a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
a(c(x1)) → c(a(b(x1)))
a(a(x1)) → a(d(d(d(x1))))
d(a(x1)) → d(d(c(x1)))
a(d(d(c(x1)))) → a(a(a(d(x1))))
e(e(f(f(x1)))) → f(f(f(e(e(x1)))))
e(x1) → a(x1)
b(d(x1)) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
a(c(x1)) → c(a(b(x1)))
a(a(x1)) → a(d(d(d(x1))))
d(a(x1)) → d(d(c(x1)))
a(d(d(c(x1)))) → a(a(a(d(x1))))
e(e(f(f(x1)))) → f(f(f(e(e(x1)))))
e(x1) → a(x1)
b(d(x1)) → d(d(x1))
D(a(x1)) → D(d(c(x1)))
A(a(x1)) → A(d(d(d(x1))))
A(b(x1)) → B(c(a(x1)))
B(d(x1)) → D(d(x1))
A(d(d(c(x1)))) → D(x1)
A(c(x1)) → B(x1)
A(b(x1)) → A(x1)
B(c(x1)) → B(b(x1))
E(x1) → A(x1)
D(a(x1)) → D(c(x1))
E(e(f(f(x1)))) → E(x1)
A(c(x1)) → A(b(x1))
A(d(d(c(x1)))) → A(d(x1))
A(a(x1)) → D(d(x1))
E(e(f(f(x1)))) → E(e(x1))
A(d(d(c(x1)))) → A(a(a(d(x1))))
A(a(x1)) → D(d(d(x1)))
A(a(x1)) → D(x1)
A(d(d(c(x1)))) → A(a(d(x1)))
B(c(x1)) → B(x1)
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
a(c(x1)) → c(a(b(x1)))
a(a(x1)) → a(d(d(d(x1))))
d(a(x1)) → d(d(c(x1)))
a(d(d(c(x1)))) → a(a(a(d(x1))))
e(e(f(f(x1)))) → f(f(f(e(e(x1)))))
e(x1) → a(x1)
b(d(x1)) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
D(a(x1)) → D(d(c(x1)))
A(a(x1)) → A(d(d(d(x1))))
A(b(x1)) → B(c(a(x1)))
B(d(x1)) → D(d(x1))
A(d(d(c(x1)))) → D(x1)
A(c(x1)) → B(x1)
A(b(x1)) → A(x1)
B(c(x1)) → B(b(x1))
E(x1) → A(x1)
D(a(x1)) → D(c(x1))
E(e(f(f(x1)))) → E(x1)
A(c(x1)) → A(b(x1))
A(d(d(c(x1)))) → A(d(x1))
A(a(x1)) → D(d(x1))
E(e(f(f(x1)))) → E(e(x1))
A(d(d(c(x1)))) → A(a(a(d(x1))))
A(a(x1)) → D(d(d(x1)))
A(a(x1)) → D(x1)
A(d(d(c(x1)))) → A(a(d(x1)))
B(c(x1)) → B(x1)
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
a(c(x1)) → c(a(b(x1)))
a(a(x1)) → a(d(d(d(x1))))
d(a(x1)) → d(d(c(x1)))
a(d(d(c(x1)))) → a(a(a(d(x1))))
e(e(f(f(x1)))) → f(f(f(e(e(x1)))))
e(x1) → a(x1)
b(d(x1)) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
B(c(x1)) → B(b(x1))
B(c(x1)) → B(x1)
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
a(c(x1)) → c(a(b(x1)))
a(a(x1)) → a(d(d(d(x1))))
d(a(x1)) → d(d(c(x1)))
a(d(d(c(x1)))) → a(a(a(d(x1))))
e(e(f(f(x1)))) → f(f(f(e(e(x1)))))
e(x1) → a(x1)
b(d(x1)) → d(d(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(c(x1)) → B(b(x1))
B(c(x1)) → B(x1)
The value of delta used in the strict ordering is 2.
POL(c(x1)) = 4 + (2)x_1
POL(B(x1)) = (1/2)x_1
POL(a(x1)) = 9/4 + (2)x_1
POL(b(x1)) = x_1
POL(d(x1)) = (1/4)x_1
b(c(x1)) → c(b(b(x1)))
d(a(x1)) → d(d(c(x1)))
b(d(x1)) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
a(c(x1)) → c(a(b(x1)))
a(a(x1)) → a(d(d(d(x1))))
d(a(x1)) → d(d(c(x1)))
a(d(d(c(x1)))) → a(a(a(d(x1))))
e(e(f(f(x1)))) → f(f(f(e(e(x1)))))
e(x1) → a(x1)
b(d(x1)) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
A(a(x1)) → A(d(d(d(x1))))
A(c(x1)) → A(b(x1))
A(d(d(c(x1)))) → A(d(x1))
A(d(d(c(x1)))) → A(a(a(d(x1))))
A(d(d(c(x1)))) → A(a(d(x1)))
A(b(x1)) → A(x1)
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
a(c(x1)) → c(a(b(x1)))
a(a(x1)) → a(d(d(d(x1))))
d(a(x1)) → d(d(c(x1)))
a(d(d(c(x1)))) → a(a(a(d(x1))))
e(e(f(f(x1)))) → f(f(f(e(e(x1)))))
e(x1) → a(x1)
b(d(x1)) → d(d(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
E(e(f(f(x1)))) → E(x1)
E(e(f(f(x1)))) → E(e(x1))
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
a(c(x1)) → c(a(b(x1)))
a(a(x1)) → a(d(d(d(x1))))
d(a(x1)) → d(d(c(x1)))
a(d(d(c(x1)))) → a(a(a(d(x1))))
e(e(f(f(x1)))) → f(f(f(e(e(x1)))))
e(x1) → a(x1)
b(d(x1)) → d(d(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
E(e(f(f(x1)))) → E(x1)
Used ordering: Polynomial interpretation [25,35]:
E(e(f(f(x1)))) → E(e(x1))
The value of delta used in the strict ordering is 14.
POL(E(x1)) = (4)x_1
POL(f(x1)) = x_1
POL(c(x1)) = 0
POL(a(x1)) = (1/2)x_1
POL(e(x1)) = 7/2 + x_1
POL(b(x1)) = (2)x_1
POL(d(x1)) = 0
a(b(x1)) → b(c(a(x1)))
a(c(x1)) → c(a(b(x1)))
b(c(x1)) → c(b(b(x1)))
d(a(x1)) → d(d(c(x1)))
e(e(f(f(x1)))) → f(f(f(e(e(x1)))))
a(a(x1)) → a(d(d(d(x1))))
a(d(d(c(x1)))) → a(a(a(d(x1))))
e(x1) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
E(e(f(f(x1)))) → E(e(x1))
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
a(c(x1)) → c(a(b(x1)))
a(a(x1)) → a(d(d(d(x1))))
d(a(x1)) → d(d(c(x1)))
a(d(d(c(x1)))) → a(a(a(d(x1))))
e(e(f(f(x1)))) → f(f(f(e(e(x1)))))
e(x1) → a(x1)
b(d(x1)) → d(d(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
E(e(f(f(x1)))) → E(e(x1))
The value of delta used in the strict ordering is 32.
POL(E(x1)) = (2)x_1
POL(f(x1)) = 2 + x_1
POL(c(x1)) = 1/2
POL(a(x1)) = (4)x_1
POL(e(x1)) = (4)x_1
POL(b(x1)) = 1
POL(d(x1)) = 0
a(b(x1)) → b(c(a(x1)))
a(c(x1)) → c(a(b(x1)))
b(c(x1)) → c(b(b(x1)))
d(a(x1)) → d(d(c(x1)))
e(e(f(f(x1)))) → f(f(f(e(e(x1)))))
a(a(x1)) → a(d(d(d(x1))))
a(d(d(c(x1)))) → a(a(a(d(x1))))
e(x1) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
a(b(x1)) → b(c(a(x1)))
b(c(x1)) → c(b(b(x1)))
a(c(x1)) → c(a(b(x1)))
a(a(x1)) → a(d(d(d(x1))))
d(a(x1)) → d(d(c(x1)))
a(d(d(c(x1)))) → a(a(a(d(x1))))
e(e(f(f(x1)))) → f(f(f(e(e(x1)))))
e(x1) → a(x1)
b(d(x1)) → d(d(x1))