a(b(x1)) → b(r(x1))
r(a(x1)) → d(r(x1))
r(x1) → d(x1)
d(a(x1)) → a(a(d(x1)))
d(x1) → a(x1)
↳ QTRS
↳ DependencyPairsProof
a(b(x1)) → b(r(x1))
r(a(x1)) → d(r(x1))
r(x1) → d(x1)
d(a(x1)) → a(a(d(x1)))
d(x1) → a(x1)
D(x1) → A(x1)
R(a(x1)) → D(r(x1))
D(a(x1)) → D(x1)
R(a(x1)) → R(x1)
D(a(x1)) → A(d(x1))
R(x1) → D(x1)
A(b(x1)) → R(x1)
D(a(x1)) → A(a(d(x1)))
a(b(x1)) → b(r(x1))
r(a(x1)) → d(r(x1))
r(x1) → d(x1)
d(a(x1)) → a(a(d(x1)))
d(x1) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
D(x1) → A(x1)
R(a(x1)) → D(r(x1))
D(a(x1)) → D(x1)
R(a(x1)) → R(x1)
D(a(x1)) → A(d(x1))
R(x1) → D(x1)
A(b(x1)) → R(x1)
D(a(x1)) → A(a(d(x1)))
a(b(x1)) → b(r(x1))
r(a(x1)) → d(r(x1))
r(x1) → d(x1)
d(a(x1)) → a(a(d(x1)))
d(x1) → a(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
D(x1) → A(x1)
R(a(x1)) → D(r(x1))
D(a(x1)) → A(d(x1))
R(x1) → D(x1)
D(a(x1)) → A(a(d(x1)))
Used ordering: Polynomial interpretation [25,35]:
D(a(x1)) → D(x1)
R(a(x1)) → R(x1)
A(b(x1)) → R(x1)
The value of delta used in the strict ordering is 1.
POL(D(x1)) = 1 + (2)x_1
POL(a(x1)) = x_1
POL(A(x1)) = x_1
POL(r(x1)) = x_1
POL(d(x1)) = x_1
POL(b(x1)) = 2 + (2)x_1
POL(R(x1)) = 2 + (2)x_1
a(b(x1)) → b(r(x1))
r(a(x1)) → d(r(x1))
r(x1) → d(x1)
d(a(x1)) → a(a(d(x1)))
d(x1) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
R(a(x1)) → R(x1)
D(a(x1)) → D(x1)
A(b(x1)) → R(x1)
a(b(x1)) → b(r(x1))
r(a(x1)) → d(r(x1))
r(x1) → d(x1)
d(a(x1)) → a(a(d(x1)))
d(x1) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
R(a(x1)) → R(x1)
a(b(x1)) → b(r(x1))
r(a(x1)) → d(r(x1))
r(x1) → d(x1)
d(a(x1)) → a(a(d(x1)))
d(x1) → a(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
R(a(x1)) → R(x1)
The value of delta used in the strict ordering is 4.
POL(a(x1)) = 1 + (4)x_1
POL(R(x1)) = (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
a(b(x1)) → b(r(x1))
r(a(x1)) → d(r(x1))
r(x1) → d(x1)
d(a(x1)) → a(a(d(x1)))
d(x1) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
D(a(x1)) → D(x1)
a(b(x1)) → b(r(x1))
r(a(x1)) → d(r(x1))
r(x1) → d(x1)
d(a(x1)) → a(a(d(x1)))
d(x1) → a(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
D(a(x1)) → D(x1)
The value of delta used in the strict ordering is 4.
POL(D(x1)) = (4)x_1
POL(a(x1)) = 1 + (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
a(b(x1)) → b(r(x1))
r(a(x1)) → d(r(x1))
r(x1) → d(x1)
d(a(x1)) → a(a(d(x1)))
d(x1) → a(x1)