Step 3 Synthesis of Decompose

An instantiation of the Decompose predicate-variable deterministically decomposes, in the non-minimal case, the induction parameter X into a vector HX of heads and a vector TX of tails, each tail 7X,- being smaller than X according to some well-founded relation. The TX are meant for the computation of the tails TY of the other parameter Y. 

The objective at Step 3 is to instantiate the predicate-variable Decompose of the divide-and-conquer schema. This amounts to transforming LAi r) into LA ir) such that it is covered by the following schema  

This objective can be achieved by the following sequence of tasks  

Task E consists of selecting one of the three decomposition strategies seen in Section 5.2.2. As a reminder, these strategies are  

An intrinsic decomposition reflects a well-founded relation selected via the Intrinsic Heuristic (Heuristic 4-3), and an extrinsic or logarithmic decomposition reflects a well-founded relation selected via the Extrinsic Heuristic (Heuristic 4-4). The selection of a strategy is a high-level decision that may significantly affect the complexity of the resulting algorithm (but probably not its existence). A reasonable implementation of this synthesis mechanism would accept a preference hint from the specifier. 

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Step 2 Synthesis of Minimal mdiNonMinimah Step 3 Synthesis of Decompose, ... 

How to discover compound induction parameters Due to our restriction to version 3 of the divide-and-conquer schema. Task A only considers simple induction parameters. Meeting this challenge is thus considered future research. According to what well-founded relation to decompose the induction parameter Step 3 (Synthesis of Decompose) does this non-deterministically by considering all predefined decomposition operators (which each reflect some well-founded relation) of a typed database, and possibly by listening to the specifier s hints. 

Pagoria and co-workers reported the nitration of A-ferf-butylpyrrole to A-fert-butyl-2,3,4-trinitropyrrole in 40 % yield over three steps. Stegel and co-workers reported the same synthesis but conducted the nitration in two steps using mixed acid. Hinshaw and co-workers used A-fert-butyl-2,3,4-trinitropyrrole for the synthesis of 2,3,4,5-tetranitropyrrole in a reaction involving initial deprotection followed by nitration with mixed acid at elevated temperature. 2,3,4,5-Tetranitropyrrole has a perfect oxygen balance but slowly decomposes on storage at room temperature. Stegel and co-workers also reported the synthesis of A-methyl-2,3,4,5-tetranitropyrrole from the nitration of A-methyl-2,3,4-trinitropyrrole with mixed acid. 

It is well known that alkyl azides also behave as 1,3-dipoles in intramolecular thermal cycloaddition reactions. The formation of two carbon-nitrogen bonds leads to triazolines, which are usually not stable. They decompose after the loss of nitrogen to aziridines, diazo compounds, and heterocyclic imines. There are a limited number of examples reported in which the triazoline was isolated [15]. The dipolar cycloaddition methodology has been extremely useful for the synthesis of many natural products with interesting biological activities [16], In recent years, the cycloaddition approach has allowed many successful syntheses of complex molecules which would be difficult to obtain by different routes. For instance, Cha and co-workers developed a general approach to functionalized indolizidine and pyrrolizidine alkaloids such as (-i-)-crotanecine [17] and (-)-slaframine [18]. The key step of the enantioselective synthesis of (-)-swainsonine (41), starting from 36, involves the construction of the bicyclic imine 38 by an intramolecular 1,3-dipolar cycloaddition of an azide derived from tosylate 36, as shown in Scheme 6 [ 19). 

Nitrogen-containing heterocycles are also available via intramolecular hetero Diels-Alder reactions. Williams employed an aza diene to prepare a complex polycyclic synthetic intermediate in his synthesis of versicolamide B. Boger reported a tandem intramolecular hetero Diels-Alder/l,3-dipolar cycloaddition sequence for the synthesis of vindorosine. Cycloaddition precursor 137 undergoes an inverse electron demand Diels-Alder reaction to yield 138. This compound decomposes via a retro dipolar cycloaddition to generate nitrogen gas and a 1,3-dipole that completes the cascade by reacting with the indole alkene to afford 139. Seven more steps enable the completion of vindorosine. ... 

Since 7r-allylpaIIadium complexes are formed by oxidative addition of allylic compounds to zerovalent palladium species, and the eliminated HPdX from tt-allylpalladium complexes readily decomposes to regenerate a Pd(0) species with liberation of HX, the elimination processes to 1,3-dienes is catalyzed by palladium complexes. It is considered that the elimination step from HPdX to Pd(0) and HX is reversible therefore, normally the elimination is carried out in the presence of suitable base (B) to capture HX. The catalytic elimination of HX from allylic compounds for the synthesis of 1,3-dienes under mild conditions provides a useful method (Scheme 2). 

Chiral alkyldihaloboranes are one of the most powerful chiral Lewis acids. However, in general, since alkyldihaloboranes readily decompose into alkanes or alkenes by protonolysis or (3-hydride elimination, it is difficult to recover them as alkylboronic acids quantitatively. Aryldichloroboranes are relatively more stable and can be reused as the corresponding boronic acids. Ishihara and Yamamoto et al. have developed chiral aryldichloroboranes 21 bearing binaphthyl skeletons with axial chirality as asymmetric catalysts for the Diels-Alder reaction of dienes and a,(3-unsaturated esters (Equation 31) [29]. (J )-2-Dihydroxyboryl-l,T-binaphthyl (20) can be synthesized from (R)-binaphthol in several steps [25]. The synthesis of racemic 20a has also been reported by Kaufmann et al. [30]. Compound 20 has been converted into 21 by two dif-... 

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