int(0, 0) → .(0, nil)
int(0, s(y)) → .(0, int(s(0), s(y)))
int(s(x), 0) → nil
int(s(x), s(y)) → int_list(int(x, y))
int_list(nil) → nil
int_list(.(x, y)) → .(s(x), int_list(y))
↳ QTRS
↳ DependencyPairsProof
int(0, 0) → .(0, nil)
int(0, s(y)) → .(0, int(s(0), s(y)))
int(s(x), 0) → nil
int(s(x), s(y)) → int_list(int(x, y))
int_list(nil) → nil
int_list(.(x, y)) → .(s(x), int_list(y))
INT(0, s(y)) → INT(s(0), s(y))
INT(s(x), s(y)) → INT(x, y)
INT_LIST(.(x, y)) → INT_LIST(y)
INT(s(x), s(y)) → INT_LIST(int(x, y))
int(0, 0) → .(0, nil)
int(0, s(y)) → .(0, int(s(0), s(y)))
int(s(x), 0) → nil
int(s(x), s(y)) → int_list(int(x, y))
int_list(nil) → nil
int_list(.(x, y)) → .(s(x), int_list(y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
INT(0, s(y)) → INT(s(0), s(y))
INT(s(x), s(y)) → INT(x, y)
INT_LIST(.(x, y)) → INT_LIST(y)
INT(s(x), s(y)) → INT_LIST(int(x, y))
int(0, 0) → .(0, nil)
int(0, s(y)) → .(0, int(s(0), s(y)))
int(s(x), 0) → nil
int(s(x), s(y)) → int_list(int(x, y))
int_list(nil) → nil
int_list(.(x, y)) → .(s(x), int_list(y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
INT_LIST(.(x, y)) → INT_LIST(y)
int(0, 0) → .(0, nil)
int(0, s(y)) → .(0, int(s(0), s(y)))
int(s(x), 0) → nil
int(s(x), s(y)) → int_list(int(x, y))
int_list(nil) → nil
int_list(.(x, y)) → .(s(x), int_list(y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
INT_LIST(.(x, y)) → INT_LIST(y)
The value of delta used in the strict ordering is 4.
POL(INT_LIST(x1)) = (4)x_1
POL(.(x1, x2)) = 1 + (4)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
int(0, 0) → .(0, nil)
int(0, s(y)) → .(0, int(s(0), s(y)))
int(s(x), 0) → nil
int(s(x), s(y)) → int_list(int(x, y))
int_list(nil) → nil
int_list(.(x, y)) → .(s(x), int_list(y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
INT(0, s(y)) → INT(s(0), s(y))
INT(s(x), s(y)) → INT(x, y)
int(0, 0) → .(0, nil)
int(0, s(y)) → .(0, int(s(0), s(y)))
int(s(x), 0) → nil
int(s(x), s(y)) → int_list(int(x, y))
int_list(nil) → nil
int_list(.(x, y)) → .(s(x), int_list(y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
INT(s(x), s(y)) → INT(x, y)
Used ordering: Polynomial interpretation [25,35]:
INT(0, s(y)) → INT(s(0), s(y))
The value of delta used in the strict ordering is 16.
POL(INT(x1, x2)) = (4)x_2
POL(s(x1)) = 4 + (2)x_1
POL(0) = 4
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
INT(0, s(y)) → INT(s(0), s(y))
int(0, 0) → .(0, nil)
int(0, s(y)) → .(0, int(s(0), s(y)))
int(s(x), 0) → nil
int(s(x), s(y)) → int_list(int(x, y))
int_list(nil) → nil
int_list(.(x, y)) → .(s(x), int_list(y))