r1(a(x1)) → a(a(a(r1(x1))))
r2(a(x1)) → a(a(a(r2(x1))))
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
r1(b(x1)) → l1(b(x1))
r2(b(x1)) → l2(a(b(x1)))
b(l1(x1)) → b(r2(x1))
b(l2(x1)) → b(r1(x1))
a(a(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
r1(a(x1)) → a(a(a(r1(x1))))
r2(a(x1)) → a(a(a(r2(x1))))
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
r1(b(x1)) → l1(b(x1))
r2(b(x1)) → l2(a(b(x1)))
b(l1(x1)) → b(r2(x1))
b(l2(x1)) → b(r1(x1))
a(a(x1)) → x1
R2(a(x1)) → A(a(a(r2(x1))))
B(l2(x1)) → R1(x1)
A(l1(x1)) → A(a(x1))
R2(b(x1)) → A(b(x1))
R2(a(x1)) → R2(x1)
A(a(l2(x1))) → A(x1)
B(l1(x1)) → R2(x1)
A(l1(x1)) → A(x1)
R2(a(x1)) → A(r2(x1))
R2(a(x1)) → A(a(r2(x1)))
R1(a(x1)) → A(a(a(r1(x1))))
R1(a(x1)) → A(r1(x1))
R1(a(x1)) → A(a(r1(x1)))
B(l2(x1)) → B(r1(x1))
B(l1(x1)) → B(r2(x1))
R1(a(x1)) → R1(x1)
A(l1(x1)) → A(a(a(x1)))
A(a(l2(x1))) → A(a(x1))
r1(a(x1)) → a(a(a(r1(x1))))
r2(a(x1)) → a(a(a(r2(x1))))
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
r1(b(x1)) → l1(b(x1))
r2(b(x1)) → l2(a(b(x1)))
b(l1(x1)) → b(r2(x1))
b(l2(x1)) → b(r1(x1))
a(a(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
R2(a(x1)) → A(a(a(r2(x1))))
B(l2(x1)) → R1(x1)
A(l1(x1)) → A(a(x1))
R2(b(x1)) → A(b(x1))
R2(a(x1)) → R2(x1)
A(a(l2(x1))) → A(x1)
B(l1(x1)) → R2(x1)
A(l1(x1)) → A(x1)
R2(a(x1)) → A(r2(x1))
R2(a(x1)) → A(a(r2(x1)))
R1(a(x1)) → A(a(a(r1(x1))))
R1(a(x1)) → A(r1(x1))
R1(a(x1)) → A(a(r1(x1)))
B(l2(x1)) → B(r1(x1))
B(l1(x1)) → B(r2(x1))
R1(a(x1)) → R1(x1)
A(l1(x1)) → A(a(a(x1)))
A(a(l2(x1))) → A(a(x1))
r1(a(x1)) → a(a(a(r1(x1))))
r2(a(x1)) → a(a(a(r2(x1))))
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
r1(b(x1)) → l1(b(x1))
r2(b(x1)) → l2(a(b(x1)))
b(l1(x1)) → b(r2(x1))
b(l2(x1)) → b(r1(x1))
a(a(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
A(l1(x1)) → A(a(x1))
A(a(l2(x1))) → A(x1)
A(l1(x1)) → A(a(a(x1)))
A(a(l2(x1))) → A(a(x1))
A(l1(x1)) → A(x1)
r1(a(x1)) → a(a(a(r1(x1))))
r2(a(x1)) → a(a(a(r2(x1))))
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
r1(b(x1)) → l1(b(x1))
r2(b(x1)) → l2(a(b(x1)))
b(l1(x1)) → b(r2(x1))
b(l2(x1)) → b(r1(x1))
a(a(x1)) → x1
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(l1(x1)) → A(a(x1))
A(l1(x1)) → A(a(a(x1)))
A(l1(x1)) → A(x1)
Used ordering: Polynomial interpretation [25,35]:
A(a(l2(x1))) → A(x1)
A(a(l2(x1))) → A(a(x1))
The value of delta used in the strict ordering is 4.
POL(l2(x1)) = (2)x_1
POL(a(x1)) = x_1
POL(A(x1)) = x_1
POL(l1(x1)) = 4 + (4)x_1
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
a(a(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
A(a(l2(x1))) → A(x1)
A(a(l2(x1))) → A(a(x1))
r1(a(x1)) → a(a(a(r1(x1))))
r2(a(x1)) → a(a(a(r2(x1))))
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
r1(b(x1)) → l1(b(x1))
r2(b(x1)) → l2(a(b(x1)))
b(l1(x1)) → b(r2(x1))
b(l2(x1)) → b(r1(x1))
a(a(x1)) → x1
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(l2(x1))) → A(x1)
Used ordering: Polynomial interpretation [25,35]:
A(a(l2(x1))) → A(a(x1))
The value of delta used in the strict ordering is 2.
POL(l2(x1)) = x_1
POL(a(x1)) = 2 + x_1
POL(A(x1)) = x_1
POL(l1(x1)) = 2
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
a(a(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
A(a(l2(x1))) → A(a(x1))
r1(a(x1)) → a(a(a(r1(x1))))
r2(a(x1)) → a(a(a(r2(x1))))
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
r1(b(x1)) → l1(b(x1))
r2(b(x1)) → l2(a(b(x1)))
b(l1(x1)) → b(r2(x1))
b(l2(x1)) → b(r1(x1))
a(a(x1)) → x1
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(l2(x1))) → A(a(x1))
The value of delta used in the strict ordering is 2.
POL(l2(x1)) = 1/2 + (4)x_1
POL(a(x1)) = x_1
POL(A(x1)) = (4)x_1
POL(l1(x1)) = (4)x_1
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
a(a(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
↳ QDP
r1(a(x1)) → a(a(a(r1(x1))))
r2(a(x1)) → a(a(a(r2(x1))))
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
r1(b(x1)) → l1(b(x1))
r2(b(x1)) → l2(a(b(x1)))
b(l1(x1)) → b(r2(x1))
b(l2(x1)) → b(r1(x1))
a(a(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
R2(a(x1)) → R2(x1)
r1(a(x1)) → a(a(a(r1(x1))))
r2(a(x1)) → a(a(a(r2(x1))))
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
r1(b(x1)) → l1(b(x1))
r2(b(x1)) → l2(a(b(x1)))
b(l1(x1)) → b(r2(x1))
b(l2(x1)) → b(r1(x1))
a(a(x1)) → x1
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
R2(a(x1)) → R2(x1)
The value of delta used in the strict ordering is 1/16.
POL(R2(x1)) = (1/4)x_1
POL(a(x1)) = 1/4 + (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
r1(a(x1)) → a(a(a(r1(x1))))
r2(a(x1)) → a(a(a(r2(x1))))
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
r1(b(x1)) → l1(b(x1))
r2(b(x1)) → l2(a(b(x1)))
b(l1(x1)) → b(r2(x1))
b(l2(x1)) → b(r1(x1))
a(a(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
R1(a(x1)) → R1(x1)
r1(a(x1)) → a(a(a(r1(x1))))
r2(a(x1)) → a(a(a(r2(x1))))
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
r1(b(x1)) → l1(b(x1))
r2(b(x1)) → l2(a(b(x1)))
b(l1(x1)) → b(r2(x1))
b(l2(x1)) → b(r1(x1))
a(a(x1)) → x1
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
R1(a(x1)) → R1(x1)
The value of delta used in the strict ordering is 1/16.
POL(a(x1)) = 1/4 + (2)x_1
POL(R1(x1)) = (1/4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
r1(a(x1)) → a(a(a(r1(x1))))
r2(a(x1)) → a(a(a(r2(x1))))
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
r1(b(x1)) → l1(b(x1))
r2(b(x1)) → l2(a(b(x1)))
b(l1(x1)) → b(r2(x1))
b(l2(x1)) → b(r1(x1))
a(a(x1)) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
B(l1(x1)) → B(r2(x1))
B(l2(x1)) → B(r1(x1))
r1(a(x1)) → a(a(a(r1(x1))))
r2(a(x1)) → a(a(a(r2(x1))))
a(l1(x1)) → l1(a(a(a(x1))))
a(a(l2(x1))) → l2(a(a(x1)))
r1(b(x1)) → l1(b(x1))
r2(b(x1)) → l2(a(b(x1)))
b(l1(x1)) → b(r2(x1))
b(l2(x1)) → b(r1(x1))
a(a(x1)) → x1