An afaik unnamed involution by tails

f=$(info $(words 1 $1) : $(subst $e ,,$(foreach x,$(subst 0, 0,$(call h,0x$(call g,$(subst $e ,,1$1)))),$(words $(subst x,x ,$(subst 0,,$x))))))$(call f$(word 99,$1),1 $1)
g=$(if $(subst 11,,$1),$(subst x1,,x$j),xx$(call g,$j))
h=$(if $(filter %1,$1),$(call h,$(subst y,,$(call i,y$(subst x,xx,$(1:1=))))),$1)
i=$(if $(findstring $t,$1),$(call i,$(subst yx,y0x,$(subst 0$t,x0,$1))),$1)
j=$(subst 11,1,$1)

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