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