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)
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( map ) = max{0, -2}
POL( app2(x1, x2) ) = max{0, 2x1 + 2x2 - 2}
POL( id ) = max{0, -1}
POL( 0 ) = 1
POL( s ) = 2
POL( APP2(x1, x2) ) = max{0, x1 + 2x2 - 1}
POL( add ) = 1
POL( cons ) = 2
app2(add, 0) -> id
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ 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))