Diamond Property: Let R be a binary relation. We say that R has diamond property if, whenever aRb and aRc, then 3d such that bRd and cRd. B-reduction as a binary relation: We can define , as a binary relation betwcen two A terms t and t2: ti , tz iff tz can be obtained from tį using 1 3 reduction step. 1. Show that , docs not have the Diamond property. That is, give an example A-term t, such that 1. t , tz 2. tį , t3 3. At, s.t. t2 ", t, and ta

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Diamond Property: Let R be a binary relation. We say that R has diamond
property if, whenever aRb and aRc, then 3d such that bRd and cRd.
B-reduction as a binary relation: We can define , as a binary relation betwcen
two A terms t, and t2:
ti , tz iff tz can be obtained from tị using 1 3 reduction step.
1. Show that , docs not have the Diamond property. That is, give an example A-term
t, such that
1. t , t2
2. t , t3
3. At, s.t. t2 ", t, and ta
Transcribed Image Text:Diamond Property: Let R be a binary relation. We say that R has diamond property if, whenever aRb and aRc, then 3d such that bRd and cRd. B-reduction as a binary relation: We can define , as a binary relation betwcen two A terms t, and t2: ti , tz iff tz can be obtained from tị using 1 3 reduction step. 1. Show that , docs not have the Diamond property. That is, give an example A-term t, such that 1. t , t2 2. t , t3 3. At, s.t. t2 ", t, and ta
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