a(c(a(x1))) → c(a(c(x1)))
a(a(b(x1))) → a(d(b(x1)))
a(b(x1)) → b(a(a(x1)))
d(d(x1)) → a(d(b(x1)))
b(b(x1)) → b(c(x1))
a(d(c(x1))) → c(a(x1))
b(c(x1)) → a(a(a(x1)))
↳ QTRS
↳ DependencyPairsProof
a(c(a(x1))) → c(a(c(x1)))
a(a(b(x1))) → a(d(b(x1)))
a(b(x1)) → b(a(a(x1)))
d(d(x1)) → a(d(b(x1)))
b(b(x1)) → b(c(x1))
a(d(c(x1))) → c(a(x1))
b(c(x1)) → a(a(a(x1)))
A(a(b(x1))) → D(b(x1))
B(b(x1)) → B(c(x1))
D(d(x1)) → B(x1)
A(a(b(x1))) → A(d(b(x1)))
D(d(x1)) → A(d(b(x1)))
B(c(x1)) → A(a(x1))
A(b(x1)) → A(x1)
B(c(x1)) → A(x1)
A(c(a(x1))) → A(c(x1))
B(c(x1)) → A(a(a(x1)))
A(b(x1)) → B(a(a(x1)))
A(b(x1)) → A(a(x1))
D(d(x1)) → D(b(x1))
A(d(c(x1))) → A(x1)
a(c(a(x1))) → c(a(c(x1)))
a(a(b(x1))) → a(d(b(x1)))
a(b(x1)) → b(a(a(x1)))
d(d(x1)) → a(d(b(x1)))
b(b(x1)) → b(c(x1))
a(d(c(x1))) → c(a(x1))
b(c(x1)) → a(a(a(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
A(a(b(x1))) → D(b(x1))
B(b(x1)) → B(c(x1))
D(d(x1)) → B(x1)
A(a(b(x1))) → A(d(b(x1)))
D(d(x1)) → A(d(b(x1)))
B(c(x1)) → A(a(x1))
A(b(x1)) → A(x1)
B(c(x1)) → A(x1)
A(c(a(x1))) → A(c(x1))
B(c(x1)) → A(a(a(x1)))
A(b(x1)) → B(a(a(x1)))
A(b(x1)) → A(a(x1))
D(d(x1)) → D(b(x1))
A(d(c(x1))) → A(x1)
a(c(a(x1))) → c(a(c(x1)))
a(a(b(x1))) → a(d(b(x1)))
a(b(x1)) → b(a(a(x1)))
d(d(x1)) → a(d(b(x1)))
b(b(x1)) → b(c(x1))
a(d(c(x1))) → c(a(x1))
b(c(x1)) → a(a(a(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
A(c(a(x1))) → A(c(x1))
a(c(a(x1))) → c(a(c(x1)))
a(a(b(x1))) → a(d(b(x1)))
a(b(x1)) → b(a(a(x1)))
d(d(x1)) → a(d(b(x1)))
b(b(x1)) → b(c(x1))
a(d(c(x1))) → c(a(x1))
b(c(x1)) → a(a(a(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(c(a(x1))) → A(c(x1))
The value of delta used in the strict ordering is 1.
POL(c(x1)) = (2)x_1
POL(a(x1)) = 1/4 + (11/4)x_1
POL(A(x1)) = (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
a(c(a(x1))) → c(a(c(x1)))
a(a(b(x1))) → a(d(b(x1)))
a(b(x1)) → b(a(a(x1)))
d(d(x1)) → a(d(b(x1)))
b(b(x1)) → b(c(x1))
a(d(c(x1))) → c(a(x1))
b(c(x1)) → a(a(a(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
B(c(x1)) → A(x1)
B(b(x1)) → B(c(x1))
B(c(x1)) → A(a(a(x1)))
A(b(x1)) → B(a(a(x1)))
A(a(b(x1))) → A(d(b(x1)))
A(b(x1)) → A(a(x1))
B(c(x1)) → A(a(x1))
A(d(c(x1))) → A(x1)
A(b(x1)) → A(x1)
a(c(a(x1))) → c(a(c(x1)))
a(a(b(x1))) → a(d(b(x1)))
a(b(x1)) → b(a(a(x1)))
d(d(x1)) → a(d(b(x1)))
b(b(x1)) → b(c(x1))
a(d(c(x1))) → c(a(x1))
b(c(x1)) → a(a(a(x1)))