g(h(x1)) → g(f(s(x1)))
f(s(s(s(x1)))) → h(f(s(h(x1))))
f(h(x1)) → h(f(s(h(x1))))
h(x1) → x1
f(f(s(s(x1)))) → s(s(s(f(f(x1)))))
b(a(x1)) → a(b(x1))
a(a(a(x1))) → b(a(a(b(x1))))
b(b(b(b(x1)))) → a(x1)
↳ QTRS
↳ DependencyPairsProof
g(h(x1)) → g(f(s(x1)))
f(s(s(s(x1)))) → h(f(s(h(x1))))
f(h(x1)) → h(f(s(h(x1))))
h(x1) → x1
f(f(s(s(x1)))) → s(s(s(f(f(x1)))))
b(a(x1)) → a(b(x1))
a(a(a(x1))) → b(a(a(b(x1))))
b(b(b(b(x1)))) → a(x1)
A(a(a(x1))) → B(x1)
F(h(x1)) → F(s(h(x1)))
B(a(x1)) → A(b(x1))
F(s(s(s(x1)))) → F(s(h(x1)))
F(s(s(s(x1)))) → H(x1)
B(b(b(b(x1)))) → A(x1)
G(h(x1)) → G(f(s(x1)))
G(h(x1)) → F(s(x1))
F(s(s(s(x1)))) → H(f(s(h(x1))))
B(a(x1)) → B(x1)
F(h(x1)) → H(f(s(h(x1))))
A(a(a(x1))) → B(a(a(b(x1))))
F(f(s(s(x1)))) → F(f(x1))
A(a(a(x1))) → A(a(b(x1)))
A(a(a(x1))) → A(b(x1))
F(f(s(s(x1)))) → F(x1)
g(h(x1)) → g(f(s(x1)))
f(s(s(s(x1)))) → h(f(s(h(x1))))
f(h(x1)) → h(f(s(h(x1))))
h(x1) → x1
f(f(s(s(x1)))) → s(s(s(f(f(x1)))))
b(a(x1)) → a(b(x1))
a(a(a(x1))) → b(a(a(b(x1))))
b(b(b(b(x1)))) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
A(a(a(x1))) → B(x1)
F(h(x1)) → F(s(h(x1)))
B(a(x1)) → A(b(x1))
F(s(s(s(x1)))) → F(s(h(x1)))
F(s(s(s(x1)))) → H(x1)
B(b(b(b(x1)))) → A(x1)
G(h(x1)) → G(f(s(x1)))
G(h(x1)) → F(s(x1))
F(s(s(s(x1)))) → H(f(s(h(x1))))
B(a(x1)) → B(x1)
F(h(x1)) → H(f(s(h(x1))))
A(a(a(x1))) → B(a(a(b(x1))))
F(f(s(s(x1)))) → F(f(x1))
A(a(a(x1))) → A(a(b(x1)))
A(a(a(x1))) → A(b(x1))
F(f(s(s(x1)))) → F(x1)
g(h(x1)) → g(f(s(x1)))
f(s(s(s(x1)))) → h(f(s(h(x1))))
f(h(x1)) → h(f(s(h(x1))))
h(x1) → x1
f(f(s(s(x1)))) → s(s(s(f(f(x1)))))
b(a(x1)) → a(b(x1))
a(a(a(x1))) → b(a(a(b(x1))))
b(b(b(b(x1)))) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
A(a(a(x1))) → B(x1)
B(a(x1)) → A(b(x1))
A(a(a(x1))) → B(a(a(b(x1))))
A(a(a(x1))) → A(a(b(x1)))
B(b(b(b(x1)))) → A(x1)
A(a(a(x1))) → A(b(x1))
B(a(x1)) → B(x1)
g(h(x1)) → g(f(s(x1)))
f(s(s(s(x1)))) → h(f(s(h(x1))))
f(h(x1)) → h(f(s(h(x1))))
h(x1) → x1
f(f(s(s(x1)))) → s(s(s(f(f(x1)))))
b(a(x1)) → a(b(x1))
a(a(a(x1))) → b(a(a(b(x1))))
b(b(b(b(x1)))) → a(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
A(a(a(x1))) → B(x1)
B(a(x1)) → A(b(x1))
A(a(a(x1))) → B(a(a(b(x1))))
A(a(a(x1))) → A(a(b(x1)))
B(b(b(b(x1)))) → A(x1)
A(a(a(x1))) → A(b(x1))
B(a(x1)) → B(x1)
The value of delta used in the strict ordering is 5/4.
POL(B(x1)) = 1/4 + x_1
POL(a(x1)) = 3/2 + (4)x_1
POL(A(x1)) = (2)x_1
POL(b(x1)) = 1/4 + (3/2)x_1
b(a(x1)) → a(b(x1))
b(b(b(b(x1)))) → a(x1)
a(a(a(x1))) → b(a(a(b(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
↳ QDP
g(h(x1)) → g(f(s(x1)))
f(s(s(s(x1)))) → h(f(s(h(x1))))
f(h(x1)) → h(f(s(h(x1))))
h(x1) → x1
f(f(s(s(x1)))) → s(s(s(f(f(x1)))))
b(a(x1)) → a(b(x1))
a(a(a(x1))) → b(a(a(b(x1))))
b(b(b(b(x1)))) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
F(s(s(s(x1)))) → F(s(h(x1)))
g(h(x1)) → g(f(s(x1)))
f(s(s(s(x1)))) → h(f(s(h(x1))))
f(h(x1)) → h(f(s(h(x1))))
h(x1) → x1
f(f(s(s(x1)))) → s(s(s(f(f(x1)))))
b(a(x1)) → a(b(x1))
a(a(a(x1))) → b(a(a(b(x1))))
b(b(b(b(x1)))) → a(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(s(s(s(x1)))) → F(s(h(x1)))
The value of delta used in the strict ordering is 195/4.
POL(h(x1)) = 2 + (4)x_1
POL(s(x1)) = 4 + (13/4)x_1
POL(F(x1)) = x_1
h(x1) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
g(h(x1)) → g(f(s(x1)))
f(s(s(s(x1)))) → h(f(s(h(x1))))
f(h(x1)) → h(f(s(h(x1))))
h(x1) → x1
f(f(s(s(x1)))) → s(s(s(f(f(x1)))))
b(a(x1)) → a(b(x1))
a(a(a(x1))) → b(a(a(b(x1))))
b(b(b(b(x1)))) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
F(f(s(s(x1)))) → F(f(x1))
F(f(s(s(x1)))) → F(x1)
g(h(x1)) → g(f(s(x1)))
f(s(s(s(x1)))) → h(f(s(h(x1))))
f(h(x1)) → h(f(s(h(x1))))
h(x1) → x1
f(f(s(s(x1)))) → s(s(s(f(f(x1)))))
b(a(x1)) → a(b(x1))
a(a(a(x1))) → b(a(a(b(x1))))
b(b(b(b(x1)))) → a(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
F(f(s(s(x1)))) → F(x1)
Used ordering: Polynomial interpretation [25,35]:
F(f(s(s(x1)))) → F(f(x1))
The value of delta used in the strict ordering is 1/16.
POL(f(x1)) = 1/4 + x_1
POL(h(x1)) = x_1
POL(s(x1)) = x_1
POL(F(x1)) = (1/4)x_1
f(h(x1)) → h(f(s(h(x1))))
f(s(s(s(x1)))) → h(f(s(h(x1))))
f(f(s(s(x1)))) → s(s(s(f(f(x1)))))
h(x1) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
F(f(s(s(x1)))) → F(f(x1))
g(h(x1)) → g(f(s(x1)))
f(s(s(s(x1)))) → h(f(s(h(x1))))
f(h(x1)) → h(f(s(h(x1))))
h(x1) → x1
f(f(s(s(x1)))) → s(s(s(f(f(x1)))))
b(a(x1)) → a(b(x1))
a(a(a(x1))) → b(a(a(b(x1))))
b(b(b(b(x1)))) → a(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
G(h(x1)) → G(f(s(x1)))
g(h(x1)) → g(f(s(x1)))
f(s(s(s(x1)))) → h(f(s(h(x1))))
f(h(x1)) → h(f(s(h(x1))))
h(x1) → x1
f(f(s(s(x1)))) → s(s(s(f(f(x1)))))
b(a(x1)) → a(b(x1))
a(a(a(x1))) → b(a(a(b(x1))))
b(b(b(b(x1)))) → a(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
G(h(x1)) → G(f(s(x1)))
The value of delta used in the strict ordering is 3/64.
POL(f(x1)) = (1/4)x_1
POL(h(x1)) = 1/2 + x_1
POL(G(x1)) = (1/4)x_1
POL(s(x1)) = 5/4 + x_1
f(s(s(s(x1)))) → h(f(s(h(x1))))
h(x1) → x1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
g(h(x1)) → g(f(s(x1)))
f(s(s(s(x1)))) → h(f(s(h(x1))))
f(h(x1)) → h(f(s(h(x1))))
h(x1) → x1
f(f(s(s(x1)))) → s(s(s(f(f(x1)))))
b(a(x1)) → a(b(x1))
a(a(a(x1))) → b(a(a(b(x1))))
b(b(b(b(x1)))) → a(x1)