a(a(x1)) → b(b(b(x1)))
a(x1) → c(d(x1))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
e(d(x1)) → a(b(c(d(e(x1)))))
b(x1) → d(d(x1))
e(c(x1)) → b(a(a(e(x1))))
c(d(d(x1))) → a(x1)
↳ QTRS
↳ DependencyPairsProof
a(a(x1)) → b(b(b(x1)))
a(x1) → c(d(x1))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
e(d(x1)) → a(b(c(d(e(x1)))))
b(x1) → d(d(x1))
e(c(x1)) → b(a(a(e(x1))))
c(d(d(x1))) → a(x1)
E(c(x1)) → A(a(e(x1)))
E(c(x1)) → E(x1)
E(d(x1)) → A(b(c(d(e(x1)))))
E(d(x1)) → C(d(e(x1)))
E(c(x1)) → B(a(a(e(x1))))
A(a(x1)) → B(x1)
C(d(d(x1))) → A(x1)
B(b(x1)) → C(c(x1))
A(a(x1)) → B(b(x1))
A(x1) → C(d(x1))
E(c(x1)) → A(e(x1))
A(a(x1)) → B(b(b(x1)))
B(b(x1)) → C(c(c(x1)))
B(b(x1)) → C(x1)
E(d(x1)) → B(c(d(e(x1))))
E(d(x1)) → E(x1)
a(a(x1)) → b(b(b(x1)))
a(x1) → c(d(x1))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
e(d(x1)) → a(b(c(d(e(x1)))))
b(x1) → d(d(x1))
e(c(x1)) → b(a(a(e(x1))))
c(d(d(x1))) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
E(c(x1)) → A(a(e(x1)))
E(c(x1)) → E(x1)
E(d(x1)) → A(b(c(d(e(x1)))))
E(d(x1)) → C(d(e(x1)))
E(c(x1)) → B(a(a(e(x1))))
A(a(x1)) → B(x1)
C(d(d(x1))) → A(x1)
B(b(x1)) → C(c(x1))
A(a(x1)) → B(b(x1))
A(x1) → C(d(x1))
E(c(x1)) → A(e(x1))
A(a(x1)) → B(b(b(x1)))
B(b(x1)) → C(c(c(x1)))
B(b(x1)) → C(x1)
E(d(x1)) → B(c(d(e(x1))))
E(d(x1)) → E(x1)
a(a(x1)) → b(b(b(x1)))
a(x1) → c(d(x1))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
e(d(x1)) → a(b(c(d(e(x1)))))
b(x1) → d(d(x1))
e(c(x1)) → b(a(a(e(x1))))
c(d(d(x1))) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
B(b(x1)) → C(c(x1))
C(d(d(x1))) → A(x1)
A(a(x1)) → B(b(x1))
A(x1) → C(d(x1))
A(a(x1)) → B(b(b(x1)))
B(b(x1)) → C(c(c(x1)))
B(b(x1)) → C(x1)
A(a(x1)) → B(x1)
a(a(x1)) → b(b(b(x1)))
a(x1) → c(d(x1))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
e(d(x1)) → a(b(c(d(e(x1)))))
b(x1) → d(d(x1))
e(c(x1)) → b(a(a(e(x1))))
c(d(d(x1))) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
E(c(x1)) → E(x1)
E(d(x1)) → E(x1)
a(a(x1)) → b(b(b(x1)))
a(x1) → c(d(x1))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
e(d(x1)) → a(b(c(d(e(x1)))))
b(x1) → d(d(x1))
e(c(x1)) → b(a(a(e(x1))))
c(d(d(x1))) → a(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
E(c(x1)) → E(x1)
Used ordering: Polynomial interpretation [25,35]:
E(d(x1)) → E(x1)
The value of delta used in the strict ordering is 8.
POL(E(x1)) = (2)x_1
POL(c(x1)) = 4 + (2)x_1
POL(d(x1)) = (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
E(d(x1)) → E(x1)
a(a(x1)) → b(b(b(x1)))
a(x1) → c(d(x1))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
e(d(x1)) → a(b(c(d(e(x1)))))
b(x1) → d(d(x1))
e(c(x1)) → b(a(a(e(x1))))
c(d(d(x1))) → a(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
E(d(x1)) → E(x1)
The value of delta used in the strict ordering is 8.
POL(E(x1)) = (2)x_1
POL(d(x1)) = 4 + (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
a(a(x1)) → b(b(b(x1)))
a(x1) → c(d(x1))
b(b(x1)) → c(c(c(x1)))
c(c(x1)) → d(d(d(x1)))
e(d(x1)) → a(b(c(d(e(x1)))))
b(x1) → d(d(x1))
e(c(x1)) → b(a(a(e(x1))))
c(d(d(x1))) → a(x1)