f(0(x1)) → s(0(x1))
d(0(x1)) → 0(x1)
d(s(x1)) → s(s(d(p(s(x1)))))
f(s(x1)) → d(f(p(s(x1))))
p(s(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
f(0(x1)) → s(0(x1))
d(0(x1)) → 0(x1)
d(s(x1)) → s(s(d(p(s(x1)))))
f(s(x1)) → d(f(p(s(x1))))
p(s(x1)) → x1
F(s(x1)) → D(f(p(s(x1))))
F(s(x1)) → F(p(s(x1)))
F(s(x1)) → P(s(x1))
D(s(x1)) → P(s(x1))
D(s(x1)) → D(p(s(x1)))
f(0(x1)) → s(0(x1))
d(0(x1)) → 0(x1)
d(s(x1)) → s(s(d(p(s(x1)))))
f(s(x1)) → d(f(p(s(x1))))
p(s(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
F(s(x1)) → D(f(p(s(x1))))
F(s(x1)) → F(p(s(x1)))
F(s(x1)) → P(s(x1))
D(s(x1)) → P(s(x1))
D(s(x1)) → D(p(s(x1)))
f(0(x1)) → s(0(x1))
d(0(x1)) → 0(x1)
d(s(x1)) → s(s(d(p(s(x1)))))
f(s(x1)) → d(f(p(s(x1))))
p(s(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
D(s(x1)) → D(p(s(x1)))
f(0(x1)) → s(0(x1))
d(0(x1)) → 0(x1)
d(s(x1)) → s(s(d(p(s(x1)))))
f(s(x1)) → d(f(p(s(x1))))
p(s(x1)) → x1
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
D(s(x1)) → D(p(s(x1)))
The value of delta used in the strict ordering is 9/16.
POL(D(x1)) = (9/4)x_1
POL(s(x1)) = 1/2 + (9/4)x_1
POL(p(x1)) = (1/2)x_1
p(s(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
f(0(x1)) → s(0(x1))
d(0(x1)) → 0(x1)
d(s(x1)) → s(s(d(p(s(x1)))))
f(s(x1)) → d(f(p(s(x1))))
p(s(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
F(s(x1)) → F(p(s(x1)))
f(0(x1)) → s(0(x1))
d(0(x1)) → 0(x1)
d(s(x1)) → s(s(d(p(s(x1)))))
f(s(x1)) → d(f(p(s(x1))))
p(s(x1)) → x1
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(s(x1)) → F(p(s(x1)))
The value of delta used in the strict ordering is 1.
POL(s(x1)) = 4 + (4)x_1
POL(p(x1)) = 7/4 + (1/2)x_1
POL(F(x1)) = (4)x_1
p(s(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
f(0(x1)) → s(0(x1))
d(0(x1)) → 0(x1)
d(s(x1)) → s(s(d(p(s(x1)))))
f(s(x1)) → d(f(p(s(x1))))
p(s(x1)) → x1