app2(id, x) -> x
app2(add, 0) -> id
app2(app2(add, app2(s, x)), y) -> app2(s, app2(app2(add, x), y))
app2(app2(map, f), nil) -> nil
app2(app2(map, f), app2(app2(cons, x), xs)) -> app2(app2(cons, app2(f, x)), app2(app2(map, f), xs))
↳ QTRS
↳ Non-Overlap Check
app2(id, x) -> x
app2(add, 0) -> id
app2(app2(add, app2(s, x)), y) -> app2(s, app2(app2(add, x), y))
app2(app2(map, f), nil) -> nil
app2(app2(map, f), app2(app2(cons, x), xs)) -> app2(app2(cons, app2(f, x)), app2(app2(map, f), xs))
↳ QTRS
↳ Non-Overlap Check
↳ QTRS
↳ DependencyPairsProof
app2(id, x) -> x
app2(add, 0) -> id
app2(app2(add, app2(s, x)), y) -> app2(s, app2(app2(add, x), y))
app2(app2(map, f), nil) -> nil
app2(app2(map, f), app2(app2(cons, x), xs)) -> app2(app2(cons, app2(f, x)), app2(app2(map, f), xs))
app2(id, x0)
app2(add, 0)
app2(app2(add, app2(s, x0)), x1)
app2(app2(map, x0), nil)
app2(app2(map, x0), app2(app2(cons, x1), x2))
APP2(app2(add, app2(s, x)), y) -> APP2(app2(add, x), y)
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(app2(cons, app2(f, x)), app2(app2(map, f), xs))
APP2(app2(add, app2(s, x)), y) -> APP2(s, app2(app2(add, x), y))
APP2(app2(add, app2(s, x)), y) -> APP2(add, x)
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(f, x)
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(app2(map, f), xs)
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(cons, app2(f, x))
app2(id, x) -> x
app2(add, 0) -> id
app2(app2(add, app2(s, x)), y) -> app2(s, app2(app2(add, x), y))
app2(app2(map, f), nil) -> nil
app2(app2(map, f), app2(app2(cons, x), xs)) -> app2(app2(cons, app2(f, x)), app2(app2(map, f), xs))
app2(id, x0)
app2(add, 0)
app2(app2(add, app2(s, x0)), x1)
app2(app2(map, x0), nil)
app2(app2(map, x0), app2(app2(cons, x1), x2))
↳ QTRS
↳ Non-Overlap Check
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
APP2(app2(add, app2(s, x)), y) -> APP2(app2(add, x), y)
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(app2(cons, app2(f, x)), app2(app2(map, f), xs))
APP2(app2(add, app2(s, x)), y) -> APP2(s, app2(app2(add, x), y))
APP2(app2(add, app2(s, x)), y) -> APP2(add, x)
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(f, x)
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(app2(map, f), xs)
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(cons, app2(f, x))
app2(id, x) -> x
app2(add, 0) -> id
app2(app2(add, app2(s, x)), y) -> app2(s, app2(app2(add, x), y))
app2(app2(map, f), nil) -> nil
app2(app2(map, f), app2(app2(cons, x), xs)) -> app2(app2(cons, app2(f, x)), app2(app2(map, f), xs))
app2(id, x0)
app2(add, 0)
app2(app2(add, app2(s, x0)), x1)
app2(app2(map, x0), nil)
app2(app2(map, x0), app2(app2(cons, x1), x2))
↳ QTRS
↳ Non-Overlap Check
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
APP2(app2(add, app2(s, x)), y) -> APP2(app2(add, x), y)
app2(id, x) -> x
app2(add, 0) -> id
app2(app2(add, app2(s, x)), y) -> app2(s, app2(app2(add, x), y))
app2(app2(map, f), nil) -> nil
app2(app2(map, f), app2(app2(cons, x), xs)) -> app2(app2(cons, app2(f, x)), app2(app2(map, f), xs))
app2(id, x0)
app2(add, 0)
app2(app2(add, app2(s, x0)), x1)
app2(app2(map, x0), nil)
app2(app2(map, x0), app2(app2(cons, x1), x2))
The following pairs can be strictly oriented and are deleted.
The remaining pairs can at least by weakly be oriented.
APP2(app2(add, app2(s, x)), y) -> APP2(app2(add, x), y)
APP1 > app1 > id
APP1 > add > id
s > add > id
0 > id
app2(add, 0) -> id
↳ QTRS
↳ Non-Overlap Check
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
app2(id, x) -> x
app2(add, 0) -> id
app2(app2(add, app2(s, x)), y) -> app2(s, app2(app2(add, x), y))
app2(app2(map, f), nil) -> nil
app2(app2(map, f), app2(app2(cons, x), xs)) -> app2(app2(cons, app2(f, x)), app2(app2(map, f), xs))
app2(id, x0)
app2(add, 0)
app2(app2(add, app2(s, x0)), x1)
app2(app2(map, x0), nil)
app2(app2(map, x0), app2(app2(cons, x1), x2))
↳ QTRS
↳ Non-Overlap Check
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(f, x)
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(app2(map, f), xs)
app2(id, x) -> x
app2(add, 0) -> id
app2(app2(add, app2(s, x)), y) -> app2(s, app2(app2(add, x), y))
app2(app2(map, f), nil) -> nil
app2(app2(map, f), app2(app2(cons, x), xs)) -> app2(app2(cons, app2(f, x)), app2(app2(map, f), xs))
app2(id, x0)
app2(add, 0)
app2(app2(add, app2(s, x0)), x1)
app2(app2(map, x0), nil)
app2(app2(map, x0), app2(app2(cons, x1), x2))
The following pairs can be strictly oriented and are deleted.
The remaining pairs can at least by weakly be oriented.
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(f, x)
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(app2(map, f), xs)
app2 > map
↳ QTRS
↳ Non-Overlap Check
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
app2(id, x) -> x
app2(add, 0) -> id
app2(app2(add, app2(s, x)), y) -> app2(s, app2(app2(add, x), y))
app2(app2(map, f), nil) -> nil
app2(app2(map, f), app2(app2(cons, x), xs)) -> app2(app2(cons, app2(f, x)), app2(app2(map, f), xs))
app2(id, x0)
app2(add, 0)
app2(app2(add, app2(s, x0)), x1)
app2(app2(map, x0), nil)
app2(app2(map, x0), app2(app2(cons, x1), x2))