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mcdp { provides trees [Nat] provides sidewalks [Nat] provides benches [Nat] requires initial_budget [$] requires community_approval [dimensionless] budget_flex = 1 + required community_approval required initial_budget * budget_flex >= (provided trees * 1000 $) + (provided sidewalks * 400 $) + (provided benches * 2000 $) }
Internal representation details
CompositeNDP                                                                                                                             
β”‚    provides   trees       SB(β‰₯0::1) β”‚ requires   initial_budget       SB(β‰₯0) $                                                         
β”‚    provides   sidewalks   SB(β‰₯0::1) β”‚ requires   community_approval   SB(β‰₯0)                                                           
β”‚    provides   benches     SB(β‰₯0::1) β”‚                                                                                                  
β”‚  11 nodes, 10 edges                                                                                                                    
β”‚   connected rec: βœ“                                                                                                                     
β”‚  provided benches                    ≀ _op provided by _mult2          equiv id                                                        
β”‚  provided sidewalks                  ≀ _op provided by _mult1          equiv id                                                        
β”‚  provided trees                      ≀ _op provided by _mult           equiv id                                                        
β”‚  budget_flex required by _invmult    ≀ _res provided by _invplusop     equiv id                                                        
β”‚  initial_budget required by _invmult ≀ required initial_budget         equiv id                                                        
β”‚  _op required by _invplusop          ≀ required community_approval     equiv id                                                        
β”‚  _res required by _mult              ≀ _res provided by _sum           equiv id                                                        
β”‚  _res2 required by _mult1            ≀ _res2 provided by _sum          equiv id                                                        
β”‚  _res3 required by _mult2            ≀ _res3 provided by _sum          equiv id                                                        
β”‚  _result required by _sum            ≀ _result2 provided by _invmult   diff  AmbientConversion SB(β‰₯0::200) USD  β‡Έ  SB(β‰₯0) USD  > D USD 
β”‚                                                                               𝒇 ≀ 𝒓                                                    
β”œ   _invmult: SimpleWrap                                                                                                                 
β”‚             β”‚  provides   _result2   SB(β‰₯0) USD β”‚ requires   initial_budget   SB(β‰₯0) $                                                 
β”‚             β”‚                                   β”‚ requires   budget_flex      SB(β‰₯1)                                                   
β”‚             β”” M_Fun_MultiplyMany_DP SB(β‰₯0) USD  β‡Έ  SB(β‰₯0)Γ—SB(β‰₯1) ⟨$,dimensionless⟩                                                     
β”‚                𝒇 ≀ 𝒓₁⋅𝒓₂                                                                                                               
β”‚               β”œ   Rs: β”œ SB(β‰₯0) $                                                                                                       
β”‚               β”‚       β”” SB(β‰₯1)                                                                                                         
β”‚               β”” algo: ApproximationAlgorithms - ApproximationAlgorithms.VAN_DER_CORPUT                                                 
β”œ _invplusop: SimpleWrap                                                                                                                 
β”‚             β”‚  provides   _res   SB(β‰₯1) β”‚ requires   _op   SB(β‰₯0)                                                                      
β”‚             β”” DP_L_LME SB(β‰₯1)  β‡Έ  SB(β‰₯0)                                                                                               
β”‚                𝒇 ≀ 𝒓 + 1                                                                                                               
β”‚               M_C_WrapUnits   dimensionless β†’ dimensionless > M_A_Add1_Lower   SB(β‰₯0)  β†’  SB(β‰₯1) x ⟼ x + 1                             
β”œ      _mult: SimpleWrap                                                                                                                 
β”‚             β”‚  provides   _op   SB(β‰₯0::1) β”‚ requires   _res   SB(β‰₯0::1000) USD                                                         
β”‚             β”” DP_L_UME SB(β‰₯0::1)  β‡Έ  SB(β‰₯0::1000) USD                                                                                  
β”‚                𝒇 β‹… 1000 ≀ 𝒓                                                                                                            
β”‚               M_C_WrapUnits   dimensionless β†’ USD > M_A_Mult1_Upper   SB(β‰₯0::1)  β†’  SB(β‰₯0::1000) x ⟼ x β‹… 1000                          
β”œ     _mult1: SimpleWrap                                                                                                                 
β”‚             β”‚  provides   _op   SB(β‰₯0::1) β”‚ requires   _res2   SB(β‰₯0::400) USD                                                         
β”‚             β”” DP_L_UME SB(β‰₯0::1)  β‡Έ  SB(β‰₯0::400) USD                                                                                   
β”‚                𝒇 β‹… 400 ≀ 𝒓                                                                                                             
β”‚               M_C_WrapUnits   dimensionless β†’ USD > M_A_Mult1_Upper   SB(β‰₯0::1)  β†’  SB(β‰₯0::400) x ⟼ x β‹… 400                            
β”œ     _mult2: SimpleWrap                                                                                                                 
β”‚             β”‚  provides   _op   SB(β‰₯0::1) β”‚ requires   _res3   SB(β‰₯0::2000) USD                                                        
β”‚             β”” DP_L_UME SB(β‰₯0::1)  β‡Έ  SB(β‰₯0::2000) USD                                                                                  
β”‚                𝒇 β‹… 2000 ≀ 𝒓                                                                                                            
β”‚               M_C_WrapUnits   dimensionless β†’ USD > M_A_Mult1_Upper   SB(β‰₯0::1)  β†’  SB(β‰₯0::2000) x ⟼ x β‹… 2000                          
β””       _sum: SimpleWrap                                                                                                                 
              β”‚  provides   _res    SB(β‰₯0::1000) USD β”‚ requires   _result   SB(β‰₯0::200) USD                                              
              β”‚  provides   _res2   SB(β‰₯0::400) USD  β”‚                                                                                   
              β”‚  provides   _res3   SB(β‰₯0::2000) USD β”‚                                                                                   
              β”” M_Res_AddMany_DP WU ⟨USD,USD,USD⟩   β‡Έ  SB(β‰₯0::200) USD                                                                   
                                 β”” Ξ <3>                                                                                                  
                                   β”œ SB(β‰₯0::1000)                                                                                        
                                   β”œ SB(β‰₯0::400)                                                                                         
                                   β”” SB(β‰₯0::2000)                                                                                        
                 𝒇₁ + 𝒇₂ + 𝒇₃ ≀ 𝒓                                                                                                        
                β”œ      Fs: β”œ SB(β‰₯0::1000) USD                                                                                            
                β”‚          β”œ SB(β‰₯0::400) USD                                                                                             
                β”‚          β”” SB(β‰₯0::2000) USD                                                                                            
                β”œ opspace: SB(β‰₯0::200) USD                                                                                               
                β””    algo: ApproximationAlgorithms - ApproximationAlgorithms.VAN_DER_CORPUT                                              

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