0 QTRS
↳1 DependencyPairsProof (⇔)
↳2 QDP
↳3 MRRProof (⇔)
↳4 QDP
↳5 DependencyGraphProof (⇔)
↳6 QDP
↳7 QDPOrderProof (⇔)
↳8 QDP
↳9 DependencyGraphProof (⇔)
↳10 TRUE
c(c(c(b(x)))) → a(1, b(c(x)))
b(c(b(c(x)))) → a(0, a(1, x))
a(0, x) → c(c(x))
a(1, x) → c(b(x))
C(c(c(b(x)))) → A(1, b(c(x)))
C(c(c(b(x)))) → B(c(x))
C(c(c(b(x)))) → C(x)
B(c(b(c(x)))) → A(0, a(1, x))
B(c(b(c(x)))) → A(1, x)
A(0, x) → C(c(x))
A(0, x) → C(x)
A(1, x) → C(b(x))
A(1, x) → B(x)
c(c(c(b(x)))) → a(1, b(c(x)))
b(c(b(c(x)))) → a(0, a(1, x))
a(0, x) → c(c(x))
a(1, x) → c(b(x))
C(c(c(b(x)))) → B(c(x))
C(c(c(b(x)))) → C(x)
B(c(b(c(x)))) → A(0, a(1, x))
B(c(b(c(x)))) → A(1, x)
A(0, x) → C(x)
A(1, x) → B(x)
POL(0) = 0
POL(1) = 0
POL(A(x1, x2)) = 2 + x1 + x2
POL(B(x1)) = 1 + x1
POL(C(x1)) = x1
POL(a(x1, x2)) = 4 + x1 + x2
POL(b(x1)) = 2 + x1
POL(c(x1)) = 2 + x1
C(c(c(b(x)))) → A(1, b(c(x)))
A(0, x) → C(c(x))
A(1, x) → C(b(x))
c(c(c(b(x)))) → a(1, b(c(x)))
b(c(b(c(x)))) → a(0, a(1, x))
a(0, x) → c(c(x))
a(1, x) → c(b(x))
A(1, x) → C(b(x))
C(c(c(b(x)))) → A(1, b(c(x)))
c(c(c(b(x)))) → a(1, b(c(x)))
b(c(b(c(x)))) → a(0, a(1, x))
a(0, x) → c(c(x))
a(1, x) → c(b(x))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(c(c(b(x)))) → A(1, b(c(x)))
The value of delta used in the strict ordering is 1/32.
POL(A(x1, x2)) = (3/4)x1 + (3/4)x2
POL(1) = 0
POL(C(x1)) = (1/2)x1
POL(b(x1)) = (3/2)x1
POL(c(x1)) = 1/4 + (3/2)x1
POL(a(x1, x2)) = 1/4 + (1/4)x1 + (9/4)x2
POL(0) = 3/2
a(0, x) → c(c(x))
b(c(b(c(x)))) → a(0, a(1, x))
a(1, x) → c(b(x))
c(c(c(b(x)))) → a(1, b(c(x)))
A(1, x) → C(b(x))
c(c(c(b(x)))) → a(1, b(c(x)))
b(c(b(c(x)))) → a(0, a(1, x))
a(0, x) → c(c(x))
a(1, x) → c(b(x))