Certification Problem

Input (TPDB TRS_Standard/AotoYamada_05/006)

The rewrite relation of the following TRS is considered.

app(app(mapbt,f),app(leaf,x))	→	app(leaf,app(f,x))	(1)
app(app(mapbt,f),app(app(app(branch,x),l),r))	→	app(app(app(branch,app(f,x)),app(app(mapbt,f),l)),app(app(mapbt,f),r))	(2)

Prove or disprove termination.

Yes.

The following set of initial dependency pairs has been identified.

app^#(app(mapbt,f),app(leaf,x))	→	app^#(f,x)	(3)
app^#(app(mapbt,f),app(leaf,x))	→	app^#(leaf,app(f,x))	(4)
app^#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app^#(app(mapbt,f),r)	(5)
app^#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app^#(app(mapbt,f),l)	(6)
app^#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app^#(f,x)	(7)
app^#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app^#(branch,app(f,x))	(8)
app^#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app^#(app(branch,app(f,x)),app(app(mapbt,f),l))	(9)
app^#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app^#(app(app(branch,app(f,x)),app(app(mapbt,f),l)),app(app(mapbt,f),r))	(10)

The dependency pairs are split into 1 component.

The 1^st component contains the pair

app^#(app(mapbt,f),app(leaf,x))	→	app^#(f,x)	(3)
app^#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app^#(f,x)	(7)
app^#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app^#(app(mapbt,f),l)	(6)
app^#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app^#(app(mapbt,f),r)	(5)

Using size-change termination in combination with the subterm criterion one obtains the following initial size-change graphs.

app^#(app(mapbt,f),app(leaf,x))	→	app^#(f,x)	(3)

2	>	2
1	>	1
app^#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app^#(f,x)	(7)

2	>	2
1	>	1
app^#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app^#(app(mapbt,f),l)	(6)

2	>	2
1	≥	1
app^#(app(mapbt,f),app(app(app(branch,x),l),r))	→	app^#(app(mapbt,f),r)	(5)

2	>	2
1	≥	1

As there is no critical graph in the transitive closure, there are no infinite chains.