app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(sumwith, f), nil) → nil
app(app(sumwith, f), app(app(cons, x), xs)) → app(app(plus, app(f, x)), app(app(sumwith, f), xs))
↳ QTRS
↳ DependencyPairsProof
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(sumwith, f), nil) → nil
app(app(sumwith, f), app(app(cons, x), xs)) → app(app(plus, app(f, x)), app(app(sumwith, f), xs))
APP(app(plus, app(s, x)), y) → APP(app(plus, x), y)
APP(app(sumwith, f), app(app(cons, x), xs)) → APP(app(sumwith, f), xs)
APP(app(plus, app(s, x)), y) → APP(s, app(app(plus, x), y))
APP(app(sumwith, f), app(app(cons, x), xs)) → APP(app(plus, app(f, x)), app(app(sumwith, f), xs))
APP(app(sumwith, f), app(app(cons, x), xs)) → APP(plus, app(f, x))
APP(app(plus, app(s, x)), y) → APP(plus, x)
APP(app(sumwith, f), app(app(cons, x), xs)) → APP(f, x)
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(sumwith, f), nil) → nil
app(app(sumwith, f), app(app(cons, x), xs)) → app(app(plus, app(f, x)), app(app(sumwith, f), xs))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
APP(app(plus, app(s, x)), y) → APP(app(plus, x), y)
APP(app(sumwith, f), app(app(cons, x), xs)) → APP(app(sumwith, f), xs)
APP(app(plus, app(s, x)), y) → APP(s, app(app(plus, x), y))
APP(app(sumwith, f), app(app(cons, x), xs)) → APP(app(plus, app(f, x)), app(app(sumwith, f), xs))
APP(app(sumwith, f), app(app(cons, x), xs)) → APP(plus, app(f, x))
APP(app(plus, app(s, x)), y) → APP(plus, x)
APP(app(sumwith, f), app(app(cons, x), xs)) → APP(f, x)
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(sumwith, f), nil) → nil
app(app(sumwith, f), app(app(cons, x), xs)) → app(app(plus, app(f, x)), app(app(sumwith, f), xs))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
APP(app(plus, app(s, x)), y) → APP(app(plus, x), y)
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(sumwith, f), nil) → nil
app(app(sumwith, f), app(app(cons, x), xs)) → app(app(plus, app(f, x)), app(app(sumwith, f), xs))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
APP(app(plus, app(s, x)), y) → APP(app(plus, x), y)
The value of delta used in the strict ordering is 1/32.
POL(APP(x1, x2)) = (1/2)x_1
POL(plus) = 0
POL(app(x1, x2)) = (1/4)x_1 + x_2
POL(s) = 1/4
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(sumwith, f), nil) → nil
app(app(sumwith, f), app(app(cons, x), xs)) → app(app(plus, app(f, x)), app(app(sumwith, f), xs))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
APP(app(sumwith, f), app(app(cons, x), xs)) → APP(app(sumwith, f), xs)
APP(app(sumwith, f), app(app(cons, x), xs)) → APP(f, x)
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(sumwith, f), nil) → nil
app(app(sumwith, f), app(app(cons, x), xs)) → app(app(plus, app(f, x)), app(app(sumwith, f), xs))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
APP(app(sumwith, f), app(app(cons, x), xs)) → APP(app(sumwith, f), xs)
APP(app(sumwith, f), app(app(cons, x), xs)) → APP(f, x)
The value of delta used in the strict ordering is 821/16.
POL(APP(x1, x2)) = (1/4)x_1 + (4)x_2
POL(cons) = 5/4
POL(app(x1, x2)) = 2 + (9/4)x_1 + (3)x_2
POL(sumwith) = 1/4
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
app(app(plus, 0), y) → y
app(app(plus, app(s, x)), y) → app(s, app(app(plus, x), y))
app(app(sumwith, f), nil) → nil
app(app(sumwith, f), app(app(cons, x), xs)) → app(app(plus, app(f, x)), app(app(sumwith, f), xs))