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We find strictly ascending HNN extensions of finite rank free groupspossessing a presentation 2-complex which is a non positively curved squarecomplex. On showing these groups are word hyperbolic, we have by results ofWise and Agol that they are linear over the integers. An example is theendomorphism of the free group on a,b with inverses A,B that sends a to aBaaband b to bAbba.

Strictly ascending HNN extensions of finite rank free groups that are linear over Z