i(0(x1)) → p(s(p(s(0(p(s(p(s(x1)))))))))
i(s(x1)) → p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))))
j(0(x1)) → p(s(p(p(s(s(0(p(s(p(s(x1)))))))))))
j(s(x1)) → s(s(s(s(p(p(s(s(i(p(s(p(s(x1)))))))))))))
p(p(s(x1))) → p(x1)
p(s(x1)) → x1
p(0(x1)) → 0(s(s(s(s(s(s(s(s(x1)))))))))
↳ QTRS
↳ DependencyPairsProof
i(0(x1)) → p(s(p(s(0(p(s(p(s(x1)))))))))
i(s(x1)) → p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))))
j(0(x1)) → p(s(p(p(s(s(0(p(s(p(s(x1)))))))))))
j(s(x1)) → s(s(s(s(p(p(s(s(i(p(s(p(s(x1)))))))))))))
p(p(s(x1))) → p(x1)
p(s(x1)) → x1
p(0(x1)) → 0(s(s(s(s(s(s(s(s(x1)))))))))
J(0(x1)) → P(p(s(s(0(p(s(p(s(x1)))))))))
P(p(s(x1))) → P(x1)
I(0(x1)) → P(s(p(s(x1))))
I(s(x1)) → P(p(p(p(s(s(s(s(x1))))))))
J(0(x1)) → P(s(x1))
J(0(x1)) → P(s(p(p(s(s(0(p(s(p(s(x1)))))))))))
I(s(x1)) → P(s(p(p(p(p(s(s(s(s(x1))))))))))
I(s(x1)) → P(p(s(s(s(s(x1))))))
J(s(x1)) → P(s(x1))
J(s(x1)) → I(p(s(p(s(x1)))))
I(0(x1)) → P(s(p(s(0(p(s(p(s(x1)))))))))
I(s(x1)) → P(s(s(s(s(x1)))))
I(s(x1)) → J(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))
J(s(x1)) → P(s(p(s(x1))))
J(s(x1)) → P(p(s(s(i(p(s(p(s(x1)))))))))
I(0(x1)) → P(s(0(p(s(p(s(x1)))))))
I(s(x1)) → P(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))
I(s(x1)) → P(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))
I(s(x1)) → P(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))))
J(0(x1)) → P(s(s(0(p(s(p(s(x1))))))))
I(0(x1)) → P(s(x1))
J(0(x1)) → P(s(p(s(x1))))
I(s(x1)) → P(p(p(s(s(s(s(x1)))))))
J(s(x1)) → P(s(s(i(p(s(p(s(x1))))))))
i(0(x1)) → p(s(p(s(0(p(s(p(s(x1)))))))))
i(s(x1)) → p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))))
j(0(x1)) → p(s(p(p(s(s(0(p(s(p(s(x1)))))))))))
j(s(x1)) → s(s(s(s(p(p(s(s(i(p(s(p(s(x1)))))))))))))
p(p(s(x1))) → p(x1)
p(s(x1)) → x1
p(0(x1)) → 0(s(s(s(s(s(s(s(s(x1)))))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
J(0(x1)) → P(p(s(s(0(p(s(p(s(x1)))))))))
P(p(s(x1))) → P(x1)
I(0(x1)) → P(s(p(s(x1))))
I(s(x1)) → P(p(p(p(s(s(s(s(x1))))))))
J(0(x1)) → P(s(x1))
J(0(x1)) → P(s(p(p(s(s(0(p(s(p(s(x1)))))))))))
I(s(x1)) → P(s(p(p(p(p(s(s(s(s(x1))))))))))
I(s(x1)) → P(p(s(s(s(s(x1))))))
J(s(x1)) → P(s(x1))
J(s(x1)) → I(p(s(p(s(x1)))))
I(0(x1)) → P(s(p(s(0(p(s(p(s(x1)))))))))
I(s(x1)) → P(s(s(s(s(x1)))))
I(s(x1)) → J(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))
J(s(x1)) → P(s(p(s(x1))))
J(s(x1)) → P(p(s(s(i(p(s(p(s(x1)))))))))
I(0(x1)) → P(s(0(p(s(p(s(x1)))))))
I(s(x1)) → P(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))
I(s(x1)) → P(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))
I(s(x1)) → P(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))))
J(0(x1)) → P(s(s(0(p(s(p(s(x1))))))))
I(0(x1)) → P(s(x1))
J(0(x1)) → P(s(p(s(x1))))
I(s(x1)) → P(p(p(s(s(s(s(x1)))))))
J(s(x1)) → P(s(s(i(p(s(p(s(x1))))))))
i(0(x1)) → p(s(p(s(0(p(s(p(s(x1)))))))))
i(s(x1)) → p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))))
j(0(x1)) → p(s(p(p(s(s(0(p(s(p(s(x1)))))))))))
j(s(x1)) → s(s(s(s(p(p(s(s(i(p(s(p(s(x1)))))))))))))
p(p(s(x1))) → p(x1)
p(s(x1)) → x1
p(0(x1)) → 0(s(s(s(s(s(s(s(s(x1)))))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
P(p(s(x1))) → P(x1)
i(0(x1)) → p(s(p(s(0(p(s(p(s(x1)))))))))
i(s(x1)) → p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))))
j(0(x1)) → p(s(p(p(s(s(0(p(s(p(s(x1)))))))))))
j(s(x1)) → s(s(s(s(p(p(s(s(i(p(s(p(s(x1)))))))))))))
p(p(s(x1))) → p(x1)
p(s(x1)) → x1
p(0(x1)) → 0(s(s(s(s(s(s(s(s(x1)))))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
P(p(s(x1))) → P(x1)
The value of delta used in the strict ordering is 2.
POL(P(x1)) = (2)x_1
POL(p(x1)) = 1 + x_1
POL(s(x1)) = x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
i(0(x1)) → p(s(p(s(0(p(s(p(s(x1)))))))))
i(s(x1)) → p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))))
j(0(x1)) → p(s(p(p(s(s(0(p(s(p(s(x1)))))))))))
j(s(x1)) → s(s(s(s(p(p(s(s(i(p(s(p(s(x1)))))))))))))
p(p(s(x1))) → p(x1)
p(s(x1)) → x1
p(0(x1)) → 0(s(s(s(s(s(s(s(s(x1)))))))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
J(s(x1)) → I(p(s(p(s(x1)))))
I(s(x1)) → J(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))
i(0(x1)) → p(s(p(s(0(p(s(p(s(x1)))))))))
i(s(x1)) → p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))))
j(0(x1)) → p(s(p(p(s(s(0(p(s(p(s(x1)))))))))))
j(s(x1)) → s(s(s(s(p(p(s(s(i(p(s(p(s(x1)))))))))))))
p(p(s(x1))) → p(x1)
p(s(x1)) → x1
p(0(x1)) → 0(s(s(s(s(s(s(s(s(x1)))))))))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
J(s(x1)) → I(p(s(p(s(x1)))))
I(s(x1)) → J(p(s(p(s(p(p(p(p(s(s(s(s(x1)))))))))))))
The value of delta used in the strict ordering is 43/2048.
POL(J(x1)) = (1/2)x_1
POL(s(x1)) = 1/4 + (4)x_1
POL(p(x1)) = (1/4)x_1
POL(0(x1)) = 0
POL(I(x1)) = (1/2)x_1
p(p(s(x1))) → p(x1)
p(0(x1)) → 0(s(s(s(s(s(s(s(s(x1)))))))))
p(s(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
i(0(x1)) → p(s(p(s(0(p(s(p(s(x1)))))))))
i(s(x1)) → p(s(p(s(s(j(p(s(p(s(p(p(p(p(s(s(s(s(x1))))))))))))))))))
j(0(x1)) → p(s(p(p(s(s(0(p(s(p(s(x1)))))))))))
j(s(x1)) → s(s(s(s(p(p(s(s(i(p(s(p(s(x1)))))))))))))
p(p(s(x1))) → p(x1)
p(s(x1)) → x1
p(0(x1)) → 0(s(s(s(s(s(s(s(s(x1)))))))))