YES
0 QTRS
↳1 QTRSRRRProof (⇔, 0 ms)
↳2 QTRS
↳3 RisEmptyProof (⇔, 0 ms)
↳4 YES
app(id, x) → x
app(plus, 0) → id
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:
POL(0) = 1
POL(app(x1, x2)) = 1 + 2·x1 + x2
POL(id) = 1
POL(plus) = 1
POL(s) = 2
app(id, x) → x
app(plus, 0) → id
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))