app(D, t) → 1
app(D, constant) → 0
app(D, app(app(+, x), y)) → app(app(+, app(D, x)), app(D, y))
app(D, app(app(*, x), y)) → app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y)))
app(D, app(app(-, x), y)) → app(app(-, app(D, x)), app(D, y))
app(D, app(minus, x)) → app(minus, app(D, x))
app(D, app(app(div, x), y)) → app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2)))
app(D, app(ln, x)) → app(app(div, app(D, x)), x)
app(D, app(app(pow, x), y)) → app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y)))
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(filter, f), nil) → nil
app(app(filter, f), app(app(cons, x), xs)) → app(app(app(app(filter2, app(f, x)), f), x), xs)
app(app(app(app(filter2, true), f), x), xs) → app(app(cons, x), app(app(filter, f), xs))
app(app(app(app(filter2, false), f), x), xs) → app(app(filter, f), xs)
↳ QTRS
↳ DependencyPairsProof
app(D, t) → 1
app(D, constant) → 0
app(D, app(app(+, x), y)) → app(app(+, app(D, x)), app(D, y))
app(D, app(app(*, x), y)) → app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y)))
app(D, app(app(-, x), y)) → app(app(-, app(D, x)), app(D, y))
app(D, app(minus, x)) → app(minus, app(D, x))
app(D, app(app(div, x), y)) → app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2)))
app(D, app(ln, x)) → app(app(div, app(D, x)), x)
app(D, app(app(pow, x), y)) → app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y)))
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(filter, f), nil) → nil
app(app(filter, f), app(app(cons, x), xs)) → app(app(app(app(filter2, app(f, x)), f), x), xs)
app(app(app(app(filter2, true), f), x), xs) → app(app(cons, x), app(app(filter, f), xs))
app(app(app(app(filter2, false), f), x), xs) → app(app(filter, f), xs)
APP(D, app(app(pow, x), y)) → APP(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1))))
APP(app(filter, f), app(app(cons, x), xs)) → APP(app(filter2, app(f, x)), f)
APP(D, app(app(*, x), y)) → APP(app(*, y), app(D, x))
APP(D, app(app(*, x), y)) → APP(app(*, x), app(D, y))
APP(D, app(app(-, x), y)) → APP(D, y)
APP(D, app(app(-, x), y)) → APP(app(-, app(D, x)), app(D, y))
APP(D, app(app(div, x), y)) → APP(D, y)
APP(app(filter, f), app(app(cons, x), xs)) → APP(app(app(app(filter2, app(f, x)), f), x), xs)
APP(D, app(app(+, x), y)) → APP(D, y)
APP(D, app(minus, x)) → APP(minus, app(D, x))
APP(D, app(app(div, x), y)) → APP(app(pow, y), 2)
APP(D, app(app(pow, x), y)) → APP(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y)))
APP(D, app(app(*, x), y)) → APP(D, x)
APP(app(app(app(filter2, false), f), x), xs) → APP(filter, f)
APP(app(filter, f), app(app(cons, x), xs)) → APP(app(app(filter2, app(f, x)), f), x)
APP(D, app(app(pow, x), y)) → APP(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x)))
APP(D, app(app(*, x), y)) → APP(D, y)
APP(D, app(app(*, x), y)) → APP(+, app(app(*, y), app(D, x)))
APP(D, app(app(div, x), y)) → APP(pow, y)
APP(D, app(app(+, x), y)) → APP(+, app(D, x))
APP(D, app(app(+, x), y)) → APP(app(+, app(D, x)), app(D, y))
APP(D, app(app(pow, x), y)) → APP(-, y)
APP(D, app(app(*, x), y)) → APP(*, y)
APP(D, app(app(pow, x), y)) → APP(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))
APP(D, app(app(div, x), y)) → APP(app(div, app(D, x)), y)
APP(D, app(minus, x)) → APP(D, x)
APP(app(map, f), app(app(cons, x), xs)) → APP(cons, app(f, x))
APP(D, app(app(pow, x), y)) → APP(ln, x)
APP(app(map, f), app(app(cons, x), xs)) → APP(app(cons, app(f, x)), app(app(map, f), xs))
APP(D, app(app(pow, x), y)) → APP(D, x)
APP(app(filter, f), app(app(cons, x), xs)) → APP(f, x)
APP(D, app(ln, x)) → APP(D, x)
APP(D, app(app(+, x), y)) → APP(D, x)
APP(D, app(app(div, x), y)) → APP(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2)))
APP(D, app(app(pow, x), y)) → APP(*, y)
APP(D, app(app(div, x), y)) → APP(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2))
APP(app(map, f), app(app(cons, x), xs)) → APP(app(map, f), xs)
APP(D, app(app(pow, x), y)) → APP(app(pow, x), app(app(-, y), 1))
APP(D, app(app(div, x), y)) → APP(app(*, x), app(D, y))
APP(D, app(app(*, x), y)) → APP(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y)))
APP(D, app(app(pow, x), y)) → APP(app(*, app(app(pow, x), y)), app(ln, x))
APP(app(app(app(filter2, false), f), x), xs) → APP(app(filter, f), xs)
APP(app(app(app(filter2, true), f), x), xs) → APP(app(filter, f), xs)
APP(D, app(app(pow, x), y)) → APP(*, app(app(*, app(app(pow, x), y)), app(ln, x)))
APP(D, app(ln, x)) → APP(div, app(D, x))
APP(D, app(app(-, x), y)) → APP(-, app(D, x))
APP(D, app(app(pow, x), y)) → APP(app(*, y), app(app(pow, x), app(app(-, y), 1)))
APP(D, app(ln, x)) → APP(app(div, app(D, x)), x)
APP(D, app(app(pow, x), y)) → APP(D, y)
APP(D, app(app(-, x), y)) → APP(D, x)
APP(D, app(app(pow, x), y)) → APP(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y))
APP(app(map, f), app(app(cons, x), xs)) → APP(f, x)
APP(D, app(app(pow, x), y)) → APP(app(-, y), 1)
APP(D, app(app(div, x), y)) → APP(div, app(D, x))
APP(D, app(app(div, x), y)) → APP(div, app(app(*, x), app(D, y)))
APP(app(app(app(filter2, true), f), x), xs) → APP(cons, x)
APP(app(filter, f), app(app(cons, x), xs)) → APP(filter2, app(f, x))
APP(D, app(app(pow, x), y)) → APP(*, app(app(pow, x), y))
APP(app(app(app(filter2, true), f), x), xs) → APP(filter, f)
APP(D, app(app(div, x), y)) → APP(-, app(app(div, app(D, x)), y))
APP(D, app(app(div, x), y)) → APP(D, x)
APP(app(app(app(filter2, true), f), x), xs) → APP(app(cons, x), app(app(filter, f), xs))
APP(D, app(app(div, x), y)) → APP(*, x)
app(D, t) → 1
app(D, constant) → 0
app(D, app(app(+, x), y)) → app(app(+, app(D, x)), app(D, y))
app(D, app(app(*, x), y)) → app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y)))
app(D, app(app(-, x), y)) → app(app(-, app(D, x)), app(D, y))
app(D, app(minus, x)) → app(minus, app(D, x))
app(D, app(app(div, x), y)) → app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2)))
app(D, app(ln, x)) → app(app(div, app(D, x)), x)
app(D, app(app(pow, x), y)) → app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y)))
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(filter, f), nil) → nil
app(app(filter, f), app(app(cons, x), xs)) → app(app(app(app(filter2, app(f, x)), f), x), xs)
app(app(app(app(filter2, true), f), x), xs) → app(app(cons, x), app(app(filter, f), xs))
app(app(app(app(filter2, false), f), x), xs) → app(app(filter, f), xs)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
APP(D, app(app(pow, x), y)) → APP(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1))))
APP(app(filter, f), app(app(cons, x), xs)) → APP(app(filter2, app(f, x)), f)
APP(D, app(app(*, x), y)) → APP(app(*, y), app(D, x))
APP(D, app(app(*, x), y)) → APP(app(*, x), app(D, y))
APP(D, app(app(-, x), y)) → APP(D, y)
APP(D, app(app(-, x), y)) → APP(app(-, app(D, x)), app(D, y))
APP(D, app(app(div, x), y)) → APP(D, y)
APP(app(filter, f), app(app(cons, x), xs)) → APP(app(app(app(filter2, app(f, x)), f), x), xs)
APP(D, app(app(+, x), y)) → APP(D, y)
APP(D, app(minus, x)) → APP(minus, app(D, x))
APP(D, app(app(div, x), y)) → APP(app(pow, y), 2)
APP(D, app(app(pow, x), y)) → APP(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y)))
APP(D, app(app(*, x), y)) → APP(D, x)
APP(app(app(app(filter2, false), f), x), xs) → APP(filter, f)
APP(app(filter, f), app(app(cons, x), xs)) → APP(app(app(filter2, app(f, x)), f), x)
APP(D, app(app(pow, x), y)) → APP(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x)))
APP(D, app(app(*, x), y)) → APP(D, y)
APP(D, app(app(*, x), y)) → APP(+, app(app(*, y), app(D, x)))
APP(D, app(app(div, x), y)) → APP(pow, y)
APP(D, app(app(+, x), y)) → APP(+, app(D, x))
APP(D, app(app(+, x), y)) → APP(app(+, app(D, x)), app(D, y))
APP(D, app(app(pow, x), y)) → APP(-, y)
APP(D, app(app(*, x), y)) → APP(*, y)
APP(D, app(app(pow, x), y)) → APP(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))
APP(D, app(app(div, x), y)) → APP(app(div, app(D, x)), y)
APP(D, app(minus, x)) → APP(D, x)
APP(app(map, f), app(app(cons, x), xs)) → APP(cons, app(f, x))
APP(D, app(app(pow, x), y)) → APP(ln, x)
APP(app(map, f), app(app(cons, x), xs)) → APP(app(cons, app(f, x)), app(app(map, f), xs))
APP(D, app(app(pow, x), y)) → APP(D, x)
APP(app(filter, f), app(app(cons, x), xs)) → APP(f, x)
APP(D, app(ln, x)) → APP(D, x)
APP(D, app(app(+, x), y)) → APP(D, x)
APP(D, app(app(div, x), y)) → APP(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2)))
APP(D, app(app(pow, x), y)) → APP(*, y)
APP(D, app(app(div, x), y)) → APP(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2))
APP(app(map, f), app(app(cons, x), xs)) → APP(app(map, f), xs)
APP(D, app(app(pow, x), y)) → APP(app(pow, x), app(app(-, y), 1))
APP(D, app(app(div, x), y)) → APP(app(*, x), app(D, y))
APP(D, app(app(*, x), y)) → APP(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y)))
APP(D, app(app(pow, x), y)) → APP(app(*, app(app(pow, x), y)), app(ln, x))
APP(app(app(app(filter2, false), f), x), xs) → APP(app(filter, f), xs)
APP(app(app(app(filter2, true), f), x), xs) → APP(app(filter, f), xs)
APP(D, app(app(pow, x), y)) → APP(*, app(app(*, app(app(pow, x), y)), app(ln, x)))
APP(D, app(ln, x)) → APP(div, app(D, x))
APP(D, app(app(-, x), y)) → APP(-, app(D, x))
APP(D, app(app(pow, x), y)) → APP(app(*, y), app(app(pow, x), app(app(-, y), 1)))
APP(D, app(ln, x)) → APP(app(div, app(D, x)), x)
APP(D, app(app(pow, x), y)) → APP(D, y)
APP(D, app(app(-, x), y)) → APP(D, x)
APP(D, app(app(pow, x), y)) → APP(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y))
APP(app(map, f), app(app(cons, x), xs)) → APP(f, x)
APP(D, app(app(pow, x), y)) → APP(app(-, y), 1)
APP(D, app(app(div, x), y)) → APP(div, app(D, x))
APP(D, app(app(div, x), y)) → APP(div, app(app(*, x), app(D, y)))
APP(app(app(app(filter2, true), f), x), xs) → APP(cons, x)
APP(app(filter, f), app(app(cons, x), xs)) → APP(filter2, app(f, x))
APP(D, app(app(pow, x), y)) → APP(*, app(app(pow, x), y))
APP(app(app(app(filter2, true), f), x), xs) → APP(filter, f)
APP(D, app(app(div, x), y)) → APP(-, app(app(div, app(D, x)), y))
APP(D, app(app(div, x), y)) → APP(D, x)
APP(app(app(app(filter2, true), f), x), xs) → APP(app(cons, x), app(app(filter, f), xs))
APP(D, app(app(div, x), y)) → APP(*, x)
app(D, t) → 1
app(D, constant) → 0
app(D, app(app(+, x), y)) → app(app(+, app(D, x)), app(D, y))
app(D, app(app(*, x), y)) → app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y)))
app(D, app(app(-, x), y)) → app(app(-, app(D, x)), app(D, y))
app(D, app(minus, x)) → app(minus, app(D, x))
app(D, app(app(div, x), y)) → app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2)))
app(D, app(ln, x)) → app(app(div, app(D, x)), x)
app(D, app(app(pow, x), y)) → app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y)))
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(filter, f), nil) → nil
app(app(filter, f), app(app(cons, x), xs)) → app(app(app(app(filter2, app(f, x)), f), x), xs)
app(app(app(app(filter2, true), f), x), xs) → app(app(cons, x), app(app(filter, f), xs))
app(app(app(app(filter2, false), f), x), xs) → app(app(filter, f), xs)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
APP(D, app(app(pow, x), y)) → APP(D, x)
APP(D, app(ln, x)) → APP(D, x)
APP(D, app(app(-, x), y)) → APP(D, y)
APP(D, app(app(pow, x), y)) → APP(D, y)
APP(D, app(app(+, x), y)) → APP(D, x)
APP(D, app(app(-, x), y)) → APP(D, x)
APP(D, app(app(div, x), y)) → APP(D, y)
APP(D, app(minus, x)) → APP(D, x)
APP(D, app(app(*, x), y)) → APP(D, y)
APP(D, app(app(*, x), y)) → APP(D, x)
APP(D, app(app(div, x), y)) → APP(D, x)
APP(D, app(app(+, x), y)) → APP(D, y)
app(D, t) → 1
app(D, constant) → 0
app(D, app(app(+, x), y)) → app(app(+, app(D, x)), app(D, y))
app(D, app(app(*, x), y)) → app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y)))
app(D, app(app(-, x), y)) → app(app(-, app(D, x)), app(D, y))
app(D, app(minus, x)) → app(minus, app(D, x))
app(D, app(app(div, x), y)) → app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2)))
app(D, app(ln, x)) → app(app(div, app(D, x)), x)
app(D, app(app(pow, x), y)) → app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y)))
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(filter, f), nil) → nil
app(app(filter, f), app(app(cons, x), xs)) → app(app(app(app(filter2, app(f, x)), f), x), xs)
app(app(app(app(filter2, true), f), x), xs) → app(app(cons, x), app(app(filter, f), xs))
app(app(app(app(filter2, false), f), x), xs) → app(app(filter, f), xs)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
APP(D, app(app(pow, x), y)) → APP(D, x)
APP(D, app(ln, x)) → APP(D, x)
APP(D, app(app(-, x), y)) → APP(D, y)
APP(D, app(app(pow, x), y)) → APP(D, y)
APP(D, app(app(+, x), y)) → APP(D, x)
APP(D, app(app(-, x), y)) → APP(D, x)
APP(D, app(app(div, x), y)) → APP(D, y)
APP(D, app(minus, x)) → APP(D, x)
APP(D, app(app(*, x), y)) → APP(D, y)
APP(D, app(app(*, x), y)) → APP(D, x)
APP(D, app(app(div, x), y)) → APP(D, x)
APP(D, app(app(+, x), y)) → APP(D, y)
The value of delta used in the strict ordering is 20.
POL(*) = 0
POL(APP(x1, x2)) = (4)x_2
POL(ln) = 4
POL(minus) = 4
POL(D) = 0
POL(-) = 4
POL(div) = 4
POL(pow) = 4
POL(app(x1, x2)) = 1 + (4)x_1 + (4)x_2
POL(+) = 4
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
app(D, t) → 1
app(D, constant) → 0
app(D, app(app(+, x), y)) → app(app(+, app(D, x)), app(D, y))
app(D, app(app(*, x), y)) → app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y)))
app(D, app(app(-, x), y)) → app(app(-, app(D, x)), app(D, y))
app(D, app(minus, x)) → app(minus, app(D, x))
app(D, app(app(div, x), y)) → app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2)))
app(D, app(ln, x)) → app(app(div, app(D, x)), x)
app(D, app(app(pow, x), y)) → app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y)))
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(filter, f), nil) → nil
app(app(filter, f), app(app(cons, x), xs)) → app(app(app(app(filter2, app(f, x)), f), x), xs)
app(app(app(app(filter2, true), f), x), xs) → app(app(cons, x), app(app(filter, f), xs))
app(app(app(app(filter2, false), f), x), xs) → app(app(filter, f), xs)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
APP(app(filter, f), app(app(cons, x), xs)) → APP(f, x)
APP(app(app(app(filter2, false), f), x), xs) → APP(app(filter, f), xs)
APP(app(app(app(filter2, true), f), x), xs) → APP(app(filter, f), xs)
APP(app(map, f), app(app(cons, x), xs)) → APP(f, x)
APP(app(map, f), app(app(cons, x), xs)) → APP(app(map, f), xs)
app(D, t) → 1
app(D, constant) → 0
app(D, app(app(+, x), y)) → app(app(+, app(D, x)), app(D, y))
app(D, app(app(*, x), y)) → app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y)))
app(D, app(app(-, x), y)) → app(app(-, app(D, x)), app(D, y))
app(D, app(minus, x)) → app(minus, app(D, x))
app(D, app(app(div, x), y)) → app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2)))
app(D, app(ln, x)) → app(app(div, app(D, x)), x)
app(D, app(app(pow, x), y)) → app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y)))
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(filter, f), nil) → nil
app(app(filter, f), app(app(cons, x), xs)) → app(app(app(app(filter2, app(f, x)), f), x), xs)
app(app(app(app(filter2, true), f), x), xs) → app(app(cons, x), app(app(filter, f), xs))
app(app(app(app(filter2, false), f), x), xs) → app(app(filter, f), xs)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
APP(app(filter, f), app(app(cons, x), xs)) → APP(f, x)
APP(app(app(app(filter2, false), f), x), xs) → APP(app(filter, f), xs)
APP(app(app(app(filter2, true), f), x), xs) → APP(app(filter, f), xs)
APP(app(map, f), app(app(cons, x), xs)) → APP(f, x)
APP(app(map, f), app(app(cons, x), xs)) → APP(app(map, f), xs)
The value of delta used in the strict ordering is 336.
POL(APP(x1, x2)) = (4)x_1 + (4)x_2
POL(cons) = 4
POL(true) = 4
POL(map) = 4
POL(false) = 1
POL(app(x1, x2)) = 4 + (4)x_1 + x_2
POL(filter2) = 2
POL(filter) = 4
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
app(D, t) → 1
app(D, constant) → 0
app(D, app(app(+, x), y)) → app(app(+, app(D, x)), app(D, y))
app(D, app(app(*, x), y)) → app(app(+, app(app(*, y), app(D, x))), app(app(*, x), app(D, y)))
app(D, app(app(-, x), y)) → app(app(-, app(D, x)), app(D, y))
app(D, app(minus, x)) → app(minus, app(D, x))
app(D, app(app(div, x), y)) → app(app(-, app(app(div, app(D, x)), y)), app(app(div, app(app(*, x), app(D, y))), app(app(pow, y), 2)))
app(D, app(ln, x)) → app(app(div, app(D, x)), x)
app(D, app(app(pow, x), y)) → app(app(+, app(app(*, app(app(*, y), app(app(pow, x), app(app(-, y), 1)))), app(D, x))), app(app(*, app(app(*, app(app(pow, x), y)), app(ln, x))), app(D, y)))
app(app(map, f), nil) → nil
app(app(map, f), app(app(cons, x), xs)) → app(app(cons, app(f, x)), app(app(map, f), xs))
app(app(filter, f), nil) → nil
app(app(filter, f), app(app(cons, x), xs)) → app(app(app(app(filter2, app(f, x)), f), x), xs)
app(app(app(app(filter2, true), f), x), xs) → app(app(cons, x), app(app(filter, f), xs))
app(app(app(app(filter2, false), f), x), xs) → app(app(filter, f), xs)