a(b(b(x1))) → P(a(b(x1)))
a(P(x1)) → P(a(x(x1)))
a(x(x1)) → x(a(x1))
b(P(x1)) → b(Q(x1))
Q(x(x1)) → a(Q(x1))
Q(a(x1)) → b(b(a(x1)))
↳ QTRS
↳ DependencyPairsProof
a(b(b(x1))) → P(a(b(x1)))
a(P(x1)) → P(a(x(x1)))
a(x(x1)) → x(a(x1))
b(P(x1)) → b(Q(x1))
Q(x(x1)) → a(Q(x1))
Q(a(x1)) → b(b(a(x1)))
Q1(x(x1)) → A(Q(x1))
B(P(x1)) → B(Q(x1))
Q1(x(x1)) → Q1(x1)
A(x(x1)) → A(x1)
A(P(x1)) → A(x(x1))
Q1(a(x1)) → B(a(x1))
B(P(x1)) → Q1(x1)
Q1(a(x1)) → B(b(a(x1)))
A(b(b(x1))) → A(b(x1))
a(b(b(x1))) → P(a(b(x1)))
a(P(x1)) → P(a(x(x1)))
a(x(x1)) → x(a(x1))
b(P(x1)) → b(Q(x1))
Q(x(x1)) → a(Q(x1))
Q(a(x1)) → b(b(a(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
Q1(x(x1)) → A(Q(x1))
B(P(x1)) → B(Q(x1))
Q1(x(x1)) → Q1(x1)
A(x(x1)) → A(x1)
A(P(x1)) → A(x(x1))
Q1(a(x1)) → B(a(x1))
B(P(x1)) → Q1(x1)
Q1(a(x1)) → B(b(a(x1)))
A(b(b(x1))) → A(b(x1))
a(b(b(x1))) → P(a(b(x1)))
a(P(x1)) → P(a(x(x1)))
a(x(x1)) → x(a(x1))
b(P(x1)) → b(Q(x1))
Q(x(x1)) → a(Q(x1))
Q(a(x1)) → b(b(a(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
A(x(x1)) → A(x1)
A(P(x1)) → A(x(x1))
A(b(b(x1))) → A(b(x1))
a(b(b(x1))) → P(a(b(x1)))
a(P(x1)) → P(a(x(x1)))
a(x(x1)) → x(a(x1))
b(P(x1)) → b(Q(x1))
Q(x(x1)) → a(Q(x1))
Q(a(x1)) → b(b(a(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
B(P(x1)) → B(Q(x1))
Q1(x(x1)) → Q1(x1)
Q1(a(x1)) → B(a(x1))
B(P(x1)) → Q1(x1)
Q1(a(x1)) → B(b(a(x1)))
a(b(b(x1))) → P(a(b(x1)))
a(P(x1)) → P(a(x(x1)))
a(x(x1)) → x(a(x1))
b(P(x1)) → b(Q(x1))
Q(x(x1)) → a(Q(x1))
Q(a(x1)) → b(b(a(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
Q1(a(x1)) → B(b(a(x1)))
Used ordering: Polynomial interpretation [25,35]:
B(P(x1)) → B(Q(x1))
Q1(x(x1)) → Q1(x1)
Q1(a(x1)) → B(a(x1))
B(P(x1)) → Q1(x1)
The value of delta used in the strict ordering is 1/4.
POL(Q(x1)) = 1/4
POL(P(x1)) = 1/4
POL(x(x1)) = 0
POL(B(x1)) = x_1
POL(a(x1)) = 1/4
POL(b(x1)) = 0
POL(Q1(x1)) = 1/4
a(b(b(x1))) → P(a(b(x1)))
a(P(x1)) → P(a(x(x1)))
a(x(x1)) → x(a(x1))
b(P(x1)) → b(Q(x1))
Q(x(x1)) → a(Q(x1))
Q(a(x1)) → b(b(a(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
B(P(x1)) → B(Q(x1))
Q1(x(x1)) → Q1(x1)
B(P(x1)) → Q1(x1)
Q1(a(x1)) → B(a(x1))
a(b(b(x1))) → P(a(b(x1)))
a(P(x1)) → P(a(x(x1)))
a(x(x1)) → x(a(x1))
b(P(x1)) → b(Q(x1))
Q(x(x1)) → a(Q(x1))
Q(a(x1)) → b(b(a(x1)))