b(a(x1)) → b(b(x1))
b(a(b(x1))) → b(a(a(x1)))
a(a(a(x1))) → a(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
b(a(x1)) → b(b(x1))
b(a(b(x1))) → b(a(a(x1)))
a(a(a(x1))) → a(b(b(x1)))
B(a(b(x1))) → A(x1)
B(a(b(x1))) → A(a(x1))
A(a(a(x1))) → B(x1)
B(a(x1)) → B(b(x1))
A(a(a(x1))) → B(b(x1))
A(a(a(x1))) → A(b(b(x1)))
B(a(x1)) → B(x1)
B(a(b(x1))) → B(a(a(x1)))
b(a(x1)) → b(b(x1))
b(a(b(x1))) → b(a(a(x1)))
a(a(a(x1))) → a(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
B(a(b(x1))) → A(x1)
B(a(b(x1))) → A(a(x1))
A(a(a(x1))) → B(x1)
B(a(x1)) → B(b(x1))
A(a(a(x1))) → B(b(x1))
A(a(a(x1))) → A(b(b(x1)))
B(a(x1)) → B(x1)
B(a(b(x1))) → B(a(a(x1)))
b(a(x1)) → b(b(x1))
b(a(b(x1))) → b(a(a(x1)))
a(a(a(x1))) → a(b(b(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(a(b(x1))) → A(x1)
B(a(b(x1))) → A(a(x1))
A(a(a(x1))) → B(x1)
A(a(a(x1))) → B(b(x1))
B(a(x1)) → B(x1)
Used ordering: Polynomial interpretation [25,35]:
B(a(x1)) → B(b(x1))
A(a(a(x1))) → A(b(b(x1)))
B(a(b(x1))) → B(a(a(x1)))
The value of delta used in the strict ordering is 1/16.
POL(B(x1)) = 1/2 + (1/4)x_1
POL(a(x1)) = 1/4 + x_1
POL(A(x1)) = 1/2 + (1/4)x_1
POL(b(x1)) = 1/4 + x_1
b(a(x1)) → b(b(x1))
b(a(b(x1))) → b(a(a(x1)))
a(a(a(x1))) → a(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
B(a(x1)) → B(b(x1))
A(a(a(x1))) → A(b(b(x1)))
B(a(b(x1))) → B(a(a(x1)))
b(a(x1)) → b(b(x1))
b(a(b(x1))) → b(a(a(x1)))
a(a(a(x1))) → a(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
A(a(a(x1))) → A(b(b(x1)))
b(a(x1)) → b(b(x1))
b(a(b(x1))) → b(a(a(x1)))
a(a(a(x1))) → a(b(b(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(a(x1))) → A(b(b(x1)))
The value of delta used in the strict ordering is 13.
POL(a(x1)) = 4
POL(A(x1)) = (4)x_1
POL(b(x1)) = 3/4
b(a(x1)) → b(b(x1))
b(a(b(x1))) → b(a(a(x1)))
a(a(a(x1))) → a(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
b(a(x1)) → b(b(x1))
b(a(b(x1))) → b(a(a(x1)))
a(a(a(x1))) → a(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
B(a(x1)) → B(b(x1))
B(a(b(x1))) → B(a(a(x1)))
b(a(x1)) → b(b(x1))
b(a(b(x1))) → b(a(a(x1)))
a(a(a(x1))) → a(b(b(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
B(a(x1)) → B(b(x1))
Used ordering: Polynomial interpretation [25,35]:
B(a(b(x1))) → B(a(a(x1)))
The value of delta used in the strict ordering is 1.
POL(B(x1)) = (4)x_1
POL(a(x1)) = 1/2
POL(b(x1)) = 1/4
b(a(x1)) → b(b(x1))
b(a(b(x1))) → b(a(a(x1)))
a(a(a(x1))) → a(b(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
B(a(b(x1))) → B(a(a(x1)))
b(a(x1)) → b(b(x1))
b(a(b(x1))) → b(a(a(x1)))
a(a(a(x1))) → a(b(b(x1)))