a(x, y) → b(x, b(0, c(y)))
c(b(y, c(x))) → c(c(b(a(0, 0), y)))
b(y, 0) → y
↳ QTRS
↳ DependencyPairsProof
a(x, y) → b(x, b(0, c(y)))
c(b(y, c(x))) → c(c(b(a(0, 0), y)))
b(y, 0) → y
C(b(y, c(x))) → A(0, 0)
C(b(y, c(x))) → C(c(b(a(0, 0), y)))
A(x, y) → C(y)
C(b(y, c(x))) → B(a(0, 0), y)
C(b(y, c(x))) → C(b(a(0, 0), y))
A(x, y) → B(0, c(y))
A(x, y) → B(x, b(0, c(y)))
a(x, y) → b(x, b(0, c(y)))
c(b(y, c(x))) → c(c(b(a(0, 0), y)))
b(y, 0) → y
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
C(b(y, c(x))) → A(0, 0)
C(b(y, c(x))) → C(c(b(a(0, 0), y)))
A(x, y) → C(y)
C(b(y, c(x))) → B(a(0, 0), y)
C(b(y, c(x))) → C(b(a(0, 0), y))
A(x, y) → B(0, c(y))
A(x, y) → B(x, b(0, c(y)))
a(x, y) → b(x, b(0, c(y)))
c(b(y, c(x))) → c(c(b(a(0, 0), y)))
b(y, 0) → y
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
C(b(y, c(x))) → A(0, 0)
C(b(y, c(x))) → C(c(b(a(0, 0), y)))
A(x, y) → C(y)
C(b(y, c(x))) → C(b(a(0, 0), y))
a(x, y) → b(x, b(0, c(y)))
c(b(y, c(x))) → c(c(b(a(0, 0), y)))
b(y, 0) → y
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
C(b(y, c(x))) → A(0, 0)
Used ordering: Polynomial interpretation [25,35]:
C(b(y, c(x))) → C(c(b(a(0, 0), y)))
A(x, y) → C(y)
C(b(y, c(x))) → C(b(a(0, 0), y))
The value of delta used in the strict ordering is 4.
POL(C(x1)) = x_1
POL(c(x1)) = 4
POL(b(x1, x2)) = x_1 + x_2
POL(a(x1, x2)) = 4 + x_1
POL(A(x1, x2)) = (2)x_2
POL(0) = 0
a(x, y) → b(x, b(0, c(y)))
c(b(y, c(x))) → c(c(b(a(0, 0), y)))
b(y, 0) → y
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
C(b(y, c(x))) → C(c(b(a(0, 0), y)))
A(x, y) → C(y)
C(b(y, c(x))) → C(b(a(0, 0), y))
a(x, y) → b(x, b(0, c(y)))
c(b(y, c(x))) → c(c(b(a(0, 0), y)))
b(y, 0) → y
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
C(b(y, c(x))) → C(c(b(a(0, 0), y)))
C(b(y, c(x))) → C(b(a(0, 0), y))
a(x, y) → b(x, b(0, c(y)))
c(b(y, c(x))) → c(c(b(a(0, 0), y)))
b(y, 0) → y