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
↳ 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(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))
↳ 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))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
APP2(app2(add, app2(s, x)), y) -> APP2(app2(add, x), y)
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))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
APP2(app2(add, app2(s, x)), y) -> APP2(app2(add, x), y)
Used ordering: Polynomial Order [17,21] with Interpretation:
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)
POL( APP2(x1, x2) ) = max{0, x1 - 3}
POL( app2(x1, x2) ) = x2 + 3
POL( 0 ) = 0
POL( id ) = 0
app2(add, 0) -> id
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ 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(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))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
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)
POL( APP2(x1, x2) ) = max{0, x2 - 3}
POL( app2(x1, x2) ) = x1 + x2 + 1
POL( cons ) = 2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ 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))