del(.(x, .(y, z))) → f(=(x, y), x, y, z)
f(true, x, y, z) → del(.(y, z))
f(false, x, y, z) → .(x, del(.(y, z)))
=(nil, nil) → true
=(.(x, y), nil) → false
=(nil, .(y, z)) → false
=(.(x, y), .(u, v)) → and(=(x, u), =(y, v))
↳ QTRS
↳ DependencyPairsProof
del(.(x, .(y, z))) → f(=(x, y), x, y, z)
f(true, x, y, z) → del(.(y, z))
f(false, x, y, z) → .(x, del(.(y, z)))
=(nil, nil) → true
=(.(x, y), nil) → false
=(nil, .(y, z)) → false
=(.(x, y), .(u, v)) → and(=(x, u), =(y, v))
F(false, x, y, z) → DEL(.(y, z))
=1(.(x, y), .(u, v)) → =1(x, u)
DEL(.(x, .(y, z))) → =1(x, y)
F(true, x, y, z) → DEL(.(y, z))
=1(.(x, y), .(u, v)) → =1(y, v)
DEL(.(x, .(y, z))) → F(=(x, y), x, y, z)
del(.(x, .(y, z))) → f(=(x, y), x, y, z)
f(true, x, y, z) → del(.(y, z))
f(false, x, y, z) → .(x, del(.(y, z)))
=(nil, nil) → true
=(.(x, y), nil) → false
=(nil, .(y, z)) → false
=(.(x, y), .(u, v)) → and(=(x, u), =(y, v))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
F(false, x, y, z) → DEL(.(y, z))
=1(.(x, y), .(u, v)) → =1(x, u)
DEL(.(x, .(y, z))) → =1(x, y)
F(true, x, y, z) → DEL(.(y, z))
=1(.(x, y), .(u, v)) → =1(y, v)
DEL(.(x, .(y, z))) → F(=(x, y), x, y, z)
del(.(x, .(y, z))) → f(=(x, y), x, y, z)
f(true, x, y, z) → del(.(y, z))
f(false, x, y, z) → .(x, del(.(y, z)))
=(nil, nil) → true
=(.(x, y), nil) → false
=(nil, .(y, z)) → false
=(.(x, y), .(u, v)) → and(=(x, u), =(y, v))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
F(false, x, y, z) → DEL(.(y, z))
F(true, x, y, z) → DEL(.(y, z))
DEL(.(x, .(y, z))) → F(=(x, y), x, y, z)
del(.(x, .(y, z))) → f(=(x, y), x, y, z)
f(true, x, y, z) → del(.(y, z))
f(false, x, y, z) → .(x, del(.(y, z)))
=(nil, nil) → true
=(.(x, y), nil) → false
=(nil, .(y, z)) → false
=(.(x, y), .(u, v)) → and(=(x, u), =(y, v))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
DEL(.(x, .(y, z))) → F(=(x, y), x, y, z)
Used ordering: Polynomial interpretation [25,35]:
F(false, x, y, z) → DEL(.(y, z))
F(true, x, y, z) → DEL(.(y, z))
The value of delta used in the strict ordering is 8.
POL(F(x1, x2, x3, x4)) = 2 + x_2 + (4)x_3 + (4)x_4
POL(v) = 3
POL(=(x1, x2)) = 0
POL(u) = 1
POL(DEL(x1)) = x_1
POL(true) = 1
POL(false) = 0
POL(and(x1, x2)) = 2 + (4)x_1 + x_2
POL(.(x1, x2)) = 2 + x_1 + (4)x_2
POL(nil) = 1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
F(false, x, y, z) → DEL(.(y, z))
F(true, x, y, z) → DEL(.(y, z))
del(.(x, .(y, z))) → f(=(x, y), x, y, z)
f(true, x, y, z) → del(.(y, z))
f(false, x, y, z) → .(x, del(.(y, z)))
=(nil, nil) → true
=(.(x, y), nil) → false
=(nil, .(y, z)) → false
=(.(x, y), .(u, v)) → and(=(x, u), =(y, v))