b(b(x1)) → c(d(x1))
c(c(x1)) → d(d(d(x1)))
c(x1) → g(x1)
d(d(x1)) → c(f(x1))
d(d(d(x1))) → g(c(x1))
f(x1) → a(g(x1))
g(x1) → d(a(b(x1)))
g(g(x1)) → b(c(x1))
↳ QTRS
↳ DependencyPairsProof
b(b(x1)) → c(d(x1))
c(c(x1)) → d(d(d(x1)))
c(x1) → g(x1)
d(d(x1)) → c(f(x1))
d(d(d(x1))) → g(c(x1))
f(x1) → a(g(x1))
g(x1) → d(a(b(x1)))
g(g(x1)) → b(c(x1))
C(c(x1)) → D(d(d(x1)))
G(x1) → B(x1)
G(x1) → D(a(b(x1)))
G(g(x1)) → B(c(x1))
C(c(x1)) → D(x1)
G(g(x1)) → C(x1)
B(b(x1)) → C(d(x1))
C(c(x1)) → D(d(x1))
F(x1) → G(x1)
B(b(x1)) → D(x1)
C(x1) → G(x1)
D(d(x1)) → C(f(x1))
D(d(d(x1))) → G(c(x1))
D(d(x1)) → F(x1)
D(d(d(x1))) → C(x1)
b(b(x1)) → c(d(x1))
c(c(x1)) → d(d(d(x1)))
c(x1) → g(x1)
d(d(x1)) → c(f(x1))
d(d(d(x1))) → g(c(x1))
f(x1) → a(g(x1))
g(x1) → d(a(b(x1)))
g(g(x1)) → b(c(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
C(c(x1)) → D(d(d(x1)))
G(x1) → B(x1)
G(x1) → D(a(b(x1)))
G(g(x1)) → B(c(x1))
C(c(x1)) → D(x1)
G(g(x1)) → C(x1)
B(b(x1)) → C(d(x1))
C(c(x1)) → D(d(x1))
F(x1) → G(x1)
B(b(x1)) → D(x1)
C(x1) → G(x1)
D(d(x1)) → C(f(x1))
D(d(d(x1))) → G(c(x1))
D(d(x1)) → F(x1)
D(d(d(x1))) → C(x1)
b(b(x1)) → c(d(x1))
c(c(x1)) → d(d(d(x1)))
c(x1) → g(x1)
d(d(x1)) → c(f(x1))
d(d(d(x1))) → g(c(x1))
f(x1) → a(g(x1))
g(x1) → d(a(b(x1)))
g(g(x1)) → b(c(x1))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
C(c(x1)) → D(d(d(x1)))
G(x1) → B(x1)
G(g(x1)) → B(c(x1))
C(c(x1)) → D(x1)
G(g(x1)) → C(x1)
B(b(x1)) → C(d(x1))
C(c(x1)) → D(d(x1))
F(x1) → G(x1)
B(b(x1)) → D(x1)
D(d(x1)) → C(f(x1))
D(d(d(x1))) → G(c(x1))
C(x1) → G(x1)
D(d(x1)) → F(x1)
D(d(d(x1))) → C(x1)
b(b(x1)) → c(d(x1))
c(c(x1)) → d(d(d(x1)))
c(x1) → g(x1)
d(d(x1)) → c(f(x1))
d(d(d(x1))) → g(c(x1))
f(x1) → a(g(x1))
g(x1) → d(a(b(x1)))
g(g(x1)) → b(c(x1))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(c(x1)) → D(x1)
G(g(x1)) → C(x1)
B(b(x1)) → C(d(x1))
C(c(x1)) → D(d(x1))
F(x1) → G(x1)
B(b(x1)) → D(x1)
D(d(x1)) → C(f(x1))
D(d(d(x1))) → G(c(x1))
C(x1) → G(x1)
D(d(x1)) → F(x1)
D(d(d(x1))) → C(x1)
Used ordering: Polynomial interpretation [25,35]:
C(c(x1)) → D(d(d(x1)))
G(x1) → B(x1)
G(g(x1)) → B(c(x1))
The value of delta used in the strict ordering is 1/4.
POL(C(x1)) = 2 + (2)x_1
POL(c(x1)) = 3 + x_1
POL(f(x1)) = 1/4 + (1/4)x_1
POL(D(x1)) = (2)x_1
POL(B(x1)) = 5/4 + (2)x_1
POL(g(x1)) = 3 + x_1
POL(a(x1)) = 0
POL(G(x1)) = 5/4 + (2)x_1
POL(d(x1)) = 2 + x_1
POL(b(x1)) = 5/2 + x_1
POL(F(x1)) = 2 + (2)x_1
b(b(x1)) → c(d(x1))
d(d(d(x1))) → g(c(x1))
c(c(x1)) → d(d(d(x1)))
c(x1) → g(x1)
g(g(x1)) → b(c(x1))
d(d(x1)) → c(f(x1))
f(x1) → a(g(x1))
g(x1) → d(a(b(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
C(c(x1)) → D(d(d(x1)))
G(x1) → B(x1)
G(g(x1)) → B(c(x1))
b(b(x1)) → c(d(x1))
c(c(x1)) → d(d(d(x1)))
c(x1) → g(x1)
d(d(x1)) → c(f(x1))
d(d(d(x1))) → g(c(x1))
f(x1) → a(g(x1))
g(x1) → d(a(b(x1)))
g(g(x1)) → b(c(x1))