0 QTRS
↳1 Overlay + Local Confluence (⇔)
↳2 QTRS
↳3 DependencyPairsProof (⇔)
↳4 QDP
↳5 DependencyGraphProof (⇔)
↳6 QDP
↳7 QDPOrderProof (⇔)
↳8 QDP
↳9 PisEmptyProof (⇔)
↳10 TRUE
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(treemap, f), app(app(node, x), xs)) → app(app(node, app(f, x)), app(app(map, app(treemap, f)), xs))
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(treemap, f), app(app(node, x), xs)) → app(app(node, app(f, x)), app(app(map, app(treemap, f)), xs))
app(app(map, x0), nil)
app(app(map, x0), app(app(cons, x1), x2))
app(app(treemap, x0), app(app(node, x1), x2))
APP(app(map, f), app(app(cons, x), xs)) → APP(app(cons, app(f, x)), app(app(map, f), xs))
APP(app(map, f), app(app(cons, x), xs)) → APP(cons, app(f, x))
APP(app(map, f), app(app(cons, x), xs)) → APP(f, x)
APP(app(map, f), app(app(cons, x), xs)) → APP(app(map, f), xs)
APP(app(treemap, f), app(app(node, x), xs)) → APP(app(node, app(f, x)), app(app(map, app(treemap, f)), xs))
APP(app(treemap, f), app(app(node, x), xs)) → APP(node, app(f, x))
APP(app(treemap, f), app(app(node, x), xs)) → APP(f, x)
APP(app(treemap, f), app(app(node, x), xs)) → APP(app(map, app(treemap, f)), xs)
APP(app(treemap, f), app(app(node, x), xs)) → APP(map, app(treemap, f))
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(treemap, f), app(app(node, x), xs)) → app(app(node, app(f, x)), app(app(map, app(treemap, f)), xs))
app(app(map, x0), nil)
app(app(map, x0), app(app(cons, x1), x2))
app(app(treemap, x0), app(app(node, x1), x2))
APP(app(map, f), app(app(cons, x), xs)) → APP(app(map, f), xs)
APP(app(map, f), app(app(cons, x), xs)) → APP(f, x)
APP(app(treemap, f), app(app(node, x), xs)) → APP(f, x)
APP(app(treemap, f), app(app(node, x), xs)) → APP(app(map, app(treemap, f)), xs)
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(treemap, f), app(app(node, x), xs)) → app(app(node, app(f, x)), app(app(map, app(treemap, f)), xs))
app(app(map, x0), nil)
app(app(map, x0), app(app(cons, x1), x2))
app(app(treemap, x0), app(app(node, x1), x2))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
APP(app(map, f), app(app(cons, x), xs)) → APP(app(map, f), xs)
APP(app(map, f), app(app(cons, x), xs)) → APP(f, x)
APP(app(treemap, f), app(app(node, x), xs)) → APP(f, x)
APP(app(treemap, f), app(app(node, x), xs)) → APP(app(map, app(treemap, f)), xs)
map > app2
cons > app2
[treemap, node] > app2
cons: multiset
map: multiset
node: multiset
app2: multiset
treemap: multiset
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(treemap, f), app(app(node, x), xs)) → app(app(node, app(f, x)), app(app(map, app(treemap, f)), xs))
app(app(map, x0), nil)
app(app(map, x0), app(app(cons, x1), x2))
app(app(treemap, x0), app(app(node, x1), x2))