loop5

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mcdp { # This is similar to `loop3` but it is always feasible. # Note that the equation $x + 1 = x$ is satisfied by $x = +inf$ # However, it might be hard to get to +inf by fixed loop... a = instance mcdp { provides f [dimensionless] requires r [dimensionless] provides f2 [dimensionless] requires r2 [dimensionless] provided f ≤ required r provided f2 + 1 ≤ required r2 } f2 provided by a ≥ r2 required by a requires r for a provides f using a }

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CompositeNDP                                                                                      
│    provides   f   SB(≥0) │ requires   r   SB(≥0)                                                
│  3 nodes, 3 edges                                                                               
│   connected rec: ✓                                                                              
│  provided f       ≤ f provided by a    equiv id                                                 
│  r required by a  ≤ required r         equiv id                                                 
│  r2 required by a ≤ f2 provided by a   diff  AmbientConversion SB(≥1)  ⇸  SB(≥0)  > D           
│                                               𝒇 ≤ 𝒓                                             
└ CompositeNDP                                                                                    
  │    provides   f    SB(≥0) │ requires   r    SB(≥0)                                            
  │    provides   f2   SB(≥0) │ requires   r2   SB(≥1)                                            
  │  5 nodes, 3 edges                                                                             
  │   connected rec: ✓                                                                            
  │  provided f             ≤ required r              equiv id                                    
  │  provided f2            ≤ _op provided by _plus   equiv id                                    
  │  _res required by _plus ≤ required r2             equiv id                                    
  └ SimpleWrap                                                                                    
    │  provides   _op   SB(≥0) │ requires   _res   SB(≥1)                                         
    └ DP_L_UME SB(≥0)  ⇸  SB(≥1)                                                                  
       𝒇 + 1 ≤ 𝒓                                                                                  
      M_C_WrapUnits   dimensionless → dimensionless > M_A_Add1_Upper   SB(≥0)  →  SB(≥1) x ⟼ x + 1