D(t) → 1
D(constant) → 0
D(+(x, y)) → +(D(x), D(y))
D(*(x, y)) → +(*(y, D(x)), *(x, D(y)))
D(-(x, y)) → -(D(x), D(y))
D(minus(x)) → minus(D(x))
D(div(x, y)) → -(div(D(x), y), div(*(x, D(y)), pow(y, 2)))
D(ln(x)) → div(D(x), x)
D(pow(x, y)) → +(*(*(y, pow(x, -(y, 1))), D(x)), *(*(pow(x, y), ln(x)), D(y)))
↳ QTRS
↳ DependencyPairsProof
D(t) → 1
D(constant) → 0
D(+(x, y)) → +(D(x), D(y))
D(*(x, y)) → +(*(y, D(x)), *(x, D(y)))
D(-(x, y)) → -(D(x), D(y))
D(minus(x)) → minus(D(x))
D(div(x, y)) → -(div(D(x), y), div(*(x, D(y)), pow(y, 2)))
D(ln(x)) → div(D(x), x)
D(pow(x, y)) → +(*(*(y, pow(x, -(y, 1))), D(x)), *(*(pow(x, y), ln(x)), D(y)))
D1(+(x, y)) → D1(y)
D1(*(x, y)) → D1(y)
D1(pow(x, y)) → D1(y)
D1(div(x, y)) → D1(x)
D1(-(x, y)) → D1(x)
D1(div(x, y)) → D1(y)
D1(minus(x)) → D1(x)
D1(-(x, y)) → D1(y)
D1(+(x, y)) → D1(x)
D1(pow(x, y)) → D1(x)
D1(*(x, y)) → D1(x)
D1(ln(x)) → D1(x)
D(t) → 1
D(constant) → 0
D(+(x, y)) → +(D(x), D(y))
D(*(x, y)) → +(*(y, D(x)), *(x, D(y)))
D(-(x, y)) → -(D(x), D(y))
D(minus(x)) → minus(D(x))
D(div(x, y)) → -(div(D(x), y), div(*(x, D(y)), pow(y, 2)))
D(ln(x)) → div(D(x), x)
D(pow(x, y)) → +(*(*(y, pow(x, -(y, 1))), D(x)), *(*(pow(x, y), ln(x)), D(y)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
D1(+(x, y)) → D1(y)
D1(*(x, y)) → D1(y)
D1(pow(x, y)) → D1(y)
D1(div(x, y)) → D1(x)
D1(-(x, y)) → D1(x)
D1(div(x, y)) → D1(y)
D1(minus(x)) → D1(x)
D1(-(x, y)) → D1(y)
D1(+(x, y)) → D1(x)
D1(pow(x, y)) → D1(x)
D1(*(x, y)) → D1(x)
D1(ln(x)) → D1(x)
D(t) → 1
D(constant) → 0
D(+(x, y)) → +(D(x), D(y))
D(*(x, y)) → +(*(y, D(x)), *(x, D(y)))
D(-(x, y)) → -(D(x), D(y))
D(minus(x)) → minus(D(x))
D(div(x, y)) → -(div(D(x), y), div(*(x, D(y)), pow(y, 2)))
D(ln(x)) → div(D(x), x)
D(pow(x, y)) → +(*(*(y, pow(x, -(y, 1))), D(x)), *(*(pow(x, y), ln(x)), D(y)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
D1(+(x, y)) → D1(y)
D1(*(x, y)) → D1(y)
D1(pow(x, y)) → D1(y)
D1(div(x, y)) → D1(x)
D1(-(x, y)) → D1(x)
D1(div(x, y)) → D1(y)
D1(minus(x)) → D1(x)
D1(-(x, y)) → D1(y)
D1(+(x, y)) → D1(x)
D1(pow(x, y)) → D1(x)
D1(*(x, y)) → D1(x)
D1(ln(x)) → D1(x)
The value of delta used in the strict ordering is 16.
POL(ln(x1)) = 4 + (4)x_1
POL(-(x1, x2)) = 4 + (4)x_1 + (4)x_2
POL(div(x1, x2)) = 4 + (2)x_1 + (4)x_2
POL(minus(x1)) = 4 + (4)x_1
POL(*(x1, x2)) = 4 + (4)x_1 + (4)x_2
POL(D1(x1)) = (4)x_1
POL(pow(x1, x2)) = 4 + (4)x_1 + (4)x_2
POL(+(x1, x2)) = 4 + (4)x_1 + (4)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
D(t) → 1
D(constant) → 0
D(+(x, y)) → +(D(x), D(y))
D(*(x, y)) → +(*(y, D(x)), *(x, D(y)))
D(-(x, y)) → -(D(x), D(y))
D(minus(x)) → minus(D(x))
D(div(x, y)) → -(div(D(x), y), div(*(x, D(y)), pow(y, 2)))
D(ln(x)) → div(D(x), x)
D(pow(x, y)) → +(*(*(y, pow(x, -(y, 1))), D(x)), *(*(pow(x, y), ln(x)), D(y)))