Term Rewriting System R:
[f, x, l, r]
app(app(mapbt, f), app(leaf, x)) -> app(leaf, app(f, x))
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))

Termination of R to be shown.

R
Dependency Pair Analysis

R contains the following Dependency Pairs:

APP(app(mapbt, f), app(leaf, x)) -> APP(leaf, app(f, x))
APP(app(mapbt, f), app(leaf, x)) -> APP(f, x)
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))
APP(app(mapbt, f), app(app(app(branch, x), l), r)) -> APP(app(branch, app(f, x)), app(app(mapbt, f), l))
APP(app(mapbt, f), app(app(app(branch, x), l), r)) -> APP(branch, app(f, x))
APP(app(mapbt, f), app(app(app(branch, x), l), r)) -> APP(f, x)
APP(app(mapbt, f), app(app(app(branch, x), l), r)) -> APP(app(mapbt, f), l)
APP(app(mapbt, f), app(app(app(branch, x), l), r)) -> APP(app(mapbt, f), r)

Furthermore, R contains one SCC.

R
DPs
→DP Problem 1
Remaining Obligation(s)

The following remains to be proven:
Dependency Pairs:

APP(app(mapbt, f), app(app(app(branch, x), l), r)) -> APP(app(mapbt, f), r)
APP(app(mapbt, f), app(app(app(branch, x), l), r)) -> APP(app(mapbt, f), l)
APP(app(mapbt, f), app(app(app(branch, x), l), r)) -> APP(f, x)
APP(app(mapbt, f), app(app(app(branch, x), l), r)) -> APP(app(branch, app(f, x)), app(app(mapbt, f), l))
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))
APP(app(mapbt, f), app(leaf, x)) -> APP(f, x)

Rules:

app(app(mapbt, f), app(leaf, x)) -> app(leaf, app(f, x))
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))

Termination of R could not be shown.
Duration:
0:00 minutes