a(x1) → b(b(x1))
a(b(b(x1))) → b(b(c(c(c(a(x1))))))
b(b(x1)) → c(c(c(x1)))
c(c(c(b(b(x1))))) → a(x1)
↳ QTRS
↳ DependencyPairsProof
a(x1) → b(b(x1))
a(b(b(x1))) → b(b(c(c(c(a(x1))))))
b(b(x1)) → c(c(c(x1)))
c(c(c(b(b(x1))))) → a(x1)
B(b(x1)) → C(c(x1))
A(b(b(x1))) → A(x1)
A(x1) → B(b(x1))
A(b(b(x1))) → C(a(x1))
A(b(b(x1))) → C(c(c(a(x1))))
B(b(x1)) → C(c(c(x1)))
C(c(c(b(b(x1))))) → A(x1)
B(b(x1)) → C(x1)
A(b(b(x1))) → C(c(a(x1)))
A(b(b(x1))) → B(c(c(c(a(x1)))))
A(x1) → B(x1)
A(b(b(x1))) → B(b(c(c(c(a(x1))))))
a(x1) → b(b(x1))
a(b(b(x1))) → b(b(c(c(c(a(x1))))))
b(b(x1)) → c(c(c(x1)))
c(c(c(b(b(x1))))) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
B(b(x1)) → C(c(x1))
A(b(b(x1))) → A(x1)
A(x1) → B(b(x1))
A(b(b(x1))) → C(a(x1))
A(b(b(x1))) → C(c(c(a(x1))))
B(b(x1)) → C(c(c(x1)))
C(c(c(b(b(x1))))) → A(x1)
B(b(x1)) → C(x1)
A(b(b(x1))) → C(c(a(x1)))
A(b(b(x1))) → B(c(c(c(a(x1)))))
A(x1) → B(x1)
A(b(b(x1))) → B(b(c(c(c(a(x1))))))
a(x1) → b(b(x1))
a(b(b(x1))) → b(b(c(c(c(a(x1))))))
b(b(x1)) → c(c(c(x1)))
c(c(c(b(b(x1))))) → a(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(b(x1)) → C(c(x1))
A(b(b(x1))) → A(x1)
A(x1) → B(b(x1))
A(b(b(x1))) → C(a(x1))
A(b(b(x1))) → C(c(c(a(x1))))
B(b(x1)) → C(c(c(x1)))
C(c(c(b(b(x1))))) → A(x1)
B(b(x1)) → C(x1)
A(b(b(x1))) → C(c(a(x1)))
A(b(b(x1))) → B(c(c(c(a(x1)))))
A(x1) → B(x1)
A(b(b(x1))) → B(b(c(c(c(a(x1))))))
The value of delta used in the strict ordering is 1/2.
POL(C(x1)) = 3/2 + (4)x_1
POL(c(x1)) = x_1
POL(B(x1)) = (4)x_1
POL(a(x1)) = 1 + x_1
POL(A(x1)) = 4 + (4)x_1
POL(b(x1)) = 1/2 + x_1
a(x1) → b(b(x1))
b(b(x1)) → c(c(c(x1)))
a(b(b(x1))) → b(b(c(c(c(a(x1))))))
c(c(c(b(b(x1))))) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
a(x1) → b(b(x1))
a(b(b(x1))) → b(b(c(c(c(a(x1))))))
b(b(x1)) → c(c(c(x1)))
c(c(c(b(b(x1))))) → a(x1)