1115.63/291.46 WORST_CASE(Omega(n^1), O(n^2)) 1115.63/291.47 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 1115.63/291.47 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 1115.63/291.47 1115.63/291.47 1115.63/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1115.63/291.47 1115.63/291.47 (0) CpxTRS 1115.63/291.47 (1) RelTrsToWeightedTrsProof [BOTH BOUNDS(ID, ID), 0 ms] 1115.63/291.47 (2) CpxWeightedTrs 1115.63/291.47 (3) TypeInferenceProof [BOTH BOUNDS(ID, ID), 0 ms] 1115.63/291.47 (4) CpxTypedWeightedTrs 1115.63/291.47 (5) CompletionProof [UPPER BOUND(ID), 0 ms] 1115.63/291.47 (6) CpxTypedWeightedCompleteTrs 1115.63/291.47 (7) CpxTypedWeightedTrsToRntsProof [UPPER BOUND(ID), 0 ms] 1115.63/291.47 (8) CpxRNTS 1115.63/291.47 (9) CompleteCoflocoProof [FINISHED, 1980 ms] 1115.63/291.47 (10) BOUNDS(1, n^2) 1115.63/291.47 (11) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms] 1115.63/291.47 (12) TRS for Loop Detection 1115.63/291.47 (13) DecreasingLoopProof [LOWER BOUND(ID), 0 ms] 1115.63/291.47 (14) BEST 1115.63/291.47 (15) proven lower bound 1115.63/291.47 (16) LowerBoundPropagationProof [FINISHED, 0 ms] 1115.63/291.47 (17) BOUNDS(n^1, INF) 1115.63/291.47 (18) TRS for Loop Detection 1115.63/291.47 1115.63/291.47 1115.63/291.47 ---------------------------------------- 1115.63/291.47 1115.63/291.47 (0) 1115.63/291.47 Obligation: 1115.63/291.47 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1115.63/291.47 1115.63/291.47 1115.63/291.47 The TRS R consists of the following rules: 1115.63/291.47 1115.63/291.47 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, s(y), z) 1115.63/291.47 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, y, s(z)) 1115.63/291.47 gt(0, v) -> false 1115.63/291.47 gt(s(u), 0) -> true 1115.63/291.47 gt(s(u), s(v)) -> gt(u, v) 1115.63/291.47 and(x, true) -> x 1115.63/291.47 and(x, false) -> false 1115.63/291.47 1115.63/291.47 S is empty. 1115.63/291.47 Rewrite Strategy: INNERMOST 1115.63/291.47 ---------------------------------------- 1115.63/291.47 1115.63/291.47 (1) RelTrsToWeightedTrsProof (BOTH BOUNDS(ID, ID)) 1115.63/291.47 Transformed relative TRS to weighted TRS 1115.63/291.47 ---------------------------------------- 1115.63/291.47 1115.63/291.47 (2) 1115.63/291.47 Obligation: 1115.63/291.47 The Runtime Complexity (innermost) of the given CpxWeightedTrs could be proven to be BOUNDS(1, n^2). 1115.63/291.47 1115.63/291.47 1115.63/291.47 The TRS R consists of the following rules: 1115.63/291.47 1115.63/291.47 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, s(y), z) [1] 1115.63/291.47 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, y, s(z)) [1] 1115.63/291.47 gt(0, v) -> false [1] 1115.63/291.47 gt(s(u), 0) -> true [1] 1115.63/291.47 gt(s(u), s(v)) -> gt(u, v) [1] 1115.63/291.47 and(x, true) -> x [1] 1115.63/291.47 and(x, false) -> false [1] 1115.63/291.47 1115.63/291.47 Rewrite Strategy: INNERMOST 1115.63/291.47 ---------------------------------------- 1115.63/291.47 1115.63/291.47 (3) TypeInferenceProof (BOTH BOUNDS(ID, ID)) 1115.63/291.47 Infered types. 1115.63/291.47 ---------------------------------------- 1115.63/291.47 1115.63/291.47 (4) 1115.63/291.47 Obligation: 1115.63/291.47 Runtime Complexity Weighted TRS with Types. 1115.63/291.47 The TRS R consists of the following rules: 1115.63/291.47 1115.63/291.47 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, s(y), z) [1] 1115.63/291.47 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, y, s(z)) [1] 1115.63/291.47 gt(0, v) -> false [1] 1115.63/291.47 gt(s(u), 0) -> true [1] 1115.63/291.47 gt(s(u), s(v)) -> gt(u, v) [1] 1115.63/291.47 and(x, true) -> x [1] 1115.63/291.47 and(x, false) -> false [1] 1115.63/291.47 1115.63/291.47 The TRS has the following type information: 1115.63/291.47 f :: true:false -> s:0 -> s:0 -> s:0 -> f 1115.63/291.47 true :: true:false 1115.63/291.47 and :: true:false -> true:false -> true:false 1115.63/291.47 gt :: s:0 -> s:0 -> true:false 1115.63/291.47 s :: s:0 -> s:0 1115.63/291.47 0 :: s:0 1115.63/291.47 false :: true:false 1115.63/291.47 1115.63/291.47 Rewrite Strategy: INNERMOST 1115.63/291.47 ---------------------------------------- 1115.63/291.47 1115.63/291.47 (5) CompletionProof (UPPER BOUND(ID)) 1115.63/291.47 The TRS is a completely defined constructor system, as every type has a constant constructor and the following rules were added: 1115.63/291.47 1115.63/291.47 f(v0, v1, v2, v3) -> null_f [0] 1115.63/291.47 1115.63/291.47 And the following fresh constants: null_f 1115.63/291.47 1115.63/291.47 ---------------------------------------- 1115.63/291.47 1115.63/291.47 (6) 1115.63/291.47 Obligation: 1115.63/291.47 Runtime Complexity Weighted TRS where all functions are completely defined. The underlying TRS is: 1115.63/291.47 1115.63/291.47 Runtime Complexity Weighted TRS with Types. 1115.63/291.47 The TRS R consists of the following rules: 1115.63/291.47 1115.63/291.47 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, s(y), z) [1] 1115.63/291.47 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, y, s(z)) [1] 1115.63/291.47 gt(0, v) -> false [1] 1115.63/291.47 gt(s(u), 0) -> true [1] 1115.63/291.47 gt(s(u), s(v)) -> gt(u, v) [1] 1115.63/291.47 and(x, true) -> x [1] 1115.63/291.47 and(x, false) -> false [1] 1115.63/291.47 f(v0, v1, v2, v3) -> null_f [0] 1115.63/291.47 1115.63/291.47 The TRS has the following type information: 1115.63/291.47 f :: true:false -> s:0 -> s:0 -> s:0 -> null_f 1115.63/291.47 true :: true:false 1115.63/291.47 and :: true:false -> true:false -> true:false 1115.63/291.47 gt :: s:0 -> s:0 -> true:false 1115.63/291.47 s :: s:0 -> s:0 1115.63/291.47 0 :: s:0 1115.63/291.47 false :: true:false 1115.63/291.47 null_f :: null_f 1115.63/291.47 1115.63/291.47 Rewrite Strategy: INNERMOST 1115.63/291.47 ---------------------------------------- 1115.63/291.47 1115.63/291.47 (7) CpxTypedWeightedTrsToRntsProof (UPPER BOUND(ID)) 1115.63/291.47 Transformed the TRS into an over-approximating RNTS by (improved) Size Abstraction. 1115.63/291.47 The constant constructors are abstracted as follows: 1115.63/291.47 1115.63/291.47 true => 1 1115.63/291.47 0 => 0 1115.63/291.47 false => 0 1115.63/291.47 null_f => 0 1115.63/291.47 1115.63/291.47 ---------------------------------------- 1115.63/291.47 1115.63/291.47 (8) 1115.63/291.47 Obligation: 1115.63/291.47 Complexity RNTS consisting of the following rules: 1115.63/291.47 1115.63/291.47 and(z', z'') -{ 1 }-> x :|: z' = x, x >= 0, z'' = 1 1115.63/291.47 and(z', z'') -{ 1 }-> 0 :|: z'' = 0, z' = x, x >= 0 1115.63/291.47 f(z', z'', z1, z2) -{ 1 }-> f(and(gt(x, y), gt(x, z)), x, y, 1 + z) :|: z1 = y, z >= 0, z2 = z, x >= 0, y >= 0, z'' = x, z' = 1 1115.63/291.47 f(z', z'', z1, z2) -{ 1 }-> f(and(gt(x, y), gt(x, z)), x, 1 + y, z) :|: z1 = y, z >= 0, z2 = z, x >= 0, y >= 0, z'' = x, z' = 1 1115.63/291.47 f(z', z'', z1, z2) -{ 0 }-> 0 :|: z2 = v3, v0 >= 0, z1 = v2, v1 >= 0, z'' = v1, v2 >= 0, v3 >= 0, z' = v0 1115.63/291.47 gt(z', z'') -{ 1 }-> gt(u, v) :|: v >= 0, z' = 1 + u, z'' = 1 + v, u >= 0 1115.63/291.47 gt(z', z'') -{ 1 }-> 1 :|: z'' = 0, z' = 1 + u, u >= 0 1115.63/291.47 gt(z', z'') -{ 1 }-> 0 :|: z'' = v, v >= 0, z' = 0 1115.63/291.47 1115.63/291.47 Only complete derivations are relevant for the runtime complexity. 1115.63/291.47 1115.63/291.47 ---------------------------------------- 1115.63/291.47 1115.63/291.47 (9) CompleteCoflocoProof (FINISHED) 1115.63/291.47 Transformed the RNTS (where only complete derivations are relevant) into cost relations for CoFloCo: 1115.63/291.47 1115.63/291.47 eq(start(V, V1, V6, V2),0,[f(V, V1, V6, V2, Out)],[V >= 0,V1 >= 0,V6 >= 0,V2 >= 0]). 1115.63/291.47 eq(start(V, V1, V6, V2),0,[gt(V, V1, Out)],[V >= 0,V1 >= 0]). 1115.63/291.47 eq(start(V, V1, V6, V2),0,[and(V, V1, Out)],[V >= 0,V1 >= 0]). 1115.63/291.47 eq(f(V, V1, V6, V2, Out),1,[gt(V4, V3, Ret00),gt(V4, V5, Ret01),and(Ret00, Ret01, Ret0),f(Ret0, V4, 1 + V3, V5, Ret)],[Out = Ret,V6 = V3,V5 >= 0,V2 = V5,V4 >= 0,V3 >= 0,V1 = V4,V = 1]). 1115.63/291.47 eq(f(V, V1, V6, V2, Out),1,[gt(V7, V9, Ret001),gt(V7, V8, Ret011),and(Ret001, Ret011, Ret02),f(Ret02, V7, V9, 1 + V8, Ret1)],[Out = Ret1,V6 = V9,V8 >= 0,V2 = V8,V7 >= 0,V9 >= 0,V1 = V7,V = 1]). 1115.63/291.47 eq(gt(V, V1, Out),1,[],[Out = 0,V1 = V10,V10 >= 0,V = 0]). 1115.63/291.47 eq(gt(V, V1, Out),1,[],[Out = 1,V1 = 0,V = 1 + V11,V11 >= 0]). 1115.63/291.47 eq(gt(V, V1, Out),1,[gt(V12, V13, Ret2)],[Out = Ret2,V13 >= 0,V = 1 + V12,V1 = 1 + V13,V12 >= 0]). 1115.63/291.47 eq(and(V, V1, Out),1,[],[Out = V14,V = V14,V14 >= 0,V1 = 1]). 1115.63/291.47 eq(and(V, V1, Out),1,[],[Out = 0,V1 = 0,V = V15,V15 >= 0]). 1115.63/291.47 eq(f(V, V1, V6, V2, Out),0,[],[Out = 0,V2 = V18,V17 >= 0,V6 = V19,V16 >= 0,V1 = V16,V19 >= 0,V18 >= 0,V = V17]). 1115.63/291.47 input_output_vars(f(V,V1,V6,V2,Out),[V,V1,V6,V2],[Out]). 1115.63/291.47 input_output_vars(gt(V,V1,Out),[V,V1],[Out]). 1115.63/291.47 input_output_vars(and(V,V1,Out),[V,V1],[Out]). 1115.63/291.47 1115.63/291.47 1115.63/291.47 CoFloCo proof output: 1115.63/291.47 Preprocessing Cost Relations 1115.63/291.47 ===================================== 1115.63/291.47 1115.63/291.47 #### Computed strongly connected components 1115.63/291.47 0. non_recursive : [and/3] 1115.63/291.47 1. recursive : [gt/3] 1115.63/291.47 2. recursive : [f/5] 1115.63/291.47 3. non_recursive : [start/4] 1115.63/291.47 1115.63/291.47 #### Obtained direct recursion through partial evaluation 1115.63/291.47 0. SCC is partially evaluated into and/3 1115.63/291.47 1. SCC is partially evaluated into gt/3 1115.63/291.47 2. SCC is partially evaluated into f/5 1115.63/291.47 3. SCC is partially evaluated into start/4 1115.63/291.47 1115.63/291.47 Control-Flow Refinement of Cost Relations 1115.63/291.47 ===================================== 1115.63/291.47 1115.63/291.47 ### Specialization of cost equations and/3 1115.63/291.47 * CE 10 is refined into CE [12] 1115.63/291.47 * CE 11 is refined into CE [13] 1115.63/291.47 1115.63/291.47 1115.63/291.47 ### Cost equations --> "Loop" of and/3 1115.63/291.47 * CEs [12] --> Loop 10 1115.63/291.47 * CEs [13] --> Loop 11 1115.63/291.47 1115.63/291.47 ### Ranking functions of CR and(V,V1,Out) 1115.63/291.47 1115.63/291.47 #### Partial ranking functions of CR and(V,V1,Out) 1115.63/291.47 1115.63/291.47 1115.63/291.47 ### Specialization of cost equations gt/3 1115.63/291.47 * CE 9 is refined into CE [14] 1115.63/291.47 * CE 8 is refined into CE [15] 1115.63/291.47 * CE 7 is refined into CE [16] 1115.63/291.47 1115.63/291.47 1115.63/291.47 ### Cost equations --> "Loop" of gt/3 1115.63/291.47 * CEs [15] --> Loop 12 1115.63/291.47 * CEs [16] --> Loop 13 1115.63/291.47 * CEs [14] --> Loop 14 1115.63/291.47 1115.63/291.47 ### Ranking functions of CR gt(V,V1,Out) 1115.63/291.47 * RF of phase [14]: [V,V1] 1115.63/291.47 1115.63/291.47 #### Partial ranking functions of CR gt(V,V1,Out) 1115.63/291.47 * Partial RF of phase [14]: 1115.63/291.47 - RF of loop [14:1]: 1115.63/291.47 V 1115.63/291.47 V1 1115.63/291.47 1115.63/291.47 1115.63/291.47 ### Specialization of cost equations f/5 1115.63/291.47 * CE 6 is refined into CE [17] 1115.63/291.47 * CE 5 is refined into CE [18,19,20,21,22,23,24,25,26,27] 1115.63/291.47 * CE 4 is refined into CE [28,29,30,31,32,33,34,35,36,37] 1115.63/291.47 1115.63/291.47 1115.63/291.47 ### Cost equations --> "Loop" of f/5 1115.63/291.47 * CEs [27] --> Loop 15 1115.63/291.47 * CEs [37] --> Loop 16 1115.63/291.47 * CEs [24] --> Loop 17 1115.63/291.47 * CEs [26] --> Loop 18 1115.63/291.47 * CEs [23] --> Loop 19 1115.63/291.47 * CEs [34] --> Loop 20 1115.63/291.47 * CEs [36] --> Loop 21 1115.63/291.47 * CEs [33] --> Loop 22 1115.63/291.47 * CEs [25] --> Loop 23 1115.63/291.47 * CEs [35] --> Loop 24 1115.63/291.47 * CEs [22] --> Loop 25 1115.63/291.47 * CEs [32] --> Loop 26 1115.63/291.47 * CEs [31] --> Loop 27 1115.63/291.47 * CEs [21] --> Loop 28 1115.63/291.47 * CEs [30] --> Loop 29 1115.63/291.47 * CEs [20] --> Loop 30 1115.63/291.47 * CEs [29] --> Loop 31 1115.63/291.47 * CEs [19] --> Loop 32 1115.63/291.47 * CEs [18] --> Loop 33 1115.63/291.47 * CEs [28] --> Loop 34 1115.63/291.47 * CEs [17] --> Loop 35 1115.63/291.47 1115.63/291.47 ### Ranking functions of CR f(V,V1,V6,V2,Out) 1115.63/291.47 * RF of phase [15,16]: [2*V1-V6-V2-1] 1115.63/291.47 * RF of phase [24]: [V1-V6] 1115.63/291.47 * RF of phase [28]: [V1-V2] 1115.63/291.47 1115.63/291.47 #### Partial ranking functions of CR f(V,V1,V6,V2,Out) 1115.63/291.47 * Partial RF of phase [15,16]: 1115.63/291.47 - RF of loop [15:1]: 1115.63/291.47 V1-V2 1115.63/291.47 - RF of loop [16:1]: 1115.63/291.47 V1-V6 1115.63/291.47 * Partial RF of phase [24]: 1115.63/291.47 - RF of loop [24:1]: 1115.63/291.47 V1-V6 1115.63/291.47 * Partial RF of phase [28]: 1115.63/291.47 - RF of loop [28:1]: 1115.63/291.47 V1-V2 1115.63/291.47 1115.63/291.47 1115.63/291.47 ### Specialization of cost equations start/4 1115.63/291.47 * CE 1 is refined into CE [38,39,40,41,42,43,44,45,46,47] 1115.63/291.47 * CE 2 is refined into CE [48,49,50,51] 1115.63/291.47 * CE 3 is refined into CE [52,53] 1115.63/291.47 1115.63/291.47 1115.63/291.47 ### Cost equations --> "Loop" of start/4 1115.63/291.47 * CEs [51] --> Loop 36 1115.63/291.47 * CEs [53] --> Loop 37 1115.63/291.47 * CEs [49,52] --> Loop 38 1115.63/291.47 * CEs [47] --> Loop 39 1115.63/291.47 * CEs [46] --> Loop 40 1115.63/291.47 * CEs [45] --> Loop 41 1115.63/291.47 * CEs [44] --> Loop 42 1115.63/291.47 * CEs [43] --> Loop 43 1115.63/291.47 * CEs [42] --> Loop 44 1115.63/291.47 * CEs [41] --> Loop 45 1115.63/291.47 * CEs [40,50] --> Loop 46 1115.63/291.47 * CEs [38,39] --> Loop 47 1115.63/291.47 * CEs [48] --> Loop 48 1115.63/291.47 1115.63/291.47 ### Ranking functions of CR start(V,V1,V6,V2) 1115.63/291.47 1115.63/291.47 #### Partial ranking functions of CR start(V,V1,V6,V2) 1115.63/291.47 1115.63/291.47 1115.63/291.47 Computing Bounds 1115.63/291.47 ===================================== 1115.63/291.47 1115.63/291.47 #### Cost of chains of and(V,V1,Out): 1115.63/291.47 * Chain [11]: 1 1115.63/291.47 with precondition: [V1=0,Out=0,V>=0] 1115.63/291.47 1115.63/291.47 * Chain [10]: 1 1115.63/291.47 with precondition: [V1=1,V=Out,V>=0] 1115.63/291.47 1115.63/291.47 1115.63/291.47 #### Cost of chains of gt(V,V1,Out): 1115.63/291.47 * Chain [[14],13]: 1*it(14)+1 1115.63/291.47 Such that:it(14) =< V 1115.63/291.47 1115.63/291.47 with precondition: [Out=0,V>=1,V1>=V] 1115.63/291.47 1115.63/291.47 * Chain [[14],12]: 1*it(14)+1 1115.63/291.47 Such that:it(14) =< V1 1115.63/291.47 1115.63/291.47 with precondition: [Out=1,V1>=1,V>=V1+1] 1115.63/291.47 1115.63/291.47 * Chain [13]: 1 1115.63/291.47 with precondition: [V=0,Out=0,V1>=0] 1115.63/291.47 1115.63/291.47 * Chain [12]: 1 1115.63/291.47 with precondition: [V1=0,Out=1,V>=1] 1115.63/291.47 1115.63/291.47 1115.63/291.47 #### Cost of chains of f(V,V1,V6,V2,Out): 1115.63/291.47 * Chain [[28],35]: 4*it(28)+1*s(3)+0 1115.63/291.47 Such that:aux(1) =< V1 1115.63/291.47 it(28) =< V1-V2 1115.63/291.47 s(3) =< it(28)*aux(1) 1115.63/291.47 1115.63/291.47 with precondition: [V=1,V6=0,Out=0,V2>=1,V1>=V2+1] 1115.63/291.47 1115.63/291.47 * Chain [[28],30,35]: 4*it(28)+1*s(3)+1*s(4)+4 1115.63/291.47 Such that:it(28) =< V1-V2 1115.63/291.47 aux(2) =< V1 1115.63/291.47 s(4) =< aux(2) 1115.63/291.47 s(3) =< it(28)*aux(2) 1115.63/291.47 1115.63/291.47 with precondition: [V=1,V6=0,Out=0,V2>=1,V1>=V2+1] 1115.63/291.47 1115.63/291.47 * Chain [[28],29,35]: 4*it(28)+1*s(3)+1*s(5)+4 1115.63/291.47 Such that:it(28) =< V1-V2 1115.63/291.47 aux(3) =< V1 1115.63/291.47 s(5) =< aux(3) 1115.63/291.47 s(3) =< it(28)*aux(3) 1115.63/291.47 1115.63/291.47 with precondition: [V=1,V6=0,Out=0,V2>=1,V1>=V2+1] 1115.63/291.47 1115.63/291.47 * Chain [[28],27,[15,16],35]: 9*it(15)+4*it(28)+1*s(3)+2*s(14)+1*s(16)+1*s(17)+4 1115.63/291.47 Such that:it(28) =< 2*V1-V2 1115.63/291.47 aux(12) =< V1 1115.63/291.47 aux(13) =< 2*V1 1115.63/291.47 it(15) =< aux(13) 1115.63/291.47 aux(7) =< aux(12)-1 1115.63/291.47 aux(6) =< aux(12)+1 1115.63/291.47 s(14) =< it(15)*aux(12) 1115.63/291.47 s(17) =< it(15)*aux(7) 1115.63/291.47 s(16) =< it(15)*aux(6) 1115.63/291.47 s(3) =< it(28)*aux(12) 1115.63/291.47 1115.63/291.47 with precondition: [V=1,V6=0,Out=0,V2>=1,V1>=V2+2] 1115.63/291.47 1115.63/291.47 * Chain [[28],27,[15,16],21,35]: 8*it(15)+4*it(28)+1*s(3)+2*s(14)+1*s(16)+1*s(17)+3*s(18)+8 1115.63/291.47 Such that:aux(15) =< 2*V1 1115.63/291.47 it(28) =< 2*V1-V2 1115.63/291.47 aux(17) =< V1 1115.63/291.47 it(15) =< aux(17) 1115.63/291.47 s(18) =< aux(17) 1115.63/291.47 it(15) =< aux(15) 1115.63/291.47 aux(7) =< aux(17)-1 1115.63/291.47 aux(6) =< aux(17)+1 1115.63/291.47 s(14) =< it(15)*aux(17) 1115.63/291.47 s(17) =< it(15)*aux(7) 1115.63/291.47 s(16) =< it(15)*aux(6) 1115.63/291.47 s(3) =< it(28)*aux(17) 1115.63/291.47 1115.63/291.47 with precondition: [V=1,V6=0,Out=0,V2>=1,V1>=V2+2] 1115.63/291.47 1115.63/291.47 * Chain [[28],27,[15,16],20,35]: 8*it(15)+4*it(28)+1*s(3)+2*s(14)+1*s(16)+1*s(17)+3*s(18)+8 1115.63/291.47 Such that:aux(19) =< 2*V1 1115.63/291.47 it(28) =< 2*V1-V2 1115.63/291.47 aux(21) =< V1 1115.63/291.47 it(15) =< aux(21) 1115.63/291.47 s(18) =< aux(21) 1115.63/291.47 it(15) =< aux(19) 1115.63/291.47 aux(7) =< aux(21)-1 1115.63/291.47 aux(6) =< aux(21)+1 1115.63/291.47 s(14) =< it(15)*aux(21) 1115.63/291.47 s(17) =< it(15)*aux(7) 1115.63/291.47 s(16) =< it(15)*aux(6) 1115.63/291.47 s(3) =< it(28)*aux(21) 1115.63/291.47 1115.63/291.47 with precondition: [V=1,V6=0,Out=0,V2>=1,V1>=V2+2] 1115.63/291.47 1115.63/291.47 * Chain [[28],27,[15,16],18,35]: 8*it(15)+4*it(28)+1*s(3)+2*s(14)+1*s(16)+1*s(17)+3*s(18)+8 1115.63/291.47 Such that:aux(23) =< 2*V1 1115.63/291.47 it(28) =< 2*V1-V2 1115.63/291.47 aux(25) =< V1 1115.63/291.47 it(15) =< aux(25) 1115.63/291.47 s(18) =< aux(25) 1115.63/291.47 it(15) =< aux(23) 1115.63/291.47 aux(7) =< aux(25)-1 1115.63/291.47 aux(6) =< aux(25)+1 1115.63/291.47 s(14) =< it(15)*aux(25) 1115.63/291.47 s(17) =< it(15)*aux(7) 1115.63/291.47 s(16) =< it(15)*aux(6) 1115.63/291.47 s(3) =< it(28)*aux(25) 1115.63/291.47 1115.63/291.47 with precondition: [V=1,V6=0,Out=0,V2>=1,V1>=V2+2] 1115.63/291.47 1115.63/291.47 * Chain [[28],27,[15,16],17,35]: 8*it(15)+4*it(28)+1*s(3)+2*s(14)+1*s(16)+1*s(17)+3*s(18)+8 1115.63/291.48 Such that:aux(27) =< 2*V1 1115.63/291.48 it(28) =< 2*V1-V2 1115.63/291.48 aux(29) =< V1 1115.63/291.48 it(15) =< aux(29) 1115.63/291.48 s(18) =< aux(29) 1115.63/291.48 it(15) =< aux(27) 1115.63/291.48 aux(7) =< aux(29)-1 1115.63/291.48 aux(6) =< aux(29)+1 1115.63/291.48 s(14) =< it(15)*aux(29) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 s(3) =< it(28)*aux(29) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,Out=0,V2>=1,V1>=V2+2] 1115.63/291.48 1115.63/291.48 * Chain [[28],27,35]: 4*it(28)+1*s(3)+1*s(18)+4 1115.63/291.48 Such that:it(28) =< V1-V2 1115.63/291.48 aux(30) =< V1 1115.63/291.48 s(18) =< aux(30) 1115.63/291.48 s(3) =< it(28)*aux(30) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,Out=0,V2>=1,V1>=V2+2] 1115.63/291.48 1115.63/291.48 * Chain [[24],35]: 4*it(24)+1*s(29)+0 1115.63/291.48 Such that:aux(31) =< V1 1115.63/291.48 it(24) =< V1-V6 1115.63/291.48 s(29) =< it(24)*aux(31) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V6>=1,V1>=V6+1] 1115.63/291.48 1115.63/291.48 * Chain [[24],26,35]: 4*it(24)+1*s(29)+1*s(30)+4 1115.63/291.48 Such that:it(24) =< V1-V6 1115.63/291.48 aux(32) =< V1 1115.63/291.48 s(30) =< aux(32) 1115.63/291.48 s(29) =< it(24)*aux(32) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V6>=1,V1>=V6+1] 1115.63/291.48 1115.63/291.48 * Chain [[24],25,35]: 4*it(24)+1*s(29)+1*s(31)+4 1115.63/291.48 Such that:it(24) =< V1-V6 1115.63/291.48 aux(33) =< V1 1115.63/291.48 s(31) =< aux(33) 1115.63/291.48 s(29) =< it(24)*aux(33) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V6>=1,V1>=V6+1] 1115.63/291.48 1115.63/291.48 * Chain [[24],23,[15,16],35]: 9*it(15)+4*it(24)+2*s(14)+1*s(16)+1*s(17)+1*s(29)+4 1115.63/291.48 Such that:it(24) =< 2*V1-V6 1115.63/291.48 aux(34) =< V1 1115.63/291.48 aux(35) =< 2*V1 1115.63/291.48 it(15) =< aux(35) 1115.63/291.48 aux(7) =< aux(34)-1 1115.63/291.48 aux(6) =< aux(34)+1 1115.63/291.48 s(14) =< it(15)*aux(34) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 s(29) =< it(24)*aux(34) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V6>=1,V1>=V6+2] 1115.63/291.48 1115.63/291.48 * Chain [[24],23,[15,16],21,35]: 8*it(15)+4*it(24)+2*s(14)+1*s(16)+1*s(17)+3*s(19)+1*s(29)+8 1115.63/291.48 Such that:aux(15) =< 2*V1 1115.63/291.48 it(24) =< 2*V1-V6 1115.63/291.48 aux(37) =< V1 1115.63/291.48 it(15) =< aux(37) 1115.63/291.48 s(19) =< aux(37) 1115.63/291.48 it(15) =< aux(15) 1115.63/291.48 aux(7) =< aux(37)-1 1115.63/291.48 aux(6) =< aux(37)+1 1115.63/291.48 s(14) =< it(15)*aux(37) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 s(29) =< it(24)*aux(37) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V6>=1,V1>=V6+2] 1115.63/291.48 1115.63/291.48 * Chain [[24],23,[15,16],20,35]: 8*it(15)+4*it(24)+2*s(14)+1*s(16)+1*s(17)+3*s(21)+1*s(29)+8 1115.63/291.48 Such that:aux(19) =< 2*V1 1115.63/291.48 it(24) =< 2*V1-V6 1115.63/291.48 aux(39) =< V1 1115.63/291.48 it(15) =< aux(39) 1115.63/291.48 s(21) =< aux(39) 1115.63/291.48 it(15) =< aux(19) 1115.63/291.48 aux(7) =< aux(39)-1 1115.63/291.48 aux(6) =< aux(39)+1 1115.63/291.48 s(14) =< it(15)*aux(39) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 s(29) =< it(24)*aux(39) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V6>=1,V1>=V6+2] 1115.63/291.48 1115.63/291.48 * Chain [[24],23,[15,16],18,35]: 8*it(15)+4*it(24)+2*s(14)+1*s(16)+1*s(17)+3*s(23)+1*s(29)+8 1115.63/291.48 Such that:aux(23) =< 2*V1 1115.63/291.48 it(24) =< 2*V1-V6 1115.63/291.48 aux(41) =< V1 1115.63/291.48 it(15) =< aux(41) 1115.63/291.48 s(23) =< aux(41) 1115.63/291.48 it(15) =< aux(23) 1115.63/291.48 aux(7) =< aux(41)-1 1115.63/291.48 aux(6) =< aux(41)+1 1115.63/291.48 s(14) =< it(15)*aux(41) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 s(29) =< it(24)*aux(41) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V6>=1,V1>=V6+2] 1115.63/291.48 1115.63/291.48 * Chain [[24],23,[15,16],17,35]: 8*it(15)+4*it(24)+2*s(14)+1*s(16)+1*s(17)+3*s(25)+1*s(29)+8 1115.63/291.48 Such that:aux(27) =< 2*V1 1115.63/291.48 it(24) =< 2*V1-V6 1115.63/291.48 aux(43) =< V1 1115.63/291.48 it(15) =< aux(43) 1115.63/291.48 s(25) =< aux(43) 1115.63/291.48 it(15) =< aux(27) 1115.63/291.48 aux(7) =< aux(43)-1 1115.63/291.48 aux(6) =< aux(43)+1 1115.63/291.48 s(14) =< it(15)*aux(43) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 s(29) =< it(24)*aux(43) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V6>=1,V1>=V6+2] 1115.63/291.48 1115.63/291.48 * Chain [[24],23,35]: 4*it(24)+1*s(29)+1*s(32)+4 1115.63/291.48 Such that:it(24) =< V1-V6 1115.63/291.48 aux(44) =< V1 1115.63/291.48 s(32) =< aux(44) 1115.63/291.48 s(29) =< it(24)*aux(44) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V6>=1,V1>=V6+2] 1115.63/291.48 1115.63/291.48 * Chain [[15,16],35]: 8*it(15)+2*s(14)+1*s(16)+1*s(17)+0 1115.63/291.48 Such that:aux(8) =< V1 1115.63/291.48 aux(11) =< 2*V1-V6-V2 1115.63/291.48 it(15) =< aux(11) 1115.63/291.48 aux(7) =< aux(8)-1 1115.63/291.48 aux(6) =< aux(8)+1 1115.63/291.48 s(14) =< it(15)*aux(8) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,Out=0,V6>=1,V2>=1,V1>=V6+1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 * Chain [[15,16],21,35]: 4*it(15)+4*it(16)+2*s(14)+1*s(16)+1*s(17)+2*s(19)+4 1115.63/291.48 Such that:it(16) =< V1-V6 1115.63/291.48 it(15) =< V1-V2 1115.63/291.48 aux(14) =< V1 1115.63/291.48 aux(15) =< 2*V1-V6-V2 1115.63/291.48 s(19) =< aux(14) 1115.63/291.48 it(15) =< aux(15) 1115.63/291.48 it(16) =< aux(15) 1115.63/291.48 aux(7) =< aux(14)-1 1115.63/291.48 aux(6) =< aux(14)+1 1115.63/291.48 s(14) =< it(15)*aux(14) 1115.63/291.48 s(17) =< it(16)*aux(7) 1115.63/291.48 s(16) =< it(16)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,Out=0,V6>=1,V2>=1,V1>=V6+1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 * Chain [[15,16],20,35]: 4*it(15)+4*it(16)+2*s(14)+1*s(16)+1*s(17)+2*s(21)+4 1115.63/291.48 Such that:it(16) =< V1-V6 1115.63/291.48 it(15) =< V1-V2 1115.63/291.48 aux(18) =< V1 1115.63/291.48 aux(19) =< 2*V1-V6-V2 1115.63/291.48 s(21) =< aux(18) 1115.63/291.48 it(15) =< aux(19) 1115.63/291.48 it(16) =< aux(19) 1115.63/291.48 aux(7) =< aux(18)-1 1115.63/291.48 aux(6) =< aux(18)+1 1115.63/291.48 s(14) =< it(15)*aux(18) 1115.63/291.48 s(17) =< it(16)*aux(7) 1115.63/291.48 s(16) =< it(16)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,Out=0,V6>=1,V2>=1,V1>=V6+1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 * Chain [[15,16],18,35]: 4*it(15)+4*it(16)+2*s(14)+1*s(16)+1*s(17)+2*s(23)+4 1115.63/291.48 Such that:it(16) =< V1-V6 1115.63/291.48 it(15) =< V1-V2 1115.63/291.48 aux(22) =< V1 1115.63/291.48 aux(23) =< 2*V1-V6-V2 1115.63/291.48 s(23) =< aux(22) 1115.63/291.48 it(15) =< aux(23) 1115.63/291.48 it(16) =< aux(23) 1115.63/291.48 aux(7) =< aux(22)-1 1115.63/291.48 aux(6) =< aux(22)+1 1115.63/291.48 s(14) =< it(15)*aux(22) 1115.63/291.48 s(17) =< it(16)*aux(7) 1115.63/291.48 s(16) =< it(16)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,Out=0,V6>=1,V2>=1,V1>=V6+1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 * Chain [[15,16],17,35]: 4*it(15)+4*it(16)+2*s(14)+1*s(16)+1*s(17)+2*s(25)+4 1115.63/291.48 Such that:it(16) =< V1-V6 1115.63/291.48 it(15) =< V1-V2 1115.63/291.48 aux(26) =< V1 1115.63/291.48 aux(27) =< 2*V1-V6-V2 1115.63/291.48 s(25) =< aux(26) 1115.63/291.48 it(15) =< aux(27) 1115.63/291.48 it(16) =< aux(27) 1115.63/291.48 aux(7) =< aux(26)-1 1115.63/291.48 aux(6) =< aux(26)+1 1115.63/291.48 s(14) =< it(15)*aux(26) 1115.63/291.48 s(17) =< it(16)*aux(7) 1115.63/291.48 s(16) =< it(16)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,Out=0,V6>=1,V2>=1,V1>=V6+1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 * Chain [35]: 0 1115.63/291.48 with precondition: [Out=0,V>=0,V1>=0,V6>=0,V2>=0] 1115.63/291.48 1115.63/291.48 * Chain [34,35]: 4 1115.63/291.48 with precondition: [V=1,V1=0,Out=0,V6>=0,V2>=0] 1115.63/291.48 1115.63/291.48 * Chain [33,35]: 4 1115.63/291.48 with precondition: [V=1,V1=0,Out=0,V6>=0,V2>=0] 1115.63/291.48 1115.63/291.48 * Chain [32,[28],35]: 4*it(28)+1*s(3)+4 1115.63/291.48 Such that:aux(45) =< V1 1115.63/291.48 it(28) =< aux(45) 1115.63/291.48 s(3) =< it(28)*aux(45) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [32,[28],30,35]: 5*it(28)+1*s(3)+8 1115.63/291.48 Such that:aux(46) =< V1 1115.63/291.48 it(28) =< aux(46) 1115.63/291.48 s(3) =< it(28)*aux(46) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [32,[28],29,35]: 5*it(28)+1*s(3)+8 1115.63/291.48 Such that:aux(47) =< V1 1115.63/291.48 it(28) =< aux(47) 1115.63/291.48 s(3) =< it(28)*aux(47) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [32,[28],27,[15,16],35]: 13*it(15)+3*s(3)+1*s(16)+1*s(17)+8 1115.63/291.48 Such that:aux(12) =< V1 1115.63/291.48 aux(48) =< 2*V1 1115.63/291.48 it(15) =< aux(48) 1115.63/291.48 aux(7) =< aux(12)-1 1115.63/291.48 aux(6) =< aux(12)+1 1115.63/291.48 s(3) =< it(15)*aux(12) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=3] 1115.63/291.48 1115.63/291.48 * Chain [32,[28],27,[15,16],21,35]: 8*it(15)+4*it(28)+1*s(3)+2*s(14)+1*s(16)+1*s(17)+3*s(18)+12 1115.63/291.48 Such that:aux(17) =< V1 1115.63/291.48 aux(49) =< 2*V1 1115.63/291.48 it(28) =< aux(49) 1115.63/291.48 it(15) =< aux(17) 1115.63/291.48 s(18) =< aux(17) 1115.63/291.48 it(15) =< aux(49) 1115.63/291.48 aux(7) =< aux(17)-1 1115.63/291.48 aux(6) =< aux(17)+1 1115.63/291.48 s(14) =< it(15)*aux(17) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 s(3) =< it(28)*aux(17) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=3] 1115.63/291.48 1115.63/291.48 * Chain [32,[28],27,[15,16],20,35]: 8*it(15)+4*it(28)+1*s(3)+2*s(14)+1*s(16)+1*s(17)+3*s(18)+12 1115.63/291.48 Such that:aux(21) =< V1 1115.63/291.48 aux(50) =< 2*V1 1115.63/291.48 it(28) =< aux(50) 1115.63/291.48 it(15) =< aux(21) 1115.63/291.48 s(18) =< aux(21) 1115.63/291.48 it(15) =< aux(50) 1115.63/291.48 aux(7) =< aux(21)-1 1115.63/291.48 aux(6) =< aux(21)+1 1115.63/291.48 s(14) =< it(15)*aux(21) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 s(3) =< it(28)*aux(21) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=3] 1115.63/291.48 1115.63/291.48 * Chain [32,[28],27,[15,16],18,35]: 8*it(15)+4*it(28)+1*s(3)+2*s(14)+1*s(16)+1*s(17)+3*s(18)+12 1115.63/291.48 Such that:aux(25) =< V1 1115.63/291.48 aux(51) =< 2*V1 1115.63/291.48 it(28) =< aux(51) 1115.63/291.48 it(15) =< aux(25) 1115.63/291.48 s(18) =< aux(25) 1115.63/291.48 it(15) =< aux(51) 1115.63/291.48 aux(7) =< aux(25)-1 1115.63/291.48 aux(6) =< aux(25)+1 1115.63/291.48 s(14) =< it(15)*aux(25) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 s(3) =< it(28)*aux(25) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=3] 1115.63/291.48 1115.63/291.48 * Chain [32,[28],27,[15,16],17,35]: 8*it(15)+4*it(28)+1*s(3)+2*s(14)+1*s(16)+1*s(17)+3*s(18)+12 1115.63/291.48 Such that:aux(29) =< V1 1115.63/291.48 aux(52) =< 2*V1 1115.63/291.48 it(28) =< aux(52) 1115.63/291.48 it(15) =< aux(29) 1115.63/291.48 s(18) =< aux(29) 1115.63/291.48 it(15) =< aux(52) 1115.63/291.48 aux(7) =< aux(29)-1 1115.63/291.48 aux(6) =< aux(29)+1 1115.63/291.48 s(14) =< it(15)*aux(29) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 s(3) =< it(28)*aux(29) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=3] 1115.63/291.48 1115.63/291.48 * Chain [32,[28],27,35]: 5*it(28)+1*s(3)+8 1115.63/291.48 Such that:aux(53) =< V1 1115.63/291.48 it(28) =< aux(53) 1115.63/291.48 s(3) =< it(28)*aux(53) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=3] 1115.63/291.48 1115.63/291.48 * Chain [32,35]: 4 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=1] 1115.63/291.48 1115.63/291.48 * Chain [32,30,35]: 1*s(4)+8 1115.63/291.48 Such that:s(4) =< 1 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V1=1,V6=0,V2=0,Out=0] 1115.63/291.48 1115.63/291.48 * Chain [32,29,35]: 1*s(5)+8 1115.63/291.48 Such that:s(5) =< 1 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V1=1,V6=0,V2=0,Out=0] 1115.63/291.48 1115.63/291.48 * Chain [32,27,[15,16],35]: 8*it(15)+2*s(14)+1*s(16)+1*s(17)+1*s(18)+8 1115.63/291.48 Such that:s(18) =< 1 1115.63/291.48 aux(8) =< V1 1115.63/291.48 aux(11) =< 2*V1 1115.63/291.48 it(15) =< aux(11) 1115.63/291.48 aux(7) =< aux(8)-1 1115.63/291.48 aux(6) =< aux(8)+1 1115.63/291.48 s(14) =< it(15)*aux(8) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [32,27,[15,16],21,35]: 8*it(15)+2*s(14)+1*s(16)+1*s(17)+1*s(18)+2*s(19)+12 1115.63/291.48 Such that:s(18) =< 1 1115.63/291.48 aux(15) =< 2*V1 1115.63/291.48 aux(54) =< V1 1115.63/291.48 it(15) =< aux(54) 1115.63/291.48 s(19) =< aux(54) 1115.63/291.48 it(15) =< aux(15) 1115.63/291.48 aux(7) =< aux(54)-1 1115.63/291.48 aux(6) =< aux(54)+1 1115.63/291.48 s(14) =< it(15)*aux(54) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [32,27,[15,16],20,35]: 8*it(15)+2*s(14)+1*s(16)+1*s(17)+1*s(18)+2*s(21)+12 1115.63/291.48 Such that:s(18) =< 1 1115.63/291.48 aux(19) =< 2*V1 1115.63/291.48 aux(55) =< V1 1115.63/291.48 it(15) =< aux(55) 1115.63/291.48 s(21) =< aux(55) 1115.63/291.48 it(15) =< aux(19) 1115.63/291.48 aux(7) =< aux(55)-1 1115.63/291.48 aux(6) =< aux(55)+1 1115.63/291.48 s(14) =< it(15)*aux(55) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [32,27,[15,16],18,35]: 8*it(15)+2*s(14)+1*s(16)+1*s(17)+1*s(18)+2*s(23)+12 1115.63/291.48 Such that:s(18) =< 1 1115.63/291.48 aux(23) =< 2*V1 1115.63/291.48 aux(56) =< V1 1115.63/291.48 it(15) =< aux(56) 1115.63/291.48 s(23) =< aux(56) 1115.63/291.48 it(15) =< aux(23) 1115.63/291.48 aux(7) =< aux(56)-1 1115.63/291.48 aux(6) =< aux(56)+1 1115.63/291.48 s(14) =< it(15)*aux(56) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [32,27,[15,16],17,35]: 8*it(15)+2*s(14)+1*s(16)+1*s(17)+1*s(18)+2*s(25)+12 1115.63/291.48 Such that:s(18) =< 1 1115.63/291.48 aux(27) =< 2*V1 1115.63/291.48 aux(57) =< V1 1115.63/291.48 it(15) =< aux(57) 1115.63/291.48 s(25) =< aux(57) 1115.63/291.48 it(15) =< aux(27) 1115.63/291.48 aux(7) =< aux(57)-1 1115.63/291.48 aux(6) =< aux(57)+1 1115.63/291.48 s(14) =< it(15)*aux(57) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [32,27,35]: 1*s(18)+8 1115.63/291.48 Such that:s(18) =< 1 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [31,[24],35]: 4*it(24)+1*s(29)+4 1115.63/291.48 Such that:aux(58) =< V1 1115.63/291.48 it(24) =< aux(58) 1115.63/291.48 s(29) =< it(24)*aux(58) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [31,[24],26,35]: 5*it(24)+1*s(29)+8 1115.63/291.48 Such that:aux(59) =< V1 1115.63/291.48 it(24) =< aux(59) 1115.63/291.48 s(29) =< it(24)*aux(59) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [31,[24],25,35]: 5*it(24)+1*s(29)+8 1115.63/291.48 Such that:aux(60) =< V1 1115.63/291.48 it(24) =< aux(60) 1115.63/291.48 s(29) =< it(24)*aux(60) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [31,[24],23,[15,16],35]: 13*it(15)+3*s(14)+1*s(16)+1*s(17)+8 1115.63/291.48 Such that:aux(34) =< V1 1115.63/291.48 aux(61) =< 2*V1 1115.63/291.48 it(15) =< aux(61) 1115.63/291.48 aux(7) =< aux(34)-1 1115.63/291.48 aux(6) =< aux(34)+1 1115.63/291.48 s(14) =< it(15)*aux(34) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=3] 1115.63/291.48 1115.63/291.48 * Chain [31,[24],23,[15,16],21,35]: 8*it(15)+4*it(24)+2*s(14)+1*s(16)+1*s(17)+3*s(19)+1*s(29)+12 1115.63/291.48 Such that:aux(37) =< V1 1115.63/291.48 aux(62) =< 2*V1 1115.63/291.48 it(24) =< aux(62) 1115.63/291.48 it(15) =< aux(37) 1115.63/291.48 s(19) =< aux(37) 1115.63/291.48 it(15) =< aux(62) 1115.63/291.48 aux(7) =< aux(37)-1 1115.63/291.48 aux(6) =< aux(37)+1 1115.63/291.48 s(14) =< it(15)*aux(37) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 s(29) =< it(24)*aux(37) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=3] 1115.63/291.48 1115.63/291.48 * Chain [31,[24],23,[15,16],20,35]: 8*it(15)+4*it(24)+2*s(14)+1*s(16)+1*s(17)+3*s(21)+1*s(29)+12 1115.63/291.48 Such that:aux(39) =< V1 1115.63/291.48 aux(63) =< 2*V1 1115.63/291.48 it(24) =< aux(63) 1115.63/291.48 it(15) =< aux(39) 1115.63/291.48 s(21) =< aux(39) 1115.63/291.48 it(15) =< aux(63) 1115.63/291.48 aux(7) =< aux(39)-1 1115.63/291.48 aux(6) =< aux(39)+1 1115.63/291.48 s(14) =< it(15)*aux(39) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 s(29) =< it(24)*aux(39) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=3] 1115.63/291.48 1115.63/291.48 * Chain [31,[24],23,[15,16],18,35]: 8*it(15)+4*it(24)+2*s(14)+1*s(16)+1*s(17)+3*s(23)+1*s(29)+12 1115.63/291.48 Such that:aux(41) =< V1 1115.63/291.48 aux(64) =< 2*V1 1115.63/291.48 it(24) =< aux(64) 1115.63/291.48 it(15) =< aux(41) 1115.63/291.48 s(23) =< aux(41) 1115.63/291.48 it(15) =< aux(64) 1115.63/291.48 aux(7) =< aux(41)-1 1115.63/291.48 aux(6) =< aux(41)+1 1115.63/291.48 s(14) =< it(15)*aux(41) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 s(29) =< it(24)*aux(41) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=3] 1115.63/291.48 1115.63/291.48 * Chain [31,[24],23,[15,16],17,35]: 8*it(15)+4*it(24)+2*s(14)+1*s(16)+1*s(17)+3*s(25)+1*s(29)+12 1115.63/291.48 Such that:aux(43) =< V1 1115.63/291.48 aux(65) =< 2*V1 1115.63/291.48 it(24) =< aux(65) 1115.63/291.48 it(15) =< aux(43) 1115.63/291.48 s(25) =< aux(43) 1115.63/291.48 it(15) =< aux(65) 1115.63/291.48 aux(7) =< aux(43)-1 1115.63/291.48 aux(6) =< aux(43)+1 1115.63/291.48 s(14) =< it(15)*aux(43) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 s(29) =< it(24)*aux(43) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=3] 1115.63/291.48 1115.63/291.48 * Chain [31,[24],23,35]: 5*it(24)+1*s(29)+8 1115.63/291.48 Such that:aux(66) =< V1 1115.63/291.48 it(24) =< aux(66) 1115.63/291.48 s(29) =< it(24)*aux(66) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=3] 1115.63/291.48 1115.63/291.48 * Chain [31,35]: 4 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=1] 1115.63/291.48 1115.63/291.48 * Chain [31,26,35]: 1*s(30)+8 1115.63/291.48 Such that:s(30) =< 1 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V1=1,V6=0,V2=0,Out=0] 1115.63/291.48 1115.63/291.48 * Chain [31,25,35]: 1*s(31)+8 1115.63/291.48 Such that:s(31) =< 1 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V1=1,V6=0,V2=0,Out=0] 1115.63/291.48 1115.63/291.48 * Chain [31,23,[15,16],35]: 8*it(15)+2*s(14)+1*s(16)+1*s(17)+1*s(32)+8 1115.63/291.48 Such that:s(32) =< 1 1115.63/291.48 aux(8) =< V1 1115.63/291.48 aux(11) =< 2*V1 1115.63/291.48 it(15) =< aux(11) 1115.63/291.48 aux(7) =< aux(8)-1 1115.63/291.48 aux(6) =< aux(8)+1 1115.63/291.48 s(14) =< it(15)*aux(8) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [31,23,[15,16],21,35]: 8*it(15)+2*s(14)+1*s(16)+1*s(17)+2*s(19)+1*s(32)+12 1115.63/291.48 Such that:s(32) =< 1 1115.63/291.48 aux(15) =< 2*V1 1115.63/291.48 aux(67) =< V1 1115.63/291.48 it(15) =< aux(67) 1115.63/291.48 s(19) =< aux(67) 1115.63/291.48 it(15) =< aux(15) 1115.63/291.48 aux(7) =< aux(67)-1 1115.63/291.48 aux(6) =< aux(67)+1 1115.63/291.48 s(14) =< it(15)*aux(67) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [31,23,[15,16],20,35]: 8*it(15)+2*s(14)+1*s(16)+1*s(17)+2*s(21)+1*s(32)+12 1115.63/291.48 Such that:s(32) =< 1 1115.63/291.48 aux(19) =< 2*V1 1115.63/291.48 aux(68) =< V1 1115.63/291.48 it(15) =< aux(68) 1115.63/291.48 s(21) =< aux(68) 1115.63/291.48 it(15) =< aux(19) 1115.63/291.48 aux(7) =< aux(68)-1 1115.63/291.48 aux(6) =< aux(68)+1 1115.63/291.48 s(14) =< it(15)*aux(68) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [31,23,[15,16],18,35]: 8*it(15)+2*s(14)+1*s(16)+1*s(17)+2*s(23)+1*s(32)+12 1115.63/291.48 Such that:s(32) =< 1 1115.63/291.48 aux(23) =< 2*V1 1115.63/291.48 aux(69) =< V1 1115.63/291.48 it(15) =< aux(69) 1115.63/291.48 s(23) =< aux(69) 1115.63/291.48 it(15) =< aux(23) 1115.63/291.48 aux(7) =< aux(69)-1 1115.63/291.48 aux(6) =< aux(69)+1 1115.63/291.48 s(14) =< it(15)*aux(69) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [31,23,[15,16],17,35]: 8*it(15)+2*s(14)+1*s(16)+1*s(17)+2*s(25)+1*s(32)+12 1115.63/291.48 Such that:s(32) =< 1 1115.63/291.48 aux(27) =< 2*V1 1115.63/291.48 aux(70) =< V1 1115.63/291.48 it(15) =< aux(70) 1115.63/291.48 s(25) =< aux(70) 1115.63/291.48 it(15) =< aux(27) 1115.63/291.48 aux(7) =< aux(70)-1 1115.63/291.48 aux(6) =< aux(70)+1 1115.63/291.48 s(14) =< it(15)*aux(70) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [31,23,35]: 1*s(32)+8 1115.63/291.48 Such that:s(32) =< 1 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2=0,Out=0,V1>=2] 1115.63/291.48 1115.63/291.48 * Chain [30,35]: 1*s(4)+4 1115.63/291.48 Such that:s(4) =< V1 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,Out=0,V1>=1,V2>=V1] 1115.63/291.48 1115.63/291.48 * Chain [29,35]: 1*s(5)+4 1115.63/291.48 Such that:s(5) =< V1 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,Out=0,V1>=1,V2>=V1] 1115.63/291.48 1115.63/291.48 * Chain [27,[15,16],35]: 8*it(15)+2*s(14)+1*s(16)+1*s(17)+1*s(18)+4 1115.63/291.48 Such that:aux(8) =< V1 1115.63/291.48 aux(11) =< 2*V1-V2 1115.63/291.48 s(18) =< V2 1115.63/291.48 it(15) =< aux(11) 1115.63/291.48 aux(7) =< aux(8)-1 1115.63/291.48 aux(6) =< aux(8)+1 1115.63/291.48 s(14) =< it(15)*aux(8) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,Out=0,V2>=1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 * Chain [27,[15,16],21,35]: 4*it(15)+4*it(16)+2*s(14)+1*s(16)+1*s(17)+1*s(18)+2*s(19)+8 1115.63/291.48 Such that:it(15) =< V1-V2 1115.63/291.48 aux(15) =< 2*V1-V2 1115.63/291.48 s(18) =< V2 1115.63/291.48 aux(16) =< V1 1115.63/291.48 it(16) =< aux(16) 1115.63/291.48 s(19) =< aux(16) 1115.63/291.48 it(15) =< aux(15) 1115.63/291.48 it(16) =< aux(15) 1115.63/291.48 aux(7) =< aux(16)-1 1115.63/291.48 aux(6) =< aux(16)+1 1115.63/291.48 s(14) =< it(15)*aux(16) 1115.63/291.48 s(17) =< it(16)*aux(7) 1115.63/291.48 s(16) =< it(16)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,Out=0,V2>=1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 * Chain [27,[15,16],20,35]: 4*it(15)+4*it(16)+2*s(14)+1*s(16)+1*s(17)+1*s(18)+2*s(21)+8 1115.63/291.48 Such that:it(15) =< V1-V2 1115.63/291.48 aux(19) =< 2*V1-V2 1115.63/291.48 s(18) =< V2 1115.63/291.48 aux(20) =< V1 1115.63/291.48 it(16) =< aux(20) 1115.63/291.48 s(21) =< aux(20) 1115.63/291.48 it(15) =< aux(19) 1115.63/291.48 it(16) =< aux(19) 1115.63/291.48 aux(7) =< aux(20)-1 1115.63/291.48 aux(6) =< aux(20)+1 1115.63/291.48 s(14) =< it(15)*aux(20) 1115.63/291.48 s(17) =< it(16)*aux(7) 1115.63/291.48 s(16) =< it(16)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,Out=0,V2>=1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 * Chain [27,[15,16],18,35]: 4*it(15)+4*it(16)+2*s(14)+1*s(16)+1*s(17)+1*s(18)+2*s(23)+8 1115.63/291.48 Such that:it(15) =< V1-V2 1115.63/291.48 aux(23) =< 2*V1-V2 1115.63/291.48 s(18) =< V2 1115.63/291.48 aux(24) =< V1 1115.63/291.48 it(16) =< aux(24) 1115.63/291.48 s(23) =< aux(24) 1115.63/291.48 it(15) =< aux(23) 1115.63/291.48 it(16) =< aux(23) 1115.63/291.48 aux(7) =< aux(24)-1 1115.63/291.48 aux(6) =< aux(24)+1 1115.63/291.48 s(14) =< it(15)*aux(24) 1115.63/291.48 s(17) =< it(16)*aux(7) 1115.63/291.48 s(16) =< it(16)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,Out=0,V2>=1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 * Chain [27,[15,16],17,35]: 4*it(15)+4*it(16)+2*s(14)+1*s(16)+1*s(17)+1*s(18)+2*s(25)+8 1115.63/291.48 Such that:it(15) =< V1-V2 1115.63/291.48 aux(27) =< 2*V1-V2 1115.63/291.48 s(18) =< V2 1115.63/291.48 aux(28) =< V1 1115.63/291.48 it(16) =< aux(28) 1115.63/291.48 s(25) =< aux(28) 1115.63/291.48 it(15) =< aux(27) 1115.63/291.48 it(16) =< aux(27) 1115.63/291.48 aux(7) =< aux(28)-1 1115.63/291.48 aux(6) =< aux(28)+1 1115.63/291.48 s(14) =< it(15)*aux(28) 1115.63/291.48 s(17) =< it(16)*aux(7) 1115.63/291.48 s(16) =< it(16)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,Out=0,V2>=1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 * Chain [27,35]: 1*s(18)+4 1115.63/291.48 Such that:s(18) =< V2 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,Out=0,V2>=1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 * Chain [26,35]: 1*s(30)+4 1115.63/291.48 Such that:s(30) =< V1 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V1>=1,V6>=V1] 1115.63/291.48 1115.63/291.48 * Chain [25,35]: 1*s(31)+4 1115.63/291.48 Such that:s(31) =< V1 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V1>=1,V6>=V1] 1115.63/291.48 1115.63/291.48 * Chain [23,[15,16],35]: 8*it(15)+2*s(14)+1*s(16)+1*s(17)+1*s(32)+4 1115.63/291.48 Such that:aux(8) =< V1 1115.63/291.48 aux(11) =< 2*V1-V6 1115.63/291.48 s(32) =< V6 1115.63/291.48 it(15) =< aux(11) 1115.63/291.48 aux(7) =< aux(8)-1 1115.63/291.48 aux(6) =< aux(8)+1 1115.63/291.48 s(14) =< it(15)*aux(8) 1115.63/291.48 s(17) =< it(15)*aux(7) 1115.63/291.48 s(16) =< it(15)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V6>=1,V1>=V6+1] 1115.63/291.48 1115.63/291.48 * Chain [23,[15,16],21,35]: 4*it(15)+4*it(16)+2*s(14)+1*s(16)+1*s(17)+2*s(19)+1*s(32)+8 1115.63/291.48 Such that:it(16) =< V1-V6 1115.63/291.48 aux(15) =< 2*V1-V6 1115.63/291.48 s(32) =< V6 1115.63/291.48 aux(36) =< V1 1115.63/291.48 it(15) =< aux(36) 1115.63/291.48 s(19) =< aux(36) 1115.63/291.48 it(15) =< aux(15) 1115.63/291.48 it(16) =< aux(15) 1115.63/291.48 aux(7) =< aux(36)-1 1115.63/291.48 aux(6) =< aux(36)+1 1115.63/291.48 s(14) =< it(15)*aux(36) 1115.63/291.48 s(17) =< it(16)*aux(7) 1115.63/291.48 s(16) =< it(16)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V6>=1,V1>=V6+1] 1115.63/291.48 1115.63/291.48 * Chain [23,[15,16],20,35]: 4*it(15)+4*it(16)+2*s(14)+1*s(16)+1*s(17)+2*s(21)+1*s(32)+8 1115.63/291.48 Such that:it(16) =< V1-V6 1115.63/291.48 aux(19) =< 2*V1-V6 1115.63/291.48 s(32) =< V6 1115.63/291.48 aux(38) =< V1 1115.63/291.48 it(15) =< aux(38) 1115.63/291.48 s(21) =< aux(38) 1115.63/291.48 it(15) =< aux(19) 1115.63/291.48 it(16) =< aux(19) 1115.63/291.48 aux(7) =< aux(38)-1 1115.63/291.48 aux(6) =< aux(38)+1 1115.63/291.48 s(14) =< it(15)*aux(38) 1115.63/291.48 s(17) =< it(16)*aux(7) 1115.63/291.48 s(16) =< it(16)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V6>=1,V1>=V6+1] 1115.63/291.48 1115.63/291.48 * Chain [23,[15,16],18,35]: 4*it(15)+4*it(16)+2*s(14)+1*s(16)+1*s(17)+2*s(23)+1*s(32)+8 1115.63/291.48 Such that:it(16) =< V1-V6 1115.63/291.48 aux(23) =< 2*V1-V6 1115.63/291.48 s(32) =< V6 1115.63/291.48 aux(40) =< V1 1115.63/291.48 it(15) =< aux(40) 1115.63/291.48 s(23) =< aux(40) 1115.63/291.48 it(15) =< aux(23) 1115.63/291.48 it(16) =< aux(23) 1115.63/291.48 aux(7) =< aux(40)-1 1115.63/291.48 aux(6) =< aux(40)+1 1115.63/291.48 s(14) =< it(15)*aux(40) 1115.63/291.48 s(17) =< it(16)*aux(7) 1115.63/291.48 s(16) =< it(16)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V6>=1,V1>=V6+1] 1115.63/291.48 1115.63/291.48 * Chain [23,[15,16],17,35]: 4*it(15)+4*it(16)+2*s(14)+1*s(16)+1*s(17)+2*s(25)+1*s(32)+8 1115.63/291.48 Such that:it(16) =< V1-V6 1115.63/291.48 aux(27) =< 2*V1-V6 1115.63/291.48 s(32) =< V6 1115.63/291.48 aux(42) =< V1 1115.63/291.48 it(15) =< aux(42) 1115.63/291.48 s(25) =< aux(42) 1115.63/291.48 it(15) =< aux(27) 1115.63/291.48 it(16) =< aux(27) 1115.63/291.48 aux(7) =< aux(42)-1 1115.63/291.48 aux(6) =< aux(42)+1 1115.63/291.48 s(14) =< it(15)*aux(42) 1115.63/291.48 s(17) =< it(16)*aux(7) 1115.63/291.48 s(16) =< it(16)*aux(6) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V6>=1,V1>=V6+1] 1115.63/291.48 1115.63/291.48 * Chain [23,35]: 1*s(32)+4 1115.63/291.48 Such that:s(32) =< V6 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,Out=0,V6>=1,V1>=V6+1] 1115.63/291.48 1115.63/291.48 * Chain [22,35]: 2*s(33)+4 1115.63/291.48 Such that:aux(71) =< V1 1115.63/291.48 s(33) =< aux(71) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,Out=0,V1>=1,V6>=V1,V2>=V1] 1115.63/291.48 1115.63/291.48 * Chain [21,35]: 1*s(19)+1*s(20)+4 1115.63/291.48 Such that:s(20) =< V1 1115.63/291.48 s(19) =< V6+1 1115.63/291.48 1115.63/291.48 with precondition: [V=1,Out=0,V6>=1,V2>=V1,V1>=V6+1] 1115.63/291.48 1115.63/291.48 * Chain [20,35]: 1*s(21)+1*s(22)+4 1115.63/291.48 Such that:s(21) =< V1 1115.63/291.48 s(22) =< V2 1115.63/291.48 1115.63/291.48 with precondition: [V=1,Out=0,V2>=1,V6>=V1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 * Chain [19,35]: 2*s(35)+4 1115.63/291.48 Such that:aux(72) =< V1 1115.63/291.48 s(35) =< aux(72) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,Out=0,V1>=1,V6>=V1,V2>=V1] 1115.63/291.48 1115.63/291.48 * Chain [18,35]: 1*s(23)+1*s(24)+4 1115.63/291.48 Such that:s(24) =< V1 1115.63/291.48 s(23) =< V6 1115.63/291.48 1115.63/291.48 with precondition: [V=1,Out=0,V6>=1,V2>=V1,V1>=V6+1] 1115.63/291.48 1115.63/291.48 * Chain [17,35]: 1*s(25)+1*s(26)+4 1115.63/291.48 Such that:s(25) =< V1 1115.63/291.48 s(26) =< V2+1 1115.63/291.48 1115.63/291.48 with precondition: [V=1,Out=0,V2>=1,V6>=V1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 1115.63/291.48 #### Cost of chains of start(V,V1,V6,V2): 1115.63/291.48 * Chain [48]: 1 1115.63/291.48 with precondition: [V=0,V1>=0] 1115.63/291.48 1115.63/291.48 * Chain [47]: 16*s(582)+128*s(583)+78*s(584)+32*s(587)+16*s(588)+16*s(589)+74*s(590)+18*s(591)+4*s(592)+4*s(593)+8*s(594)+12 1115.63/291.48 Such that:s(579) =< 1 1115.63/291.48 s(580) =< V1 1115.63/291.48 s(581) =< 2*V1 1115.63/291.48 s(582) =< s(579) 1115.63/291.48 s(583) =< s(580) 1115.63/291.48 s(584) =< s(580) 1115.63/291.48 s(583) =< s(581) 1115.63/291.48 s(585) =< s(580)-1 1115.63/291.48 s(586) =< s(580)+1 1115.63/291.48 s(587) =< s(583)*s(580) 1115.63/291.48 s(588) =< s(583)*s(585) 1115.63/291.48 s(589) =< s(583)*s(586) 1115.63/291.48 s(590) =< s(581) 1115.63/291.48 s(591) =< s(590)*s(580) 1115.63/291.48 s(592) =< s(590)*s(585) 1115.63/291.48 s(593) =< s(590)*s(586) 1115.63/291.48 s(594) =< s(584)*s(580) 1115.63/291.48 1115.63/291.48 with precondition: [V>=0,V1>=0,V6>=0,V2>=0] 1115.63/291.48 1115.63/291.48 * Chain [46]: 2*s(596)+1*s(597)+4 1115.63/291.48 Such that:s(597) =< V 1115.63/291.48 s(595) =< V1 1115.63/291.48 s(596) =< s(595) 1115.63/291.48 1115.63/291.48 with precondition: [V>=1,V1>=V] 1115.63/291.48 1115.63/291.48 * Chain [45]: 16*s(603)+16*s(604)+28*s(605)+6*s(606)+7*s(609)+1*s(610)+1*s(611)+4*s(612)+16*s(613)+23*s(614)+8*s(615)+4*s(616)+4*s(617)+32*s(618)+8*s(619)+4*s(620)+4*s(621)+9*s(622)+2*s(623)+1*s(624)+1*s(625)+8 1115.63/291.48 Such that:s(598) =< V1 1115.63/291.48 s(599) =< V1-V2 1115.63/291.48 s(600) =< 2*V1 1115.63/291.48 s(601) =< 2*V1-V2 1115.63/291.48 s(602) =< V2 1115.63/291.48 s(603) =< s(599) 1115.63/291.48 s(604) =< s(599) 1115.63/291.48 s(605) =< s(601) 1115.63/291.48 s(606) =< s(602) 1115.63/291.48 s(607) =< s(598)-1 1115.63/291.48 s(608) =< s(598)+1 1115.63/291.48 s(609) =< s(605)*s(598) 1115.63/291.48 s(610) =< s(605)*s(607) 1115.63/291.48 s(611) =< s(605)*s(608) 1115.63/291.48 s(612) =< s(604)*s(598) 1115.63/291.48 s(613) =< s(598) 1115.63/291.48 s(614) =< s(598) 1115.63/291.48 s(603) =< s(601) 1115.63/291.48 s(613) =< s(601) 1115.63/291.48 s(615) =< s(603)*s(598) 1115.63/291.48 s(616) =< s(613)*s(607) 1115.63/291.48 s(617) =< s(613)*s(608) 1115.63/291.48 s(618) =< s(598) 1115.63/291.48 s(618) =< s(600) 1115.63/291.48 s(619) =< s(618)*s(598) 1115.63/291.48 s(620) =< s(618)*s(607) 1115.63/291.48 s(621) =< s(618)*s(608) 1115.63/291.48 s(622) =< s(600) 1115.63/291.48 s(623) =< s(622)*s(598) 1115.63/291.48 s(624) =< s(622)*s(607) 1115.63/291.48 s(625) =< s(622)*s(608) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6=0,V2>=1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 * Chain [44]: 2*s(627)+4 1115.63/291.48 Such that:s(626) =< V1 1115.63/291.48 s(627) =< s(626) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,V1>=1,V6>=V1] 1115.63/291.48 1115.63/291.48 * Chain [43]: 16*s(633)+16*s(634)+28*s(635)+6*s(636)+7*s(639)+1*s(640)+1*s(641)+4*s(642)+16*s(643)+23*s(644)+8*s(645)+4*s(646)+4*s(647)+32*s(648)+8*s(649)+4*s(650)+4*s(651)+9*s(652)+2*s(653)+1*s(654)+1*s(655)+8 1115.63/291.48 Such that:s(628) =< V1 1115.63/291.48 s(629) =< V1-V6 1115.63/291.48 s(630) =< 2*V1 1115.63/291.48 s(631) =< 2*V1-V6 1115.63/291.48 s(632) =< V6 1115.63/291.48 s(633) =< s(629) 1115.63/291.48 s(634) =< s(629) 1115.63/291.48 s(635) =< s(631) 1115.63/291.48 s(636) =< s(632) 1115.63/291.48 s(637) =< s(628)-1 1115.63/291.48 s(638) =< s(628)+1 1115.63/291.48 s(639) =< s(635)*s(628) 1115.63/291.48 s(640) =< s(635)*s(637) 1115.63/291.48 s(641) =< s(635)*s(638) 1115.63/291.48 s(642) =< s(634)*s(628) 1115.63/291.48 s(643) =< s(628) 1115.63/291.48 s(644) =< s(628) 1115.63/291.48 s(643) =< s(631) 1115.63/291.48 s(633) =< s(631) 1115.63/291.48 s(645) =< s(643)*s(628) 1115.63/291.48 s(646) =< s(633)*s(637) 1115.63/291.48 s(647) =< s(633)*s(638) 1115.63/291.48 s(648) =< s(628) 1115.63/291.48 s(648) =< s(630) 1115.63/291.48 s(649) =< s(648)*s(628) 1115.63/291.48 s(650) =< s(648)*s(637) 1115.63/291.48 s(651) =< s(648)*s(638) 1115.63/291.48 s(652) =< s(630) 1115.63/291.48 s(653) =< s(652)*s(628) 1115.63/291.48 s(654) =< s(652)*s(637) 1115.63/291.48 s(655) =< s(652)*s(638) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2=0,V6>=1,V1>=V6+1] 1115.63/291.48 1115.63/291.48 * Chain [42]: 4*s(657)+4 1115.63/291.48 Such that:s(656) =< V1 1115.63/291.48 s(657) =< s(656) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V1>=1,V6>=V1,V2>=V1] 1115.63/291.48 1115.63/291.48 * Chain [41]: 16*s(662)+16*s(663)+8*s(664)+2*s(667)+1*s(668)+1*s(669)+8*s(670)+8*s(671)+4*s(672)+4*s(673)+4 1115.63/291.48 Such that:s(658) =< V1 1115.63/291.48 s(659) =< V1-V6 1115.63/291.48 s(660) =< V1-V2 1115.63/291.48 s(661) =< 2*V1-V6-V2 1115.63/291.48 s(662) =< s(659) 1115.63/291.48 s(663) =< s(660) 1115.63/291.48 s(664) =< s(661) 1115.63/291.48 s(665) =< s(658)-1 1115.63/291.48 s(666) =< s(658)+1 1115.63/291.48 s(667) =< s(664)*s(658) 1115.63/291.48 s(668) =< s(664)*s(665) 1115.63/291.48 s(669) =< s(664)*s(666) 1115.63/291.48 s(670) =< s(658) 1115.63/291.48 s(663) =< s(661) 1115.63/291.48 s(662) =< s(661) 1115.63/291.48 s(671) =< s(663)*s(658) 1115.63/291.48 s(672) =< s(662)*s(665) 1115.63/291.48 s(673) =< s(662)*s(666) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6>=1,V2>=1,V1>=V6+1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 * Chain [40]: 1*s(674)+1*s(675)+2*s(677)+4 1115.63/291.48 Such that:s(676) =< V1 1115.63/291.48 s(674) =< V6 1115.63/291.48 s(675) =< V6+1 1115.63/291.48 s(677) =< s(676) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V6>=1,V2>=V1,V1>=V6+1] 1115.63/291.48 1115.63/291.48 * Chain [39]: 1*s(678)+1*s(679)+2*s(681)+4 1115.63/291.48 Such that:s(680) =< V1 1115.63/291.48 s(678) =< V2 1115.63/291.48 s(679) =< V2+1 1115.63/291.48 s(681) =< s(680) 1115.63/291.48 1115.63/291.48 with precondition: [V=1,V2>=1,V6>=V1,V1>=V2+1] 1115.63/291.48 1115.63/291.48 * Chain [38]: 1 1115.63/291.48 with precondition: [V1=0,V>=0] 1115.63/291.48 1115.63/291.48 * Chain [37]: 1 1115.63/291.48 with precondition: [V1=1,V>=0] 1115.63/291.48 1115.63/291.48 * Chain [36]: 1*s(682)+1 1115.63/291.48 Such that:s(682) =< V1 1115.63/291.48 1115.63/291.48 with precondition: [V1>=1,V>=V1+1] 1115.63/291.48 1115.63/291.48 1115.63/291.48 Closed-form bounds of start(V,V1,V6,V2): 1115.63/291.48 ------------------------------------- 1115.63/291.48 * Chain [48] with precondition: [V=0,V1>=0] 1115.63/291.48 - Upper bound: 1 1115.63/291.48 - Complexity: constant 1115.63/291.48 * Chain [47] with precondition: [V>=0,V1>=0,V6>=0,V2>=0] 1115.63/291.48 - Upper bound: 222*V1+28+56*V1*V1+16*V1*nat(V1-1)+22*V1*(2*V1)+nat(V1-1)*4*(2*V1)+156*V1 1115.63/291.48 - Complexity: n^2 1115.63/291.48 * Chain [46] with precondition: [V>=1,V1>=V] 1115.63/291.48 - Upper bound: V+2*V1+4 1115.63/291.48 - Complexity: n 1115.63/291.48 * Chain [45] with precondition: [V=1,V6=0,V2>=1,V1>=V2+1] 1115.63/291.48 - Upper bound: 58*V1-29*V2+(32*V1-32*V2+(79*V1+8+16*V1*V1+(V1-1)*(8*V1)+3*V1*(2*V1)+(V1-V2)*(12*V1)+(2*V1-V2)*(8*V1)+6*V2+(V1-1)*(2*V1)+(2*V1-V2)*(V1-1)+20*V1)) 1115.63/291.48 - Complexity: n^2 1115.63/291.48 * Chain [44] with precondition: [V=1,V2=0,V1>=1,V6>=V1] 1115.63/291.48 - Upper bound: 2*V1+4 1115.63/291.48 - Complexity: n 1115.63/291.48 * Chain [43] with precondition: [V=1,V2=0,V6>=1,V1>=V6+1] 1115.63/291.48 - Upper bound: 58*V1-29*V6+(36*V1-36*V6+(75*V1+8+20*V1*V1+(V1-1)*(4*V1)+3*V1*(2*V1)+(V1-V6)*(8*V1)+(2*V1-V6)*(8*V1)+6*V6+(V1-1)*(2*V1)+(4*V1-4)*(V1-V6)+(2*V1-V6)*(V1-1)+20*V1)) 1115.63/291.48 - Complexity: n^2 1115.63/291.48 * Chain [42] with precondition: [V=1,V1>=1,V6>=V1,V2>=V1] 1115.63/291.48 - Upper bound: 4*V1+4 1115.63/291.48 - Complexity: n 1115.63/291.48 * Chain [41] with precondition: [V=1,V6>=1,V2>=1,V1>=V6+1,V1>=V2+1] 1115.63/291.48 - Upper bound: 18*V1-9*V6-9*V2+(16*V1-16*V2+(20*V1-20*V6+(8*V1+4+(V1-V6)*(4*V1)+(V1-V2)*(8*V1)+(2*V1-V6-V2)*(3*V1)+(4*V1-4)*(V1-V6)+(2*V1-V6-V2)*(V1-1)))) 1115.63/291.48 - Complexity: n^2 1115.63/291.48 * Chain [40] with precondition: [V=1,V6>=1,V2>=V1,V1>=V6+1] 1115.63/291.48 - Upper bound: 2*V1+2*V6+5 1115.63/291.48 - Complexity: n 1115.63/291.48 * Chain [39] with precondition: [V=1,V2>=1,V6>=V1,V1>=V2+1] 1115.63/291.48 - Upper bound: 2*V1+2*V2+5 1115.63/291.48 - Complexity: n 1115.63/291.48 * Chain [38] with precondition: [V1=0,V>=0] 1115.63/291.48 - Upper bound: 1 1115.63/291.48 - Complexity: constant 1115.63/291.48 * Chain [37] with precondition: [V1=1,V>=0] 1115.63/291.48 - Upper bound: 1 1115.63/291.48 - Complexity: constant 1115.63/291.48 * Chain [36] with precondition: [V1>=1,V>=V1+1] 1115.63/291.48 - Upper bound: V1+1 1115.63/291.48 - Complexity: n 1115.63/291.48 1115.63/291.48 ### Maximum cost of start(V,V1,V6,V2): V1+3+max([max([V,nat(V6+1)+nat(V6),nat(V2+1)+nat(V2)]),4*V1+max([67*V1+4+16*V1*V1+4*V1*nat(V1-1)+3*V1*(2*V1)+2*V1*nat(V1-1)+20*V1+max([4*V1*nat(V1-1)+4*V1+max([12*V1*nat(V1-V2)+8*V1*nat(2*V1-V2)+nat(V2)*6+nat(2*V1-V2)*nat(V1-1)+nat(V1-V2)*32+nat(2*V1-V2)*29,143*V1+20+40*V1*V1+8*V1*nat(V1-1)+19*V1*(2*V1)+nat(V1-1)*3*(2*V1)+136*V1]),8*V1*nat(V1-V6)+4*V1*V1+8*V1*nat(2*V1-V6)+nat(V6)*6+nat(V1-1)*4*nat(V1-V6)+nat(2*V1-V6)*nat(V1-1)+nat(V1-V6)*36+nat(2*V1-V6)*29]),8*V1*nat(V1-V2)+4*V1*nat(V1-V6)+3*V1*nat(2*V1-V6-V2)+nat(V1-1)*4*nat(V1-V6)+nat(2*V1-V6-V2)*nat(V1-1)+nat(V1-V6)*20+nat(V1-V2)*16+nat(2*V1-V6-V2)*9])+2*V1])+V1+1 1115.63/291.48 Asymptotic class: n^2 1115.63/291.48 * Total analysis performed in 1826 ms. 1115.63/291.48 1115.63/291.48 1115.63/291.48 ---------------------------------------- 1115.63/291.48 1115.63/291.48 (10) 1115.63/291.48 BOUNDS(1, n^2) 1115.63/291.48 1115.63/291.48 ---------------------------------------- 1115.63/291.48 1115.63/291.48 (11) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID)) 1115.63/291.48 Transformed a relative TRS into a decreasing-loop problem. 1115.63/291.48 ---------------------------------------- 1115.63/291.48 1115.63/291.48 (12) 1115.63/291.48 Obligation: 1115.63/291.48 Analyzing the following TRS for decreasing loops: 1115.63/291.48 1115.63/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1115.63/291.48 1115.63/291.48 1115.63/291.48 The TRS R consists of the following rules: 1115.63/291.48 1115.63/291.48 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, s(y), z) 1115.63/291.48 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, y, s(z)) 1115.63/291.48 gt(0, v) -> false 1115.63/291.48 gt(s(u), 0) -> true 1115.63/291.48 gt(s(u), s(v)) -> gt(u, v) 1115.63/291.48 and(x, true) -> x 1115.63/291.48 and(x, false) -> false 1115.63/291.48 1115.63/291.48 S is empty. 1115.63/291.48 Rewrite Strategy: INNERMOST 1115.63/291.48 ---------------------------------------- 1115.63/291.48 1115.63/291.48 (13) DecreasingLoopProof (LOWER BOUND(ID)) 1115.63/291.48 The following loop(s) give(s) rise to the lower bound Omega(n^1): 1115.63/291.48 1115.63/291.48 The rewrite sequence 1115.63/291.48 1115.63/291.48 gt(s(u), s(v)) ->^+ gt(u, v) 1115.63/291.48 1115.63/291.48 gives rise to a decreasing loop by considering the right hand sides subterm at position []. 1115.63/291.48 1115.63/291.48 The pumping substitution is [u / s(u), v / s(v)]. 1115.63/291.48 1115.63/291.48 The result substitution is [ ]. 1115.63/291.48 1115.63/291.48 1115.63/291.48 1115.63/291.48 1115.63/291.48 ---------------------------------------- 1115.63/291.48 1115.63/291.48 (14) 1115.63/291.48 Complex Obligation (BEST) 1115.63/291.48 1115.63/291.48 ---------------------------------------- 1115.63/291.48 1115.63/291.48 (15) 1115.63/291.48 Obligation: 1115.63/291.48 Proved the lower bound n^1 for the following obligation: 1115.63/291.48 1115.63/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1115.63/291.48 1115.63/291.48 1115.63/291.48 The TRS R consists of the following rules: 1115.63/291.48 1115.63/291.48 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, s(y), z) 1115.63/291.48 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, y, s(z)) 1115.63/291.48 gt(0, v) -> false 1115.63/291.48 gt(s(u), 0) -> true 1115.63/291.48 gt(s(u), s(v)) -> gt(u, v) 1115.63/291.48 and(x, true) -> x 1115.63/291.48 and(x, false) -> false 1115.63/291.48 1115.63/291.48 S is empty. 1115.63/291.48 Rewrite Strategy: INNERMOST 1115.63/291.48 ---------------------------------------- 1115.63/291.48 1115.63/291.48 (16) LowerBoundPropagationProof (FINISHED) 1115.63/291.48 Propagated lower bound. 1115.63/291.48 ---------------------------------------- 1115.63/291.48 1115.63/291.48 (17) 1115.63/291.48 BOUNDS(n^1, INF) 1115.63/291.48 1115.63/291.48 ---------------------------------------- 1115.63/291.48 1115.63/291.48 (18) 1115.63/291.48 Obligation: 1115.63/291.48 Analyzing the following TRS for decreasing loops: 1115.63/291.48 1115.63/291.48 The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(n^1, n^2). 1115.63/291.48 1115.63/291.48 1115.63/291.48 The TRS R consists of the following rules: 1115.63/291.48 1115.63/291.48 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, s(y), z) 1115.63/291.48 f(true, x, y, z) -> f(and(gt(x, y), gt(x, z)), x, y, s(z)) 1115.63/291.48 gt(0, v) -> false 1115.63/291.48 gt(s(u), 0) -> true 1115.63/291.48 gt(s(u), s(v)) -> gt(u, v) 1115.63/291.48 and(x, true) -> x 1115.63/291.48 and(x, false) -> false 1115.63/291.48 1115.63/291.48 S is empty. 1115.63/291.48 Rewrite Strategy: INNERMOST 1115.79/291.54 EOF