a(a(a(a(x1)))) → b(b(b(b(b(b(x1))))))
b(b(b(b(x1)))) → c(c(c(c(c(c(x1))))))
c(c(c(c(x1)))) → d(d(d(d(d(d(x1))))))
b(b(x1)) → d(d(d(d(x1))))
c(c(d(d(d(d(x1)))))) → a(a(x1))
↳ QTRS
↳ DependencyPairsProof
a(a(a(a(x1)))) → b(b(b(b(b(b(x1))))))
b(b(b(b(x1)))) → c(c(c(c(c(c(x1))))))
c(c(c(c(x1)))) → d(d(d(d(d(d(x1))))))
b(b(x1)) → d(d(d(d(x1))))
c(c(d(d(d(d(x1)))))) → a(a(x1))
C(c(d(d(d(d(x1)))))) → A(a(x1))
A(a(a(a(x1)))) → B(b(x1))
B(b(b(b(x1)))) → C(c(c(x1)))
B(b(b(b(x1)))) → C(c(x1))
C(c(d(d(d(d(x1)))))) → A(x1)
A(a(a(a(x1)))) → B(b(b(b(x1))))
B(b(b(b(x1)))) → C(c(c(c(c(c(x1))))))
B(b(b(b(x1)))) → C(c(c(c(x1))))
B(b(b(b(x1)))) → C(c(c(c(c(x1)))))
A(a(a(a(x1)))) → B(b(b(b(b(b(x1))))))
A(a(a(a(x1)))) → B(x1)
A(a(a(a(x1)))) → B(b(b(b(b(x1)))))
B(b(b(b(x1)))) → C(x1)
A(a(a(a(x1)))) → B(b(b(x1)))
a(a(a(a(x1)))) → b(b(b(b(b(b(x1))))))
b(b(b(b(x1)))) → c(c(c(c(c(c(x1))))))
c(c(c(c(x1)))) → d(d(d(d(d(d(x1))))))
b(b(x1)) → d(d(d(d(x1))))
c(c(d(d(d(d(x1)))))) → a(a(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
C(c(d(d(d(d(x1)))))) → A(a(x1))
A(a(a(a(x1)))) → B(b(x1))
B(b(b(b(x1)))) → C(c(c(x1)))
B(b(b(b(x1)))) → C(c(x1))
C(c(d(d(d(d(x1)))))) → A(x1)
A(a(a(a(x1)))) → B(b(b(b(x1))))
B(b(b(b(x1)))) → C(c(c(c(c(c(x1))))))
B(b(b(b(x1)))) → C(c(c(c(x1))))
B(b(b(b(x1)))) → C(c(c(c(c(x1)))))
A(a(a(a(x1)))) → B(b(b(b(b(b(x1))))))
A(a(a(a(x1)))) → B(x1)
A(a(a(a(x1)))) → B(b(b(b(b(x1)))))
B(b(b(b(x1)))) → C(x1)
A(a(a(a(x1)))) → B(b(b(x1)))
a(a(a(a(x1)))) → b(b(b(b(b(b(x1))))))
b(b(b(b(x1)))) → c(c(c(c(c(c(x1))))))
c(c(c(c(x1)))) → d(d(d(d(d(d(x1))))))
b(b(x1)) → d(d(d(d(x1))))
c(c(d(d(d(d(x1)))))) → a(a(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(a(a(x1)))) → B(b(x1))
B(b(b(b(x1)))) → C(c(c(x1)))
B(b(b(b(x1)))) → C(c(x1))
C(c(d(d(d(d(x1)))))) → A(x1)
A(a(a(a(x1)))) → B(b(b(b(x1))))
B(b(b(b(x1)))) → C(c(c(c(c(c(x1))))))
B(b(b(b(x1)))) → C(c(c(c(x1))))
B(b(b(b(x1)))) → C(c(c(c(c(x1)))))
A(a(a(a(x1)))) → B(b(b(b(b(b(x1))))))
A(a(a(a(x1)))) → B(x1)
A(a(a(a(x1)))) → B(b(b(b(b(x1)))))
B(b(b(b(x1)))) → C(x1)
A(a(a(a(x1)))) → B(b(b(x1)))
Used ordering: Polynomial interpretation [25,35]:
C(c(d(d(d(d(x1)))))) → A(a(x1))
The value of delta used in the strict ordering is 1/16.
POL(C(x1)) = 7/4 + (1/4)x_1
POL(c(x1)) = 3/2 + x_1
POL(B(x1)) = 2 + (1/4)x_1
POL(a(x1)) = 7/2 + x_1
POL(A(x1)) = 9/4 + (1/4)x_1
POL(d(x1)) = 1 + x_1
POL(b(x1)) = 9/4 + x_1
c(c(c(c(x1)))) → d(d(d(d(d(d(x1))))))
a(a(a(a(x1)))) → b(b(b(b(b(b(x1))))))
b(b(b(b(x1)))) → c(c(c(c(c(c(x1))))))
c(c(d(d(d(d(x1)))))) → a(a(x1))
b(b(x1)) → d(d(d(d(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
C(c(d(d(d(d(x1)))))) → A(a(x1))
a(a(a(a(x1)))) → b(b(b(b(b(b(x1))))))
b(b(b(b(x1)))) → c(c(c(c(c(c(x1))))))
c(c(c(c(x1)))) → d(d(d(d(d(d(x1))))))
b(b(x1)) → d(d(d(d(x1))))
c(c(d(d(d(d(x1)))))) → a(a(x1))