1*it(18)+1 Such that:it(18) =< Out with precondition: [V=Out,V>=1,V1>=V] * Chain [20]: 1 with precondition: [Out=0,V1>=0,V>=0] * Chain [19]: 1 with precondition: [V=0,Out=0,V1>=0] #### Cost of chains of minus(V1,V,Out): * Chain [[21],23]: 1*it(21)+1 Such that:it(21) =< V with precondition: [V1=Out+V,V>=1,V1>=V] * Chain [[21],22]: 1*it(21)+0 Such that:it(21) =< V with precondition: [Out=0,V1>=1,V>=1] * Chain [23]: 1 with precondition: [V=0,V1=Out,V1>=0] * Chain [22]: 0 with precondition: [Out=0,V1>=0,V>=0] #### Cost of chains of gcd(V1,V,Out): * Chain [[37,39],41]: 5*it(37)+6*it(39)+1*s(8)+0 Such that:aux(13) =< V1 aux(14) =< V1+V aux(15) =< V aux(6) =< aux(14) it(37) =< aux(14) it(39) =< aux(14) aux(6) =< aux(15)+aux(13) it(37) =< aux(15)+aux(13) s(8) =< aux(6) with precondition: [Out=0,V1>=1,V>=1] * Chain [[37,39],40,41]: 5*it(37)+15*it(39)+1*s(8)+15*s(10)+4 Such that:aux(23) =< 1 aux(24) =< V1 aux(25) =< V1+V aux(26) =< V s(10) =< aux(23) it(39) =< aux(25) aux(6) =< aux(25) it(37) =< aux(25) aux(6) =< aux(26)+aux(24) it(37) =< aux(26)+aux(24) s(8) =< aux(6) with precondition: [Out=0,V1>=1,V>=1,V+V1>=3] * Chain [[37,39],38,41]: 5*it(37)+6*it(39)+1*s(8)+1*s(34)+4 Such that:s(34) =< 1 aux(27) =< V1 aux(28) =< V1+V aux(29) =< V aux(6) =< aux(28) it(37) =< aux(28) it(39) =< aux(28) aux(6) =< aux(29)+aux(27) it(37) =< aux(29)+aux(27) s(8) =< aux(6) with precondition: [Out=0,V1>=1,V>=1,V+V1>=3] * Chain [[24,25,26,27,28,36],[37,39],41]: 18*it(24)+20*it(25)+5*it(37)+1*s(8)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+0 Such that:aux(90) =< V1 aux(91) =< V1+V aux(92) =< V aux(6) =< aux(91) it(37) =< aux(91) it(25) =< aux(91) aux(6) =< aux(91)+aux(91) it(37) =< aux(91)+aux(91) s(8) =< aux(6) aux(61) =< aux(91) it(24) =< aux(91) aux(55) =< aux(91) aux(52) =< aux(92) aux(62) =< aux(91)-1 aux(61) =< aux(92)+aux(92)+aux(90) it(24) =< aux(92)+aux(92)+aux(90) s(133) =< it(25)*aux(91) s(132) =< aux(92)+aux(92)+aux(90) s(155) =< aux(92)+aux(92)+aux(90) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(92) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2] * Chain [[24,25,26,27,28,36],[37,39],40,41]: 18*it(24)+29*it(25)+5*it(37)+1*s(8)+15*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4 Such that:aux(23) =< 1 aux(93) =< V1 aux(94) =< V1+V aux(95) =< V s(10) =< aux(23) it(25) =< aux(94) aux(6) =< aux(94) it(37) =< aux(94) aux(6) =< aux(94)+aux(94) it(37) =< aux(94)+aux(94) s(8) =< aux(6) aux(61) =< aux(94) it(24) =< aux(94) aux(55) =< aux(94) aux(52) =< aux(95) aux(62) =< aux(94)-1 aux(61) =< aux(95)+aux(95)+aux(93) it(24) =< aux(95)+aux(95)+aux(93) s(133) =< it(25)*aux(94) s(132) =< aux(95)+aux(95)+aux(93) s(155) =< aux(95)+aux(95)+aux(93) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(95) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2] * Chain [[24,25,26,27,28,36],[37,39],38,41]: 18*it(24)+20*it(25)+5*it(37)+1*s(8)+1*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4 Such that:s(34) =< 1 aux(96) =< V1 aux(97) =< V1+V aux(98) =< V aux(6) =< aux(97) it(37) =< aux(97) it(25) =< aux(97) aux(6) =< aux(97)+aux(97) it(37) =< aux(97)+aux(97) s(8) =< aux(6) aux(61) =< aux(97) it(24) =< aux(97) aux(55) =< aux(97) aux(52) =< aux(98) aux(62) =< aux(97)-1 aux(61) =< aux(98)+aux(98)+aux(96) it(24) =< aux(98)+aux(98)+aux(96) s(133) =< it(25)*aux(97) s(132) =< aux(98)+aux(98)+aux(96) s(155) =< aux(98)+aux(98)+aux(96) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(98) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2] * Chain [[24,25,26,27,28,36],41]: 18*it(24)+14*it(25)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+0 Such that:aux(99) =< V1 aux(100) =< V1+V aux(101) =< V aux(61) =< aux(100) it(24) =< aux(100) it(25) =< aux(100) aux(55) =< aux(100) aux(52) =< aux(101) aux(62) =< aux(100)-1 aux(61) =< aux(101)+aux(101)+aux(99) it(24) =< aux(101)+aux(101)+aux(99) s(133) =< it(25)*aux(100) s(132) =< aux(101)+aux(101)+aux(99) s(155) =< aux(101)+aux(101)+aux(99) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(101) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2] * Chain [[24,25,26,27,28,36],40,41]: 18*it(24)+32*it(25)+6*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4 Such that:aux(20) =< 1 aux(102) =< V1 aux(103) =< V1+V aux(104) =< V s(10) =< aux(20) it(25) =< aux(103) aux(61) =< aux(103) it(24) =< aux(103) aux(55) =< aux(103) aux(52) =< aux(104) aux(62) =< aux(103)-1 aux(61) =< aux(104)+aux(104)+aux(102) it(24) =< aux(104)+aux(104)+aux(102) s(133) =< it(25)*aux(103) s(132) =< aux(104)+aux(104)+aux(102) s(155) =< aux(104)+aux(104)+aux(102) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(104) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2] * Chain [[24,25,26,27,28,36],35,41]: 18*it(24)+14*it(25)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9*s(160)+1*s(161)+4 Such that:s(161) =< 1 aux(109) =< V1 aux(110) =< V1+V aux(111) =< V s(160) =< aux(111) aux(61) =< aux(110) it(24) =< aux(110) it(25) =< aux(110) aux(55) =< aux(110) aux(52) =< aux(111) aux(62) =< aux(110)-1 aux(61) =< aux(111)+aux(111)+aux(109) it(24) =< aux(111)+aux(111)+aux(109) s(133) =< it(25)*aux(110) s(132) =< aux(111)+aux(111)+aux(109) s(155) =< aux(111)+aux(111)+aux(109) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(111) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],34,[37,39],41]: 18*it(24)+21*it(25)+5*it(37)+1*s(8)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(171)+5 Such that:aux(112) =< 1 aux(114) =< V1 aux(115) =< V1+V aux(116) =< V it(25) =< aux(115) s(171) =< aux(112) aux(6) =< aux(115) it(37) =< aux(115) aux(6) =< aux(112)+aux(115) it(37) =< aux(112)+aux(115) s(8) =< aux(6) aux(61) =< aux(115) it(24) =< aux(115) aux(55) =< aux(115) aux(52) =< aux(116) aux(62) =< aux(115)-1 aux(61) =< aux(116)+aux(116)+aux(114) it(24) =< aux(116)+aux(116)+aux(114) s(133) =< it(25)*aux(115) s(132) =< aux(116)+aux(116)+aux(114) s(155) =< aux(116)+aux(116)+aux(114) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(116) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],34,[37,39],40,41]: 18*it(24)+30*it(25)+5*it(37)+1*s(8)+16*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(117) =< 1 aux(119) =< V1 aux(120) =< V1+V aux(121) =< V it(25) =< aux(120) s(10) =< aux(117) aux(6) =< aux(120) it(37) =< aux(120) aux(6) =< aux(117)+aux(120) it(37) =< aux(117)+aux(120) s(8) =< aux(6) aux(61) =< aux(120) it(24) =< aux(120) aux(55) =< aux(120) aux(52) =< aux(121) aux(62) =< aux(120)-1 aux(61) =< aux(121)+aux(121)+aux(119) it(24) =< aux(121)+aux(121)+aux(119) s(133) =< it(25)*aux(120) s(132) =< aux(121)+aux(121)+aux(119) s(155) =< aux(121)+aux(121)+aux(119) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(121) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=6] * Chain [[24,25,26,27,28,36],34,[37,39],38,41]: 18*it(24)+21*it(25)+5*it(37)+1*s(8)+2*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(122) =< 1 aux(124) =< V1 aux(125) =< V1+V aux(126) =< V it(25) =< aux(125) s(34) =< aux(122) aux(6) =< aux(125) it(37) =< aux(125) aux(6) =< aux(122)+aux(125) it(37) =< aux(122)+aux(125) s(8) =< aux(6) aux(61) =< aux(125) it(24) =< aux(125) aux(55) =< aux(125) aux(52) =< aux(126) aux(62) =< aux(125)-1 aux(61) =< aux(126)+aux(126)+aux(124) it(24) =< aux(126)+aux(126)+aux(124) s(133) =< it(25)*aux(125) s(132) =< aux(126)+aux(126)+aux(124) s(155) =< aux(126)+aux(126)+aux(124) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(126) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=6] * Chain [[24,25,26,27,28,36],34,41]: 18*it(24)+14*it(25)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(170)+1*s(171)+5 Such that:s(171) =< 1 aux(127) =< V1 aux(128) =< V1+V aux(129) =< V s(170) =< aux(129) aux(61) =< aux(128) it(24) =< aux(128) it(25) =< aux(128) aux(55) =< aux(128) aux(52) =< aux(129) aux(62) =< aux(128)-1 aux(61) =< aux(129)+aux(129)+aux(127) it(24) =< aux(129)+aux(129)+aux(127) s(133) =< it(25)*aux(128) s(132) =< aux(129)+aux(129)+aux(127) s(155) =< aux(129)+aux(129)+aux(127) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(129) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],34,40,41]: 18*it(24)+24*it(25)+16*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(130) =< 1 aux(131) =< V1 aux(132) =< V1+V aux(133) =< V it(25) =< aux(132) s(10) =< aux(130) aux(61) =< aux(132) it(24) =< aux(132) aux(55) =< aux(132) aux(52) =< aux(133) aux(62) =< aux(132)-1 aux(61) =< aux(133)+aux(133)+aux(131) it(24) =< aux(133)+aux(133)+aux(131) s(133) =< it(25)*aux(132) s(132) =< aux(133)+aux(133)+aux(131) s(155) =< aux(133)+aux(133)+aux(131) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(133) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],34,38,41]: 18*it(24)+14*it(25)+2*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(170)+9 Such that:aux(134) =< 1 aux(135) =< V1 aux(136) =< V1+V aux(137) =< V s(170) =< aux(137) s(34) =< aux(134) aux(61) =< aux(136) it(24) =< aux(136) it(25) =< aux(136) aux(55) =< aux(136) aux(52) =< aux(137) aux(62) =< aux(136)-1 aux(61) =< aux(137)+aux(137)+aux(135) it(24) =< aux(137)+aux(137)+aux(135) s(133) =< it(25)*aux(136) s(132) =< aux(137)+aux(137)+aux(135) s(155) =< aux(137)+aux(137)+aux(135) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(137) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],33,[37,39],41]: 18*it(24)+21*it(25)+5*it(37)+1*s(8)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(173)+5 Such that:aux(138) =< 1 aux(140) =< V1 aux(141) =< V1+V aux(142) =< V it(25) =< aux(141) s(173) =< aux(138) aux(6) =< aux(141) it(37) =< aux(141) aux(6) =< aux(138)+aux(141) it(37) =< aux(138)+aux(141) s(8) =< aux(6) aux(61) =< aux(141) it(24) =< aux(141) aux(55) =< aux(141) aux(52) =< aux(142) aux(62) =< aux(141)-1 aux(61) =< aux(142)+aux(142)+aux(140) it(24) =< aux(142)+aux(142)+aux(140) s(133) =< it(25)*aux(141) s(132) =< aux(142)+aux(142)+aux(140) s(155) =< aux(142)+aux(142)+aux(140) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(142) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],33,[37,39],40,41]: 18*it(24)+30*it(25)+5*it(37)+1*s(8)+16*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(143) =< 1 aux(145) =< V1 aux(146) =< V1+V aux(147) =< V it(25) =< aux(146) s(10) =< aux(143) aux(6) =< aux(146) it(37) =< aux(146) aux(6) =< aux(143)+aux(146) it(37) =< aux(143)+aux(146) s(8) =< aux(6) aux(61) =< aux(146) it(24) =< aux(146) aux(55) =< aux(146) aux(52) =< aux(147) aux(62) =< aux(146)-1 aux(61) =< aux(147)+aux(147)+aux(145) it(24) =< aux(147)+aux(147)+aux(145) s(133) =< it(25)*aux(146) s(132) =< aux(147)+aux(147)+aux(145) s(155) =< aux(147)+aux(147)+aux(145) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(147) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3] * Chain [[24,25,26,27,28,36],33,[37,39],38,41]: 18*it(24)+21*it(25)+5*it(37)+1*s(8)+2*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(148) =< 1 aux(150) =< V1 aux(151) =< V1+V aux(152) =< V it(25) =< aux(151) s(34) =< aux(148) aux(6) =< aux(151) it(37) =< aux(151) aux(6) =< aux(148)+aux(151) it(37) =< aux(148)+aux(151) s(8) =< aux(6) aux(61) =< aux(151) it(24) =< aux(151) aux(55) =< aux(151) aux(52) =< aux(152) aux(62) =< aux(151)-1 aux(61) =< aux(152)+aux(152)+aux(150) it(24) =< aux(152)+aux(152)+aux(150) s(133) =< it(25)*aux(151) s(132) =< aux(152)+aux(152)+aux(150) s(155) =< aux(152)+aux(152)+aux(150) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(152) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3] * Chain [[24,25,26,27,28,36],33,41]: 18*it(24)+14*it(25)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(172)+1*s(173)+5 Such that:s(173) =< 1 aux(153) =< V1 aux(154) =< V1+V aux(155) =< V s(172) =< aux(153) aux(61) =< aux(154) it(24) =< aux(154) it(25) =< aux(154) aux(55) =< aux(154) aux(52) =< aux(155) aux(62) =< aux(154)-1 aux(61) =< aux(155)+aux(155)+aux(153) it(24) =< aux(155)+aux(155)+aux(153) s(133) =< it(25)*aux(154) s(132) =< aux(155)+aux(155)+aux(153) s(155) =< aux(155)+aux(155)+aux(153) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(155) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],33,40,41]: 18*it(24)+24*it(25)+16*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(156) =< 1 aux(157) =< V1 aux(158) =< V1+V aux(159) =< V it(25) =< aux(158) s(10) =< aux(156) aux(61) =< aux(158) it(24) =< aux(158) aux(55) =< aux(158) aux(52) =< aux(159) aux(62) =< aux(158)-1 aux(61) =< aux(159)+aux(159)+aux(157) it(24) =< aux(159)+aux(159)+aux(157) s(133) =< it(25)*aux(158) s(132) =< aux(159)+aux(159)+aux(157) s(155) =< aux(159)+aux(159)+aux(157) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(159) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],33,38,41]: 18*it(24)+14*it(25)+2*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(172)+9 Such that:aux(160) =< 1 aux(161) =< V1 aux(162) =< V1+V aux(163) =< V s(172) =< aux(161) s(34) =< aux(160) aux(61) =< aux(162) it(24) =< aux(162) it(25) =< aux(162) aux(55) =< aux(162) aux(52) =< aux(163) aux(62) =< aux(162)-1 aux(61) =< aux(163)+aux(163)+aux(161) it(24) =< aux(163)+aux(163)+aux(161) s(133) =< it(25)*aux(162) s(132) =< aux(163)+aux(163)+aux(161) s(155) =< aux(163)+aux(163)+aux(161) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(163) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],32,[37,39],41]: 18*it(24)+24*it(25)+5*it(37)+1*s(8)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4 Such that:aux(15) =< 1 aux(88) =< V aux(89) =< V+1 aux(166) =< V1 aux(167) =< V1+V it(25) =< aux(167) aux(6) =< aux(167) it(37) =< aux(167) aux(6) =< aux(15)+aux(167) it(37) =< aux(15)+aux(167) s(8) =< aux(6) aux(61) =< aux(167) it(24) =< aux(167) aux(39) =< aux(88) aux(39) =< aux(89) aux(55) =< aux(167) aux(52) =< aux(88) aux(62) =< aux(167)-1 aux(61) =< aux(39)+aux(39)+aux(166) it(24) =< aux(39)+aux(39)+aux(166) s(133) =< it(25)*aux(167) s(132) =< aux(39)+aux(39)+aux(166) s(155) =< aux(39)+aux(39)+aux(166) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(88) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3,V+V1>=7] * Chain [[24,25,26,27,28,36],32,[37,39],40,41]: 18*it(24)+33*it(25)+5*it(37)+1*s(8)+15*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+8 Such that:aux(168) =< 1 aux(88) =< V aux(89) =< V+1 aux(170) =< V1 aux(171) =< V1+V it(25) =< aux(171) s(10) =< aux(168) aux(6) =< aux(171) it(37) =< aux(171) aux(6) =< aux(168)+aux(171) it(37) =< aux(168)+aux(171) s(8) =< aux(6) aux(61) =< aux(171) it(24) =< aux(171) aux(39) =< aux(88) aux(39) =< aux(89) aux(55) =< aux(171) aux(52) =< aux(88) aux(62) =< aux(171)-1 aux(61) =< aux(39)+aux(39)+aux(170) it(24) =< aux(39)+aux(39)+aux(170) s(133) =< it(25)*aux(171) s(132) =< aux(39)+aux(39)+aux(170) s(155) =< aux(39)+aux(39)+aux(170) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(88) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=4,V>=4,V+V1>=9] * Chain [[24,25,26,27,28,36],32,[37,39],38,41]: 18*it(24)+24*it(25)+5*it(37)+1*s(8)+1*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+8 Such that:aux(172) =< 1 aux(88) =< V aux(89) =< V+1 aux(174) =< V1 aux(175) =< V1+V s(34) =< aux(172) it(25) =< aux(175) aux(6) =< aux(175) it(37) =< aux(175) aux(6) =< aux(172)+aux(175) it(37) =< aux(172)+aux(175) s(8) =< aux(6) aux(61) =< aux(175) it(24) =< aux(175) aux(39) =< aux(88) aux(39) =< aux(89) aux(55) =< aux(175) aux(52) =< aux(88) aux(62) =< aux(175)-1 aux(61) =< aux(39)+aux(39)+aux(174) it(24) =< aux(39)+aux(39)+aux(174) s(133) =< it(25)*aux(175) s(132) =< aux(39)+aux(39)+aux(174) s(155) =< aux(39)+aux(39)+aux(174) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(88) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=4,V>=4,V+V1>=9] * Chain [[24,25,26,27,28,36],32,41]: 18*it(24)+14*it(25)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4*s(174)+4 Such that:aux(177) =< V1 aux(178) =< V1+V aux(179) =< V s(174) =< aux(179) aux(61) =< aux(178) it(24) =< aux(178) it(25) =< aux(178) aux(55) =< aux(178) aux(52) =< aux(179) aux(62) =< aux(178)-1 aux(61) =< aux(179)+aux(179)+aux(177) it(24) =< aux(179)+aux(179)+aux(177) s(133) =< it(25)*aux(178) s(132) =< aux(179)+aux(179)+aux(177) s(155) =< aux(179)+aux(179)+aux(177) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(179) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],32,40,41]: 18*it(24)+14*it(25)+15*s(10)+13*s(22)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+8 Such that:aux(180) =< 1 aux(182) =< V1 aux(183) =< V1+V aux(184) =< V s(22) =< aux(184) s(10) =< aux(180) aux(61) =< aux(183) it(24) =< aux(183) it(25) =< aux(183) aux(55) =< aux(183) aux(52) =< aux(184) aux(62) =< aux(183)-1 aux(61) =< aux(184)+aux(184)+aux(182) it(24) =< aux(184)+aux(184)+aux(182) s(133) =< it(25)*aux(183) s(132) =< aux(184)+aux(184)+aux(182) s(155) =< aux(184)+aux(184)+aux(182) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(184) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3,V+V1>=7] * Chain [[24,25,26,27,28,36],32,38,41]: 18*it(24)+14*it(25)+1*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4*s(174)+8 Such that:s(34) =< 1 aux(186) =< V1 aux(187) =< V1+V aux(188) =< V s(174) =< aux(188) aux(61) =< aux(187) it(24) =< aux(187) it(25) =< aux(187) aux(55) =< aux(187) aux(52) =< aux(188) aux(62) =< aux(187)-1 aux(61) =< aux(188)+aux(188)+aux(186) it(24) =< aux(188)+aux(188)+aux(186) s(133) =< it(25)*aux(187) s(132) =< aux(188)+aux(188)+aux(186) s(155) =< aux(188)+aux(188)+aux(186) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(188) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3,V+V1>=7] * Chain [[24,25,26,27,28,36],31,[37,39],41]: 18*it(24)+21*it(25)+5*it(37)+1*s(8)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(179)+4 Such that:aux(189) =< 1 aux(191) =< V1 aux(192) =< V1+V aux(193) =< V s(179) =< aux(189) it(25) =< aux(192) aux(6) =< aux(192) it(37) =< aux(192) aux(6) =< aux(189)+aux(192) it(37) =< aux(189)+aux(192) s(8) =< aux(6) aux(61) =< aux(192) it(24) =< aux(192) aux(55) =< aux(192) aux(52) =< aux(193) aux(62) =< aux(192)-1 aux(61) =< aux(193)+aux(193)+aux(191) it(24) =< aux(193)+aux(193)+aux(191) s(133) =< it(25)*aux(192) s(132) =< aux(193)+aux(193)+aux(191) s(155) =< aux(193)+aux(193)+aux(191) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(193) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],31,[37,39],40,41]: 18*it(24)+30*it(25)+5*it(37)+1*s(8)+16*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+8 Such that:aux(194) =< 1 aux(196) =< V1 aux(197) =< V1+V aux(198) =< V s(10) =< aux(194) it(25) =< aux(197) aux(6) =< aux(197) it(37) =< aux(197) aux(6) =< aux(194)+aux(197) it(37) =< aux(194)+aux(197) s(8) =< aux(6) aux(61) =< aux(197) it(24) =< aux(197) aux(55) =< aux(197) aux(52) =< aux(198) aux(62) =< aux(197)-1 aux(61) =< aux(198)+aux(198)+aux(196) it(24) =< aux(198)+aux(198)+aux(196) s(133) =< it(25)*aux(197) s(132) =< aux(198)+aux(198)+aux(196) s(155) =< aux(198)+aux(198)+aux(196) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(198) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3,V+V1>=7] * Chain [[24,25,26,27,28,36],31,[37,39],38,41]: 18*it(24)+21*it(25)+5*it(37)+1*s(8)+2*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+8 Such that:aux(199) =< 1 aux(201) =< V1 aux(202) =< V1+V aux(203) =< V s(34) =< aux(199) it(25) =< aux(202) aux(6) =< aux(202) it(37) =< aux(202) aux(6) =< aux(199)+aux(202) it(37) =< aux(199)+aux(202) s(8) =< aux(6) aux(61) =< aux(202) it(24) =< aux(202) aux(55) =< aux(202) aux(52) =< aux(203) aux(62) =< aux(202)-1 aux(61) =< aux(203)+aux(203)+aux(201) it(24) =< aux(203)+aux(203)+aux(201) s(133) =< it(25)*aux(202) s(132) =< aux(203)+aux(203)+aux(201) s(155) =< aux(203)+aux(203)+aux(201) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(203) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3,V+V1>=7] * Chain [[24,25,26,27,28,36],31,41]: 18*it(24)+14*it(25)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(178)+1*s(179)+4 Such that:s(179) =< 1 aux(204) =< V1 aux(205) =< V1+V aux(206) =< V s(178) =< aux(206) aux(61) =< aux(205) it(24) =< aux(205) it(25) =< aux(205) aux(55) =< aux(205) aux(52) =< aux(206) aux(62) =< aux(205)-1 aux(61) =< aux(206)+aux(206)+aux(204) it(24) =< aux(206)+aux(206)+aux(204) s(133) =< it(25)*aux(205) s(132) =< aux(206)+aux(206)+aux(204) s(155) =< aux(206)+aux(206)+aux(204) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(206) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],31,40,41]: 18*it(24)+24*it(25)+16*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+8 Such that:aux(207) =< 1 aux(209) =< V1 aux(210) =< V1+V aux(211) =< V s(10) =< aux(207) it(25) =< aux(210) aux(61) =< aux(210) it(24) =< aux(210) aux(55) =< aux(210) aux(52) =< aux(211) aux(62) =< aux(210)-1 aux(61) =< aux(211)+aux(211)+aux(209) it(24) =< aux(211)+aux(211)+aux(209) s(133) =< it(25)*aux(210) s(132) =< aux(211)+aux(211)+aux(209) s(155) =< aux(211)+aux(211)+aux(209) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(211) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],31,38,41]: 18*it(24)+14*it(25)+2*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+1*s(178)+8 Such that:aux(212) =< 1 aux(213) =< V1 aux(214) =< V1+V aux(215) =< V s(178) =< aux(215) s(34) =< aux(212) aux(61) =< aux(214) it(24) =< aux(214) it(25) =< aux(214) aux(55) =< aux(214) aux(52) =< aux(215) aux(62) =< aux(214)-1 aux(61) =< aux(215)+aux(215)+aux(213) it(24) =< aux(215)+aux(215)+aux(213) s(133) =< it(25)*aux(214) s(132) =< aux(215)+aux(215)+aux(213) s(155) =< aux(215)+aux(215)+aux(213) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(215) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],30,[37,39],41]: 18*it(24)+10*it(25)+5*it(37)+10*it(39)+1*s(8)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(134)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+5 Such that:aux(15) =< 1 aux(88) =< V aux(89) =< V+1 aux(218) =< V1 aux(219) =< V1+V aux(220) =< V1+V+1 it(39) =< aux(220) aux(6) =< aux(220) it(37) =< aux(220) aux(6) =< aux(15)+aux(219) it(37) =< aux(15)+aux(219) s(8) =< aux(6) aux(61) =< aux(219) aux(64) =< aux(219) it(24) =< aux(219) it(25) =< aux(219) aux(61) =< aux(220) aux(64) =< aux(220) it(24) =< aux(220) it(25) =< aux(220) aux(39) =< aux(88) aux(39) =< aux(89) aux(55) =< aux(219) aux(52) =< aux(88) aux(62) =< aux(219)-1 aux(61) =< aux(39)+aux(39)+aux(218) it(24) =< aux(39)+aux(39)+aux(218) s(134) =< aux(64) s(133) =< it(25)*aux(219) s(132) =< aux(39)+aux(39)+aux(218) s(155) =< aux(39)+aux(39)+aux(218) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(88) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3] * Chain [[24,25,26,27,28,36],30,[37,39],40,41]: 18*it(24)+10*it(25)+5*it(37)+19*it(39)+1*s(8)+15*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(134)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(221) =< 1 aux(88) =< V aux(89) =< V+1 aux(223) =< V1 aux(224) =< V1+V aux(225) =< V1+V+1 it(39) =< aux(225) s(10) =< aux(221) aux(6) =< aux(225) it(37) =< aux(225) aux(6) =< aux(221)+aux(224) it(37) =< aux(221)+aux(224) s(8) =< aux(6) aux(61) =< aux(224) aux(64) =< aux(224) it(24) =< aux(224) it(25) =< aux(224) aux(61) =< aux(225) aux(64) =< aux(225) it(24) =< aux(225) it(25) =< aux(225) aux(39) =< aux(88) aux(39) =< aux(89) aux(55) =< aux(224) aux(52) =< aux(88) aux(62) =< aux(224)-1 aux(61) =< aux(39)+aux(39)+aux(223) it(24) =< aux(39)+aux(39)+aux(223) s(134) =< aux(64) s(133) =< it(25)*aux(224) s(132) =< aux(39)+aux(39)+aux(223) s(155) =< aux(39)+aux(39)+aux(223) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(88) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=4,V>=4] * Chain [[24,25,26,27,28,36],30,[37,39],38,41]: 18*it(24)+10*it(25)+5*it(37)+10*it(39)+1*s(8)+1*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(134)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(226) =< 1 aux(88) =< V aux(89) =< V+1 aux(228) =< V1 aux(229) =< V1+V aux(230) =< V1+V+1 it(39) =< aux(230) s(34) =< aux(226) aux(6) =< aux(230) it(37) =< aux(230) aux(6) =< aux(226)+aux(229) it(37) =< aux(226)+aux(229) s(8) =< aux(6) aux(61) =< aux(229) aux(64) =< aux(229) it(24) =< aux(229) it(25) =< aux(229) aux(61) =< aux(230) aux(64) =< aux(230) it(24) =< aux(230) it(25) =< aux(230) aux(39) =< aux(88) aux(39) =< aux(89) aux(55) =< aux(229) aux(52) =< aux(88) aux(62) =< aux(229)-1 aux(61) =< aux(39)+aux(39)+aux(228) it(24) =< aux(39)+aux(39)+aux(228) s(134) =< aux(64) s(133) =< it(25)*aux(229) s(132) =< aux(39)+aux(39)+aux(228) s(155) =< aux(39)+aux(39)+aux(228) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(88) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=4,V>=4] * Chain [[24,25,26,27,28,36],30,41]: 18*it(24)+14*it(25)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4*s(180)+5 Such that:aux(232) =< V1 aux(233) =< V1+V aux(234) =< V s(180) =< aux(232) aux(61) =< aux(233) it(24) =< aux(233) it(25) =< aux(233) aux(55) =< aux(233) aux(52) =< aux(234) aux(62) =< aux(233)-1 aux(61) =< aux(234)+aux(234)+aux(232) it(24) =< aux(234)+aux(234)+aux(232) s(133) =< it(25)*aux(233) s(132) =< aux(234)+aux(234)+aux(232) s(155) =< aux(234)+aux(234)+aux(232) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(234) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],30,40,41]: 18*it(24)+27*it(25)+15*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(235) =< 1 aux(237) =< V1 aux(238) =< V1+V aux(239) =< V it(25) =< aux(238) s(10) =< aux(235) aux(61) =< aux(238) it(24) =< aux(238) aux(55) =< aux(238) aux(52) =< aux(239) aux(62) =< aux(238)-1 aux(61) =< aux(239)+aux(239)+aux(237) it(24) =< aux(239)+aux(239)+aux(237) s(133) =< it(25)*aux(238) s(132) =< aux(239)+aux(239)+aux(237) s(155) =< aux(239)+aux(239)+aux(237) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(239) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3] * Chain [[24,25,26,27,28,36],30,38,41]: 18*it(24)+14*it(25)+1*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4*s(180)+9 Such that:s(34) =< 1 aux(241) =< V1 aux(242) =< V1+V aux(243) =< V s(180) =< aux(241) aux(61) =< aux(242) it(24) =< aux(242) it(25) =< aux(242) aux(55) =< aux(242) aux(52) =< aux(243) aux(62) =< aux(242)-1 aux(61) =< aux(243)+aux(243)+aux(241) it(24) =< aux(243)+aux(243)+aux(241) s(133) =< it(25)*aux(242) s(132) =< aux(243)+aux(243)+aux(241) s(155) =< aux(243)+aux(243)+aux(241) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(243) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=3,V>=3] * Chain [[24,25,26,27,28,36],29,[37,39],41]: 18*it(24)+10*it(25)+5*it(37)+10*it(39)+1*s(8)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(134)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+5 Such that:aux(15) =< 1 aux(246) =< V1 aux(247) =< V1+V aux(248) =< V1+V+1 aux(249) =< V it(39) =< aux(248) aux(6) =< aux(248) it(37) =< aux(248) aux(6) =< aux(15)+aux(247) it(37) =< aux(15)+aux(247) s(8) =< aux(6) aux(61) =< aux(247) aux(64) =< aux(247) it(24) =< aux(247) it(25) =< aux(247) aux(61) =< aux(248) aux(64) =< aux(248) it(24) =< aux(248) it(25) =< aux(248) aux(55) =< aux(247) aux(52) =< aux(249) aux(62) =< aux(247)-1 aux(61) =< aux(249)+aux(249)+aux(246) it(24) =< aux(249)+aux(249)+aux(246) s(134) =< aux(64) s(133) =< it(25)*aux(247) s(132) =< aux(249)+aux(249)+aux(246) s(155) =< aux(249)+aux(249)+aux(246) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(249) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=6] * Chain [[24,25,26,27,28,36],29,[37,39],40,41]: 18*it(24)+10*it(25)+5*it(37)+19*it(39)+1*s(8)+15*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(134)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(250) =< 1 aux(252) =< V1 aux(253) =< V1+V aux(254) =< V1+V+1 aux(255) =< V it(39) =< aux(254) s(10) =< aux(250) aux(6) =< aux(254) it(37) =< aux(254) aux(6) =< aux(250)+aux(253) it(37) =< aux(250)+aux(253) s(8) =< aux(6) aux(61) =< aux(253) aux(64) =< aux(253) it(24) =< aux(253) it(25) =< aux(253) aux(61) =< aux(254) aux(64) =< aux(254) it(24) =< aux(254) it(25) =< aux(254) aux(55) =< aux(253) aux(52) =< aux(255) aux(62) =< aux(253)-1 aux(61) =< aux(255)+aux(255)+aux(252) it(24) =< aux(255)+aux(255)+aux(252) s(134) =< aux(64) s(133) =< it(25)*aux(253) s(132) =< aux(255)+aux(255)+aux(252) s(155) =< aux(255)+aux(255)+aux(252) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(255) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=7] * Chain [[24,25,26,27,28,36],29,[37,39],38,41]: 18*it(24)+10*it(25)+5*it(37)+10*it(39)+1*s(8)+1*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(134)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(256) =< 1 aux(258) =< V1 aux(259) =< V1+V aux(260) =< V1+V+1 aux(261) =< V it(39) =< aux(260) s(34) =< aux(256) aux(6) =< aux(260) it(37) =< aux(260) aux(6) =< aux(256)+aux(259) it(37) =< aux(256)+aux(259) s(8) =< aux(6) aux(61) =< aux(259) aux(64) =< aux(259) it(24) =< aux(259) it(25) =< aux(259) aux(61) =< aux(260) aux(64) =< aux(260) it(24) =< aux(260) it(25) =< aux(260) aux(55) =< aux(259) aux(52) =< aux(261) aux(62) =< aux(259)-1 aux(61) =< aux(261)+aux(261)+aux(258) it(24) =< aux(261)+aux(261)+aux(258) s(134) =< aux(64) s(133) =< it(25)*aux(259) s(132) =< aux(261)+aux(261)+aux(258) s(155) =< aux(261)+aux(261)+aux(258) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(261) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=7] * Chain [[24,25,26,27,28,36],29,41]: 18*it(24)+14*it(25)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4*s(184)+5 Such that:aux(263) =< V1 aux(264) =< V1+V aux(265) =< V s(184) =< aux(265) aux(61) =< aux(264) it(24) =< aux(264) it(25) =< aux(264) aux(55) =< aux(264) aux(52) =< aux(265) aux(62) =< aux(264)-1 aux(61) =< aux(265)+aux(265)+aux(263) it(24) =< aux(265)+aux(265)+aux(263) s(133) =< it(25)*aux(264) s(132) =< aux(265)+aux(265)+aux(263) s(155) =< aux(265)+aux(265)+aux(263) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(265) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=5] * Chain [[24,25,26,27,28,36],29,40,41]: 18*it(24)+27*it(25)+15*s(10)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+9 Such that:aux(266) =< 1 aux(268) =< V1 aux(269) =< V1+V aux(270) =< V it(25) =< aux(269) s(10) =< aux(266) aux(61) =< aux(269) it(24) =< aux(269) aux(55) =< aux(269) aux(52) =< aux(270) aux(62) =< aux(269)-1 aux(61) =< aux(270)+aux(270)+aux(268) it(24) =< aux(270)+aux(270)+aux(268) s(133) =< it(25)*aux(269) s(132) =< aux(270)+aux(270)+aux(268) s(155) =< aux(270)+aux(270)+aux(268) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(270) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=6] * Chain [[24,25,26,27,28,36],29,38,41]: 18*it(24)+14*it(25)+1*s(34)+2*s(128)+3*s(129)+8*s(130)+1*s(133)+4*s(135)+1*s(138)+6*s(139)+28*s(140)+1*s(142)+3*s(154)+4*s(184)+9 Such that:s(34) =< 1 aux(272) =< V1 aux(273) =< V1+V aux(274) =< V s(184) =< aux(274) aux(61) =< aux(273) it(24) =< aux(273) it(25) =< aux(273) aux(55) =< aux(273) aux(52) =< aux(274) aux(62) =< aux(273)-1 aux(61) =< aux(274)+aux(274)+aux(272) it(24) =< aux(274)+aux(274)+aux(272) s(133) =< it(25)*aux(273) s(132) =< aux(274)+aux(274)+aux(272) s(155) =< aux(274)+aux(274)+aux(272) s(136) =< it(25)*aux(55) s(142) =< it(25)*aux(55) s(141) =< it(24)*aux(55) s(131) =< it(24)*aux(52) s(155) =< it(24)*aux(55) s(128) =< it(24)*aux(52) s(139) =< aux(61) s(138) =< it(24)*aux(62) s(132) =< it(24)*aux(274) s(140) =< s(141) s(130) =< s(131) s(154) =< s(155) s(135) =< s(136) s(129) =< s(132) with precondition: [Out=0,V1>=2,V>=2,V+V1>=6] * Chain [41]: 0 with precondition: [Out=0,V1>=0,V>=0] * Chain [40,41]: 6*s(10)+9*s(14)+9*s(22)+4 Such that:aux(20) =< 1 aux(21) =< V1 aux(22) =< V s(10) =< aux(20) s(22) =< aux(21) s(14) =< aux(22) with precondition: [Out=0,V1>=1,V>=1] * Chain [38,41]: 1*s(34)+4 Such that:s(34) =< 1 with precondition: [V=1,Out=0,V1>=1] * Chain [35,41]: 9*s(160)+1*s(161)+4 Such that:s(161) =< 1 aux(108) =< V s(160) =< aux(108) with precondition: [Out=0,V>=2,V1>=V] * Chain [34,[37,39],41]: 5*it(37)+6*it(39)+1*s(8)+1*s(170)+1*s(171)+5 Such that:s(170) =< V aux(112) =< 1 aux(113) =< V1 s(171) =< aux(112) aux(6) =< aux(113) it(37) =< aux(113) it(39) =< aux(113) aux(6) =< aux(112)+aux(113) it(37) =< aux(112)+aux(113) s(8) =< aux(6) with precondition: [Out=0,V>=2,V1>=V] * Chain [34,[37,39],40,41]: 5*it(37)+15*it(39)+1*s(8)+16*s(10)+1*s(170)+9 Such that:s(170) =< V aux(117) =< 1 aux(118) =< V1 s(10) =< aux(117) it(39) =< aux(118) aux(6) =< aux(118) it(37) =< aux(118) aux(6) =< aux(117)+aux(118) it(37) =< aux(117)+aux(118) s(8) =< aux(6) with precondition: [Out=0,V1>=3,V>=2,V1>=V] * Chain [34,[37,39],38,41]: 5*it(37)+6*it(39)+1*s(8)+2*s(34)+1*s(170)+9 Such that:s(170) =< V aux(122) =< 1 aux(123) =< V1 s(34) =< aux(122) aux(6) =< aux(123) it(37) =< aux(123) it(39) =< aux(123) aux(6) =< aux(122)+aux(123) it(37) =< aux(122)+aux(123) s(8) =< aux(6) with precondition: [Out=0,V1>=3,V>=2,V1>=V] * Chain [34,41]: 1*s(170)+1*s(171)+5 Such that:s(171) =< 1 s(170) =< V with precondition: [Out=0,V>=2,V1>=V] * Chain [34,40,41]: 16*s(10)+9*s(22)+1*s(170)+9 Such that:aux(21) =< V1 s(170) =< V aux(130) =< 1 s(10) =< aux(130) s(22) =< aux(21) with precondition: [Out=0,V>=2,V1>=V] * Chain [34,38,41]: 2*s(34)+1*s(170)+9 Such that:s(170) =< V aux(134) =< 1 s(34) =< aux(134) with precondition: [Out=0,V>=2,V1>=V] * Chain [33,[37,39],41]: 5*it(37)+6*it(39)+1*s(8)+1*s(172)+1*s(173)+5 Such that:s(172) =< V1 aux(138) =< 1 aux(139) =< V s(173) =< aux(138) aux(6) =< aux(139) it(37) =< aux(139) it(39) =< aux(139) aux(6) =< aux(138)+aux(139) it(37) =< aux(138)+aux(139) s(8) =< aux(6) with precondition: [Out=0,V1>=2,V>=V1] * Chain [33,[37,39],40,41]: 5*it(37)+15*it(39)+1*s(8)+16*s(10)+1*s(172)+9 Such that:s(172) =< V1 aux(143) =< 1 aux(144) =< V s(10) =< aux(143) it(39) =< aux(144) aux(6) =< aux(144) it(37) =< aux(144) aux(6) =< aux(143)+aux(144) it(37) =< aux(143)+aux(144) s(8) =< aux(6) with precondition: [Out=0,V1>=2,V>=3,V>=V1] * Chain [33,[37,39],38,41]: 5*it(37)+6*it(39)+1*s(8)+2*s(34)+1*s(172)+9 Such that:s(172) =< V1 aux(148) =< 1 aux(149) =< V s(34) =< aux(148) aux(6) =< aux(149) it(37) =< aux(149) it(39) =< aux(149) aux(6) =< aux(148)+aux(149) it(37) =< aux(148)+aux(149) s(8) =< aux(6) with precondition: [Out=0,V1>=2,V>=3,V>=V1] * Chain [33,41]: 1*s(172)+1*s(173)+5 Such that:s(173) =< 1 s(172) =< V1 with precondition: [Out=0,V1>=2,V>=V1] * Chain [33,40,41]: 16*s(10)+9*s(22)+1*s(172)+9 Such that:s(172) =< V1 aux(21) =< V aux(156) =< 1 s(10) =< aux(156) s(22) =< aux(21) with precondition: [Out=0,V1>=2,V>=V1] * Chain [33,38,41]: 2*s(34)+1*s(172)+9 Such that:s(172) =< V1 aux(160) =< 1 s(34) =< aux(160) with precondition: [Out=0,V1>=2,V>=V1] * Chain [32,[37,39],41]: 5*it(37)+6*it(39)+1*s(8)+4*s(174)+4 Such that:aux(15) =< 1 aux(14) =< V+1 aux(165) =< V s(174) =< aux(165) aux(6) =< aux(14) it(37) =< aux(14) it(39) =< aux(14) aux(6) =< aux(15)+aux(165) it(37) =< aux(15)+aux(165) s(8) =< aux(6) with precondition: [Out=0,V1>=3,V>=3] * Chain [32,[37,39],40,41]: 5*it(37)+15*it(39)+1*s(8)+15*s(10)+4*s(174)+8 Such that:aux(25) =< V+1 aux(168) =< 1 aux(169) =< V s(174) =< aux(169) s(10) =< aux(168) it(39) =< aux(25) aux(6) =< aux(25) it(37) =< aux(25) aux(6) =< aux(168)+aux(169) it(37) =< aux(168)+aux(169) s(8) =< aux(6) with precondition: [Out=0,V1>=4,V>=4] * Chain [32,[37,39],38,41]: 5*it(37)+6*it(39)+1*s(8)+1*s(34)+4*s(174)+8 Such that:aux(28) =< V+1 aux(172) =< 1 aux(173) =< V s(34) =< aux(172) s(174) =< aux(173) aux(6) =< aux(28) it(37) =< aux(28) it(39) =< aux(28) aux(6) =< aux(172)+aux(173) it(37) =< aux(172)+aux(173) s(8) =< aux(6) with precondition: [Out=0,V1>=4,V>=4] * Chain [32,41]: 4*s(174)+4 Such that:aux(176) =< V s(174) =< aux(176) with precondition: [Out=0,V1>=2,V>=2] * Chain [32,40,41]: 15*s(10)+13*s(22)+8 Such that:aux(180) =< 1 aux(181) =< V s(22) =< aux(181) s(10) =< aux(180) with precondition: [Out=0,V1>=3,V>=3] * Chain [32,38,41]: 1*s(34)+4*s(174)+8 Such that:s(34) =< 1 aux(185) =< V s(174) =< aux(185) with precondition: [Out=0,V1>=3,V>=3] * Chain [31,[37,39],41]: 5*it(37)+7*it(39)+1*s(8)+1*s(179)+4 Such that:aux(189) =< 1 aux(190) =< V1 s(179) =< aux(189) it(39) =< aux(190) aux(6) =< aux(190) it(37) =< aux(190) aux(6) =< aux(189)+aux(190) it(37) =< aux(189)+aux(190) s(8) =< aux(6) with precondition: [Out=0,V1>=2,V>=2] * Chain [31,[37,39],40,41]: 5*it(37)+16*it(39)+1*s(8)+16*s(10)+8 Such that:aux(194) =< 1 aux(195) =< V1 s(10) =< aux(194) it(39) =< aux(195) aux(6) =< aux(195) it(37) =< aux(195) aux(6) =< aux(194)+aux(195) it(37) =< aux(194)+aux(195) s(8) =< aux(6) with precondition: [Out=0,V1>=3,V>=3] * Chain [31,[37,39],38,41]: 5*it(37)+7*it(39)+1*s(8)+2*s(34)+8 Such that:aux(199) =< 1 aux(200) =< V1 s(34) =< aux(199) it(39) =< aux(200) aux(6) =< aux(200) it(37) =< aux(200) aux(6) =< aux(199)+aux(200) it(37) =< aux(199)+aux(200) s(8) =< aux(6) with precondition: [Out=0,V1>=3,V>=3] * Chain [31,41]: 1*s(178)+1*s(179)+4 Such that:s(179) =< 1 s(178) =< V with precondition: [Out=0,V1>=2,V>=2] * Chain [31,40,41]: 16*s(10)+10*s(22)+8 Such that:aux(207) =< 1 aux(208) =< V1 s(10) =< aux(207) s(22) =< aux(208) with precondition: [Out=0,V1>=2,V>=2] * Chain [31,38,41]: 2*s(34)+1*s(178)+8 Such that:s(178) =< V aux(212) =< 1 s(34) =< aux(212) with precondition: [Out=0,V1>=2,V>=2] * Chain [30,[37,39],41]: 5*it(37)+9*it(39)+1*s(8)+1*s(180)+5 Such that:aux(15) =< 1 s(180) =< V1 aux(13) =< V aux(217) =< V+1 aux(6) =< aux(217) it(37) =< aux(217) it(39) =< aux(217) aux(6) =< aux(15)+aux(13) it(37) =< aux(15)+aux(13) s(8) =< aux(6) with precondition: [Out=0,V1>=2,V>=3,V>=V1] * Chain [30,[37,39],40,41]: 5*it(37)+18*it(39)+1*s(8)+15*s(10)+1*s(180)+9 Such that:s(180) =< V1 aux(24) =< V aux(221) =< 1 aux(222) =< V+1 s(10) =< aux(221) it(39) =< aux(222) aux(6) =< aux(222) it(37) =< aux(222) aux(6) =< aux(221)+aux(24) it(37) =< aux(221)+aux(24) s(8) =< aux(6) with precondition: [Out=0,V1>=2,V>=4,V>=V1] * Chain [30,[37,39],38,41]: 5*it(37)+9*it(39)+1*s(8)+1*s(34)+1*s(180)+9 Such that:s(180) =< V1 aux(27) =< V aux(226) =< 1 aux(227) =< V+1 s(34) =< aux(226) aux(6) =< aux(227) it(37) =< aux(227) it(39) =< aux(227) aux(6) =< aux(226)+aux(27) it(37) =< aux(226)+aux(27) s(8) =< aux(6) with precondition: [Out=0,V1>=2,V>=4,V>=V1] * Chain [30,41]: 4*s(180)+5 Such that:aux(231) =< V1 s(180) =< aux(231) with precondition: [Out=0,V1>=2,V>=V1] * Chain [30,40,41]: 15*s(10)+12*s(22)+1*s(180)+9 Such that:s(180) =< V1 aux(235) =< 1 aux(236) =< V s(10) =< aux(235) s(22) =< aux(236) with precondition: [Out=0,V1>=2,V>=3,V>=V1] * Chain [30,38,41]: 1*s(34)+4*s(180)+9 Such that:s(34) =< 1 aux(240) =< V1 s(180) =< aux(240) with precondition: [Out=0,V1>=2,V>=3,V>=V1] * Chain [29,[37,39],41]: 5*it(37)+9*it(39)+1*s(8)+1*s(184)+5 Such that:aux(15) =< 1 aux(13) =< V1 s(184) =< V aux(245) =< V1+1 aux(6) =< aux(245) it(37) =< aux(245) it(39) =< aux(245) aux(6) =< aux(15)+aux(13) it(37) =< aux(15)+aux(13) s(8) =< aux(6) with precondition: [Out=0,V1>=3,V>=2,V1>=V] * Chain [29,[37,39],40,41]: 5*it(37)+18*it(39)+1*s(8)+15*s(10)+1*s(184)+9 Such that:aux(24) =< V1 s(184) =< V aux(250) =< 1 aux(251) =< V1+1 s(10) =< aux(250) it(39) =< aux(251) aux(6) =< aux(251) it(37) =< aux(251) aux(6) =< aux(250)+aux(24) it(37) =< aux(250)+aux(24) s(8) =< aux(6) with precondition: [Out=0,V1>=4,V>=2,V1>=V] * Chain [29,[37,39],38,41]: 5*it(37)+9*it(39)+1*s(8)+1*s(34)+1*s(184)+9 Such that:aux(27) =< V1 s(184) =< V aux(256) =< 1 aux(257) =< V1+1 s(34) =< aux(256) aux(6) =< aux(257) it(37) =< aux(257) it(39) =< aux(257) aux(6) =< aux(256)+aux(27) it(37) =< aux(256)+aux(27) s(8) =< aux(6) with precondition: [Out=0,V1>=4,V>=2,V1>=V] * Chain [29,41]: 4*s(184)+5 Such that:aux(262) =< V s(184) =< aux(262) with precondition: [Out=0,V>=2,V1>=V] * Chain [29,40,41]: 15*s(10)+12*s(22)+1*s(184)+9 Such that:s(184) =< V aux(266) =< 1 aux(267) =< V1 s(10) =< aux(266) s(22) =< aux(267) with precondition: [Out=0,V1>=3,V>=2,V1>=V] * Chain [29,38,41]: 1*s(34)+4*s(184)+9 Such that:s(34) =< 1 aux(271) =< V s(184) =< aux(271) with precondition: [Out=0,V1>=3,V>=2,V1>=V] #### Cost of chains of start(V1,V): * Chain [43]: 167*s(1612)+126*s(1614)+467*s(1625)+15*s(1629)+36*s(1630)+3*s(1631)+30*s(1633)+63*s(1634)+6*s(1635)+30*s(1637)+6*s(1638)+594*s(1640)+761*s(1641)+36*s(1645)+36*s(1649)+66*s(1652)+198*s(1653)+33*s(1654)+924*s(1655)+264*s(1656)+99*s(1657)+144*s(1658)+99*s(1659)+78*s(1660)+30*s(1662)+6*s(1663)+54*s(1666)+60*s(1667)+24*s(1668)+6*s(1669)+6*s(1673)+6*s(1676)+18*s(1677)+3*s(1678)+84*s(1679)+24*s(1680)+9*s(1681)+24*s(1682)+9*s(1683)+54*s(1685)+6*s(1691)+18*s(1692)+3*s(1693)+84*s(1694)+24*s(1695)+9*s(1696)+9*s(1697)+60*s(1699)+12*s(1700)+54*s(1702)+6*s(1707)+18*s(1708)+3*s(1709)+84*s(1710)+24*s(1711)+9*s(1712)+9*s(1713)+15*s(1715)+3*s(1716)+15*s(1718)+3*s(1719)+15*s(1721)+3*s(1722)+9 Such that:s(1618) =< 1 s(1620) =< V1+1 s(1621) =< V1+V s(1622) =< V1+V+1 s(1624) =< V+1 aux(282) =< V1 aux(283) =< V s(1614) =< aux(282) s(1612) =< aux(283) s(1625) =< s(1618) s(1628) =< s(1620) s(1629) =< s(1620) s(1630) =< s(1620) s(1628) =< s(1618)+aux(282) s(1629) =< s(1618)+aux(282) s(1631) =< s(1628) s(1632) =< s(1624) s(1633) =< s(1624) s(1634) =< s(1624) s(1632) =< s(1618)+aux(283) s(1633) =< s(1618)+aux(283) s(1635) =< s(1632) s(1636) =< aux(282) s(1637) =< aux(282) s(1636) =< s(1618)+aux(282) s(1637) =< s(1618)+aux(282) s(1638) =< s(1636) s(1639) =< s(1621) s(1640) =< s(1621) s(1641) =< s(1621) s(1642) =< s(1621) s(1643) =< aux(283) s(1644) =< s(1621)-1 s(1639) =< aux(283)+aux(283)+aux(282) s(1640) =< aux(283)+aux(283)+aux(282) s(1645) =< s(1641)*s(1621) s(1646) =< aux(283)+aux(283)+aux(282) s(1647) =< aux(283)+aux(283)+aux(282) s(1648) =< s(1641)*s(1642) s(1649) =< s(1641)*s(1642) s(1650) =< s(1640)*s(1642) s(1651) =< s(1640)*s(1643) s(1647) =< s(1640)*s(1642) s(1652) =< s(1640)*s(1643) s(1653) =< s(1639) s(1654) =< s(1640)*s(1644) s(1646) =< s(1640)*aux(283) s(1655) =< s(1650) s(1656) =< s(1651) s(1657) =< s(1647) s(1658) =< s(1648) s(1659) =< s(1646) s(1660) =< s(1622) s(1661) =< s(1622) s(1662) =< s(1622) s(1661) =< s(1618)+s(1621) s(1662) =< s(1618)+s(1621) s(1663) =< s(1661) s(1664) =< s(1621) s(1665) =< s(1621) s(1666) =< s(1621) s(1667) =< s(1621) s(1664) =< s(1622) s(1665) =< s(1622) s(1666) =< s(1622) s(1667) =< s(1622) s(1664) =< aux(283)+aux(283)+aux(282) s(1666) =< aux(283)+aux(283)+aux(282) s(1668) =< s(1665) s(1669) =< s(1667)*s(1621) s(1670) =< aux(283)+aux(283)+aux(282) s(1671) =< aux(283)+aux(283)+aux(282) s(1672) =< s(1667)*s(1642) s(1673) =< s(1667)*s(1642) s(1674) =< s(1666)*s(1642) s(1675) =< s(1666)*s(1643) s(1671) =< s(1666)*s(1642) s(1676) =< s(1666)*s(1643) s(1677) =< s(1664) s(1678) =< s(1666)*s(1644) s(1670) =< s(1666)*aux(283) s(1679) =< s(1674) s(1680) =< s(1675) s(1681) =< s(1671) s(1682) =< s(1672) s(1683) =< s(1670) s(1684) =< s(1621) s(1685) =< s(1621) s(1684) =< s(1622) s(1685) =< s(1622) s(1686) =< aux(283) s(1686) =< s(1624) s(1684) =< s(1686)+s(1686)+aux(282) s(1685) =< s(1686)+s(1686)+aux(282) s(1687) =< s(1686)+s(1686)+aux(282) s(1688) =< s(1686)+s(1686)+aux(282) s(1689) =< s(1685)*s(1642) s(1690) =< s(1685)*s(1643) s(1688) =< s(1685)*s(1642) s(1691) =< s(1685)*s(1643) s(1692) =< s(1684) s(1693) =< s(1685)*s(1644) s(1687) =< s(1685)*aux(283) s(1694) =< s(1689) s(1695) =< s(1690) s(1696) =< s(1688) s(1697) =< s(1687) s(1698) =< s(1621) s(1699) =< s(1621) s(1698) =< s(1618)+s(1621) s(1699) =< s(1618)+s(1621) s(1700) =< s(1698) s(1701) =< s(1621) s(1702) =< s(1621) s(1701) =< s(1686)+s(1686)+aux(282) s(1702) =< s(1686)+s(1686)+aux(282) s(1703) =< s(1686)+s(1686)+aux(282) s(1704) =< s(1686)+s(1686)+aux(282) s(1705) =< s(1702)*s(1642) s(1706) =< s(1702)*s(1643) s(1704) =< s(1702)*s(1642) s(1707) =< s(1702)*s(1643) s(1708) =< s(1701) s(1709) =< s(1702)*s(1644) s(1703) =< s(1702)*aux(283) s(1710) =< s(1705) s(1711) =< s(1706) s(1712) =< s(1704) s(1713) =< s(1703) s(1714) =< s(1621) s(1715) =< s(1621) s(1714) =< s(1621)+s(1621) s(1715) =< s(1621)+s(1621) s(1716) =< s(1714) s(1717) =< s(1621) s(1718) =< s(1621) s(1717) =< aux(283)+aux(282) s(1718) =< aux(283)+aux(282) s(1719) =< s(1717) s(1720) =< aux(283) s(1721) =< aux(283) s(1720) =< s(1618)+aux(283) s(1721) =< s(1618)+aux(283) s(1722) =< s(1720) with precondition: [V1>=0,V>=0] * Chain [42]: 1 with precondition: [V=0,V1>=0] Closed-form bounds of start(V1,V): ------------------------------------- * Chain [43] with precondition: [V1>=0,V>=0] - Upper bound: 414*V1+689*V+476+(V1+V)*(420*V)+(V1+V)*(nat(V1+V-1)*42)+(1961*V1+1961*V)+(1428*V1+1428*V)*(V1+V)+(54*V1+54)+(99*V+99)+(114*V1+114*V+114) - Complexity: n^2 * Chain [42] with precondition: [V=0,V1>=0] - Upper bound: 1 - Complexity: constant ### Maximum cost of start(V1,V): 414*V1+689*V+475+(V1+V)*(420*V)+(V1+V)*(nat(V1+V-1)*42)+(1961*V1+1961*V)+(1428*V1+1428*V)*(V1+V)+(54*V1+54)+(99*V+99)+(114*V1+114*V+114)+1 Asymptotic class: n^2 * Total analysis performed in 6727 ms. ---------------------------------------- (12) BOUNDS(1, n^2) ---------------------------------------- (13) RenamingProof (BOTH BOUNDS(ID, ID)) Renamed function symbols to avoid clashes with predefined symbol. ---------------------------------------- (14) Obligation: The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, INF). The TRS R consists of the following rules: min(x, 0') -> 0' min(0', y) -> 0' min(s(x), s(y)) -> s(min(x, y)) max(x, 0') -> x max(0', y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0') -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) S is empty. Rewrite Strategy: INNERMOST ---------------------------------------- (15) TypeInferenceProof (BOTH BOUNDS(ID, ID)) Infered types. ---------------------------------------- (16) Obligation: Innermost TRS: Rules: min(x, 0') -> 0' min(0', y) -> 0' min(s(x), s(y)) -> s(min(x, y)) max(x, 0') -> x max(0', y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0') -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) Types: min :: 0':s -> 0':s -> 0':s 0' :: 0':s s :: 0':s -> 0':s max :: 0':s -> 0':s -> 0':s - :: 0':s -> 0':s -> 0':s gcd :: 0':s -> 0':s -> gcd hole_0':s1_0 :: 0':s hole_gcd2_0 :: gcd gen_0':s3_0 :: Nat -> 0':s ---------------------------------------- (17) OrderProof (LOWER BOUND(ID)) Heuristically decided to analyse the following defined symbols: min, max, -, gcd They will be analysed ascendingly in the following order: min < gcd max < gcd - < gcd ---------------------------------------- (18) Obligation: Innermost TRS: Rules: min(x, 0') -> 0' min(0', y) -> 0' min(s(x), s(y)) -> s(min(x, y)) max(x, 0') -> x max(0', y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0') -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) Types: min :: 0':s -> 0':s -> 0':s 0' :: 0':s s :: 0':s -> 0':s max :: 0':s -> 0':s -> 0':s - :: 0':s -> 0':s -> 0':s gcd :: 0':s -> 0':s -> gcd hole_0':s1_0 :: 0':s hole_gcd2_0 :: gcd gen_0':s3_0 :: Nat -> 0':s Generator Equations: gen_0':s3_0(0) <=> 0' gen_0':s3_0(+(x, 1)) <=> s(gen_0':s3_0(x)) The following defined symbols remain to be analysed: min, max, -, gcd They will be analysed ascendingly in the following order: min < gcd max < gcd - < gcd ---------------------------------------- (19) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: min(gen_0':s3_0(n5_0), gen_0':s3_0(n5_0)) -> gen_0':s3_0(n5_0), rt in Omega(1 + n5_0) Induction Base: min(gen_0':s3_0(0), gen_0':s3_0(0)) ->_R^Omega(1) 0' Induction Step: min(gen_0':s3_0(+(n5_0, 1)), gen_0':s3_0(+(n5_0, 1))) ->_R^Omega(1) s(min(gen_0':s3_0(n5_0), gen_0':s3_0(n5_0))) ->_IH s(gen_0':s3_0(c6_0)) 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: min(x, 0') -> 0' min(0', y) -> 0' min(s(x), s(y)) -> s(min(x, y)) max(x, 0') -> x max(0', y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0') -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) Types: min :: 0':s -> 0':s -> 0':s 0' :: 0':s s :: 0':s -> 0':s max :: 0':s -> 0':s -> 0':s - :: 0':s -> 0':s -> 0':s gcd :: 0':s -> 0':s -> gcd hole_0':s1_0 :: 0':s hole_gcd2_0 :: gcd gen_0':s3_0 :: Nat -> 0':s Generator Equations: gen_0':s3_0(0) <=> 0' gen_0':s3_0(+(x, 1)) <=> s(gen_0':s3_0(x)) The following defined symbols remain to be analysed: min, max, -, gcd They will be analysed ascendingly in the following order: min < gcd max < gcd - < gcd ---------------------------------------- (22) LowerBoundPropagationProof (FINISHED) Propagated lower bound. ---------------------------------------- (23) BOUNDS(n^1, INF) ---------------------------------------- (24) Obligation: Innermost TRS: Rules: min(x, 0') -> 0' min(0', y) -> 0' min(s(x), s(y)) -> s(min(x, y)) max(x, 0') -> x max(0', y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0') -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) Types: min :: 0':s -> 0':s -> 0':s 0' :: 0':s s :: 0':s -> 0':s max :: 0':s -> 0':s -> 0':s - :: 0':s -> 0':s -> 0':s gcd :: 0':s -> 0':s -> gcd hole_0':s1_0 :: 0':s hole_gcd2_0 :: gcd gen_0':s3_0 :: Nat -> 0':s Lemmas: min(gen_0':s3_0(n5_0), gen_0':s3_0(n5_0)) -> gen_0':s3_0(n5_0), rt in Omega(1 + n5_0) Generator Equations: gen_0':s3_0(0) <=> 0' gen_0':s3_0(+(x, 1)) <=> s(gen_0':s3_0(x)) The following defined symbols remain to be analysed: max, -, gcd They will be analysed ascendingly in the following order: max < gcd - < gcd ---------------------------------------- (25) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: max(gen_0':s3_0(n343_0), gen_0':s3_0(n343_0)) -> gen_0':s3_0(n343_0), rt in Omega(1 + n343_0) Induction Base: max(gen_0':s3_0(0), gen_0':s3_0(0)) ->_R^Omega(1) gen_0':s3_0(0) Induction Step: max(gen_0':s3_0(+(n343_0, 1)), gen_0':s3_0(+(n343_0, 1))) ->_R^Omega(1) s(max(gen_0':s3_0(n343_0), gen_0':s3_0(n343_0))) ->_IH s(gen_0':s3_0(c344_0)) 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: min(x, 0') -> 0' min(0', y) -> 0' min(s(x), s(y)) -> s(min(x, y)) max(x, 0') -> x max(0', y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0') -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) Types: min :: 0':s -> 0':s -> 0':s 0' :: 0':s s :: 0':s -> 0':s max :: 0':s -> 0':s -> 0':s - :: 0':s -> 0':s -> 0':s gcd :: 0':s -> 0':s -> gcd hole_0':s1_0 :: 0':s hole_gcd2_0 :: gcd gen_0':s3_0 :: Nat -> 0':s Lemmas: min(gen_0':s3_0(n5_0), gen_0':s3_0(n5_0)) -> gen_0':s3_0(n5_0), rt in Omega(1 + n5_0) max(gen_0':s3_0(n343_0), gen_0':s3_0(n343_0)) -> gen_0':s3_0(n343_0), rt in Omega(1 + n343_0) Generator Equations: gen_0':s3_0(0) <=> 0' gen_0':s3_0(+(x, 1)) <=> s(gen_0':s3_0(x)) The following defined symbols remain to be analysed: -, gcd They will be analysed ascendingly in the following order: - < gcd ---------------------------------------- (27) RewriteLemmaProof (LOWER BOUND(ID)) Proved the following rewrite lemma: -(gen_0':s3_0(n773_0), gen_0':s3_0(n773_0)) -> gen_0':s3_0(0), rt in Omega(1 + n773_0) Induction Base: -(gen_0':s3_0(0), gen_0':s3_0(0)) ->_R^Omega(1) gen_0':s3_0(0) Induction Step: -(gen_0':s3_0(+(n773_0, 1)), gen_0':s3_0(+(n773_0, 1))) ->_R^Omega(1) -(gen_0':s3_0(n773_0), gen_0':s3_0(n773_0)) ->_IH gen_0':s3_0(0) 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: min(x, 0') -> 0' min(0', y) -> 0' min(s(x), s(y)) -> s(min(x, y)) max(x, 0') -> x max(0', y) -> y max(s(x), s(y)) -> s(max(x, y)) -(x, 0') -> x -(s(x), s(y)) -> -(x, y) gcd(s(x), s(y)) -> gcd(-(s(max(x, y)), s(min(x, y))), s(min(x, y))) Types: min :: 0':s -> 0':s -> 0':s 0' :: 0':s s :: 0':s -> 0':s max :: 0':s -> 0':s -> 0':s - :: 0':s -> 0':s -> 0':s gcd :: 0':s -> 0':s -> gcd hole_0':s1_0 :: 0':s hole_gcd2_0 :: gcd gen_0':s3_0 :: Nat -> 0':s Lemmas: min(gen_0':s3_0(n5_0), gen_0':s3_0(n5_0)) -> gen_0':s3_0(n5_0), rt in Omega(1 + n5_0) max(gen_0':s3_0(n343_0), gen_0':s3_0(n343_0)) -> gen_0':s3_0(n343_0), rt in Omega(1 + n343_0) -(gen_0':s3_0(n773_0), gen_0':s3_0(n773_0)) -> gen_0':s3_0(0), rt in Omega(1 + n773_0) Generator Equations: gen_0':s3_0(0) <=> 0' gen_0':s3_0(+(x, 1)) <=> s(gen_0':s3_0(x)) The following defined symbols remain to be analysed: gcd