Term Rewriting System R:
[x, y, f, g]
app(app(const, x), y) -> x
app(app(app(subst, f), g), x) -> app(app(f, x), app(g, x))
app(app(fix, f), x) -> app(app(f, app(fix, f)), x)

Innermost Termination of R to be shown.

R
Dependency Pair Analysis

R contains the following Dependency Pairs:

APP(app(app(subst, f), g), x) -> APP(app(f, x), app(g, x))
APP(app(app(subst, f), g), x) -> APP(f, x)
APP(app(app(subst, f), g), x) -> APP(g, x)
APP(app(fix, f), x) -> APP(app(f, app(fix, f)), x)
APP(app(fix, f), x) -> APP(f, app(fix, f))

Furthermore, R contains one SCC.

R
DPs
→DP Problem 1
Remaining Obligation(s)

The following remains to be proven:
Dependency Pairs:

APP(app(fix, f), x) -> APP(f, app(fix, f))
APP(app(fix, f), x) -> APP(app(f, app(fix, f)), x)
APP(app(app(subst, f), g), x) -> APP(g, x)
APP(app(app(subst, f), g), x) -> APP(f, x)
APP(app(app(subst, f), g), x) -> APP(app(f, x), app(g, x))

Rules:

app(app(const, x), y) -> x
app(app(app(subst, f), g), x) -> app(app(f, x), app(g, x))
app(app(fix, f), x) -> app(app(f, app(fix, f)), x)

Strategy:

innermost

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