app2(app2(plus, 0), y) -> y
app2(app2(plus, app2(s, x)), y) -> app2(s, app2(app2(plus, x), y))
app2(inc, xs) -> app2(app2(map, app2(plus, app2(s, 0))), xs)
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(app2(plus, 0), y) -> y
app2(app2(plus, app2(s, x)), y) -> app2(s, app2(app2(plus, x), y))
app2(inc, xs) -> app2(app2(map, app2(plus, app2(s, 0))), xs)
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(app2(plus, 0), y) -> y
app2(app2(plus, app2(s, x)), y) -> app2(s, app2(app2(plus, x), y))
app2(inc, xs) -> app2(app2(map, app2(plus, app2(s, 0))), xs)
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(app2(plus, 0), x0)
app2(app2(plus, app2(s, x0)), x1)
app2(inc, x0)
app2(app2(map, x0), nil)
app2(app2(map, x0), app2(app2(cons, x1), x2))
APP2(app2(plus, app2(s, x)), y) -> APP2(s, app2(app2(plus, x), y))
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(app2(cons, app2(f, x)), app2(app2(map, f), xs))
APP2(app2(plus, app2(s, x)), y) -> APP2(app2(plus, x), y)
APP2(inc, xs) -> APP2(app2(map, app2(plus, app2(s, 0))), xs)
APP2(inc, xs) -> APP2(s, 0)
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(f, x)
APP2(app2(plus, app2(s, x)), y) -> APP2(plus, 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(inc, xs) -> APP2(map, app2(plus, app2(s, 0)))
APP2(inc, xs) -> APP2(plus, app2(s, 0))
app2(app2(plus, 0), y) -> y
app2(app2(plus, app2(s, x)), y) -> app2(s, app2(app2(plus, x), y))
app2(inc, xs) -> app2(app2(map, app2(plus, app2(s, 0))), xs)
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(app2(plus, 0), x0)
app2(app2(plus, app2(s, x0)), x1)
app2(inc, x0)
app2(app2(map, x0), nil)
app2(app2(map, x0), app2(app2(cons, x1), x2))
↳ QTRS
↳ Non-Overlap Check
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
APP2(app2(plus, app2(s, x)), y) -> APP2(s, app2(app2(plus, x), y))
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(app2(cons, app2(f, x)), app2(app2(map, f), xs))
APP2(app2(plus, app2(s, x)), y) -> APP2(app2(plus, x), y)
APP2(inc, xs) -> APP2(app2(map, app2(plus, app2(s, 0))), xs)
APP2(inc, xs) -> APP2(s, 0)
APP2(app2(map, f), app2(app2(cons, x), xs)) -> APP2(f, x)
APP2(app2(plus, app2(s, x)), y) -> APP2(plus, 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(inc, xs) -> APP2(map, app2(plus, app2(s, 0)))
APP2(inc, xs) -> APP2(plus, app2(s, 0))
app2(app2(plus, 0), y) -> y
app2(app2(plus, app2(s, x)), y) -> app2(s, app2(app2(plus, x), y))
app2(inc, xs) -> app2(app2(map, app2(plus, app2(s, 0))), xs)
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(app2(plus, 0), x0)
app2(app2(plus, app2(s, x0)), x1)
app2(inc, x0)
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(plus, app2(s, x)), y) -> APP2(app2(plus, x), y)
app2(app2(plus, 0), y) -> y
app2(app2(plus, app2(s, x)), y) -> app2(s, app2(app2(plus, x), y))
app2(inc, xs) -> app2(app2(map, app2(plus, app2(s, 0))), xs)
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(app2(plus, 0), x0)
app2(app2(plus, app2(s, x0)), x1)
app2(inc, x0)
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(plus, app2(s, x)), y) -> APP2(app2(plus, x), y)
APP1 > app2
plus > app2
s > app2
↳ QTRS
↳ Non-Overlap Check
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
app2(app2(plus, 0), y) -> y
app2(app2(plus, app2(s, x)), y) -> app2(s, app2(app2(plus, x), y))
app2(inc, xs) -> app2(app2(map, app2(plus, app2(s, 0))), xs)
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(app2(plus, 0), x0)
app2(app2(plus, app2(s, x0)), x1)
app2(inc, x0)
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(inc, xs) -> APP2(app2(map, app2(plus, app2(s, 0))), xs)
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(plus, 0), y) -> y
app2(app2(plus, app2(s, x)), y) -> app2(s, app2(app2(plus, x), y))
app2(inc, xs) -> app2(app2(map, app2(plus, app2(s, 0))), xs)
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(app2(plus, 0), x0)
app2(app2(plus, app2(s, x0)), x1)
app2(inc, x0)
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(inc, xs) -> APP2(app2(map, app2(plus, app2(s, 0))), xs)
Used ordering: Combined order from the following AFS and order.
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)
APP1 > 0
inc > 0
plus > 0
s > 0
cons > map > 0
↳ QTRS
↳ Non-Overlap Check
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ 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(app2(plus, 0), y) -> y
app2(app2(plus, app2(s, x)), y) -> app2(s, app2(app2(plus, x), y))
app2(inc, xs) -> app2(app2(map, app2(plus, app2(s, 0))), xs)
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(app2(plus, 0), x0)
app2(app2(plus, app2(s, x0)), x1)
app2(inc, x0)
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
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
app2(app2(plus, 0), y) -> y
app2(app2(plus, app2(s, x)), y) -> app2(s, app2(app2(plus, x), y))
app2(inc, xs) -> app2(app2(map, app2(plus, app2(s, 0))), xs)
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(app2(plus, 0), x0)
app2(app2(plus, app2(s, x0)), x1)
app2(inc, x0)
app2(app2(map, x0), nil)
app2(app2(map, x0), app2(app2(cons, x1), x2))