p(a(a(x0)), p(x1, p(a(x2), x3))) → p(x2, p(a(a(b(x1))), p(a(a(x0)), x3)))
↳ QTRS
↳ DependencyPairsProof
p(a(a(x0)), p(x1, p(a(x2), x3))) → p(x2, p(a(a(b(x1))), p(a(a(x0)), x3)))
P(a(a(x0)), p(x1, p(a(x2), x3))) → P(a(a(x0)), x3)
P(a(a(x0)), p(x1, p(a(x2), x3))) → P(a(a(b(x1))), p(a(a(x0)), x3))
P(a(a(x0)), p(x1, p(a(x2), x3))) → P(x2, p(a(a(b(x1))), p(a(a(x0)), x3)))
p(a(a(x0)), p(x1, p(a(x2), x3))) → p(x2, p(a(a(b(x1))), p(a(a(x0)), x3)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
P(a(a(x0)), p(x1, p(a(x2), x3))) → P(a(a(x0)), x3)
P(a(a(x0)), p(x1, p(a(x2), x3))) → P(a(a(b(x1))), p(a(a(x0)), x3))
P(a(a(x0)), p(x1, p(a(x2), x3))) → P(x2, p(a(a(b(x1))), p(a(a(x0)), x3)))
p(a(a(x0)), p(x1, p(a(x2), x3))) → p(x2, p(a(a(b(x1))), p(a(a(x0)), x3)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
P(a(a(x0)), p(x1, p(a(x2), x3))) → P(a(a(x0)), x3)
P(a(a(x0)), p(x1, p(a(x2), x3))) → P(a(a(b(x1))), p(a(a(x0)), x3))
Used ordering: Polynomial interpretation [25,35]:
P(a(a(x0)), p(x1, p(a(x2), x3))) → P(x2, p(a(a(b(x1))), p(a(a(x0)), x3)))
The value of delta used in the strict ordering is 1/1.
POL(P(x1, x2)) = (1/4)x_2
POL(a(x1)) = 0
POL(p(x1, x2)) = 2 + (2)x_2
POL(b(x1)) = 0
p(a(a(x0)), p(x1, p(a(x2), x3))) → p(x2, p(a(a(b(x1))), p(a(a(x0)), x3)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
P(a(a(x0)), p(x1, p(a(x2), x3))) → P(x2, p(a(a(b(x1))), p(a(a(x0)), x3)))
p(a(a(x0)), p(x1, p(a(x2), x3))) → p(x2, p(a(a(b(x1))), p(a(a(x0)), x3)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
P(a(a(x0)), p(x1, p(a(x2), x3))) → P(x2, p(a(a(b(x1))), p(a(a(x0)), x3)))
The value of delta used in the strict ordering is 3/2.
POL(P(x1, x2)) = (1/2)x_1 + (1/2)x_2
POL(a(x1)) = 2 + (4)x_1
POL(p(x1, x2)) = (1/2)x_1 + (1/2)x_2
POL(b(x1)) = 0
p(a(a(x0)), p(x1, p(a(x2), x3))) → p(x2, p(a(a(b(x1))), p(a(a(x0)), x3)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
p(a(a(x0)), p(x1, p(a(x2), x3))) → p(x2, p(a(a(b(x1))), p(a(a(x0)), x3)))