0(q0(0(x1))) → 0(0(q0(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(1(x1))) → 0(1(q0(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
1(q1(1(x1))) → 1(1(q1(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
0(q1(h(x1))) → 0(0(q2(h(x1))))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q2(0(x1))) → 1(0(q2(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q4(1(x1))) → 1(1(q5(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
1(q5(1(x1))) → 0(1(q1(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q4(x1)) → h(0(q4(x1)))
h(q5(x1)) → h(0(q5(x1)))
↳ QTRS
↳ DependencyPairsProof
0(q0(0(x1))) → 0(0(q0(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(1(x1))) → 0(1(q0(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
1(q1(1(x1))) → 1(1(q1(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
0(q1(h(x1))) → 0(0(q2(h(x1))))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q2(0(x1))) → 1(0(q2(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q4(1(x1))) → 1(1(q5(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
1(q5(1(x1))) → 0(1(q1(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q4(x1)) → h(0(q4(x1)))
h(q5(x1)) → h(0(q5(x1)))
11(q0(0(x1))) → 01(q1(x1))
H(q3(x1)) → 01(q3(x1))
01(q1(0(x1))) → 01(q2(x1))
01(q3(x1)) → 01(x1)
11(q1(1(x1))) → 11(q1(x1))
11(q1(0(x1))) → 11(0(q1(x1)))
11(q5(0(x1))) → 01(0(q1(x1)))
01(q2(x1)) → 11(x1)
11(q2(0(x1))) → 01(q2(x1))
11(q2(h(x1))) → 01(q2(h(x1)))
01(q0(h(x1))) → 01(q0(h(x1)))
01(q0(h(x1))) → 01(0(q0(h(x1))))
11(q2(0(x1))) → 11(0(q2(x1)))
01(q1(1(x1))) → 01(1(q2(x1)))
H(q1(x1)) → H(0(q1(x1)))
11(q3(x1)) → 11(x1)
01(q0(1(x1))) → 11(q0(x1))
11(q2(h(x1))) → 11(0(q2(h(x1))))
11(q2(1(x1))) → 11(1(q2(x1)))
01(q0(0(x1))) → 01(q0(x1))
H(q5(x1)) → H(0(q5(x1)))
11(q5(h(x1))) → 01(q1(h(x1)))
01(q4(h(x1))) → 11(0(q5(h(x1))))
11(q0(1(x1))) → 01(1(q1(x1)))
11(q0(1(x1))) → 11(q1(x1))
11(q4(x1)) → 11(x1)
11(q0(0(x1))) → 01(0(q1(x1)))
01(q1(h(x1))) → 01(0(q2(h(x1))))
11(q1(0(x1))) → 01(q1(x1))
H(q3(x1)) → H(0(q3(x1)))
H(q0(x1)) → 01(q0(x1))
01(q4(1(x1))) → 11(1(q5(x1)))
01(q0(1(x1))) → 01(1(q0(x1)))
H(q4(x1)) → H(0(q4(x1)))
H(q4(x1)) → 01(q4(x1))
11(q5(1(x1))) → 11(q1(x1))
11(q1(h(x1))) → 11(0(q1(h(x1))))
H(q2(x1)) → 01(q2(x1))
H(q1(x1)) → 01(q1(x1))
H(q0(x1)) → H(0(q0(x1)))
H(q5(x1)) → 01(q5(x1))
01(q4(0(x1))) → 11(0(q5(x1)))
11(q0(h(x1))) → 01(0(q1(h(x1))))
01(q1(1(x1))) → 11(q2(x1))
11(q5(0(x1))) → 01(q1(x1))
11(q0(h(x1))) → 01(q1(h(x1)))
11(q5(h(x1))) → 01(0(q1(h(x1))))
11(q5(1(x1))) → 01(1(q1(x1)))
01(q1(0(x1))) → 01(0(q2(x1)))
11(q2(1(x1))) → 11(q2(x1))
01(q4(h(x1))) → 01(q5(h(x1)))
11(q1(1(x1))) → 11(1(q1(x1)))
11(q1(h(x1))) → 01(q1(h(x1)))
01(q4(0(x1))) → 01(q5(x1))
01(q1(h(x1))) → 01(q2(h(x1)))
01(q4(1(x1))) → 11(q5(x1))
H(q2(x1)) → H(0(q2(x1)))
01(q0(0(x1))) → 01(0(q0(x1)))
0(q0(0(x1))) → 0(0(q0(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(1(x1))) → 0(1(q0(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
1(q1(1(x1))) → 1(1(q1(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
0(q1(h(x1))) → 0(0(q2(h(x1))))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q2(0(x1))) → 1(0(q2(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q4(1(x1))) → 1(1(q5(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
1(q5(1(x1))) → 0(1(q1(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q4(x1)) → h(0(q4(x1)))
h(q5(x1)) → h(0(q5(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
11(q0(0(x1))) → 01(q1(x1))
H(q3(x1)) → 01(q3(x1))
01(q1(0(x1))) → 01(q2(x1))
01(q3(x1)) → 01(x1)
11(q1(1(x1))) → 11(q1(x1))
11(q1(0(x1))) → 11(0(q1(x1)))
11(q5(0(x1))) → 01(0(q1(x1)))
01(q2(x1)) → 11(x1)
11(q2(0(x1))) → 01(q2(x1))
11(q2(h(x1))) → 01(q2(h(x1)))
01(q0(h(x1))) → 01(q0(h(x1)))
01(q0(h(x1))) → 01(0(q0(h(x1))))
11(q2(0(x1))) → 11(0(q2(x1)))
01(q1(1(x1))) → 01(1(q2(x1)))
H(q1(x1)) → H(0(q1(x1)))
11(q3(x1)) → 11(x1)
01(q0(1(x1))) → 11(q0(x1))
11(q2(h(x1))) → 11(0(q2(h(x1))))
11(q2(1(x1))) → 11(1(q2(x1)))
01(q0(0(x1))) → 01(q0(x1))
H(q5(x1)) → H(0(q5(x1)))
11(q5(h(x1))) → 01(q1(h(x1)))
01(q4(h(x1))) → 11(0(q5(h(x1))))
11(q0(1(x1))) → 01(1(q1(x1)))
11(q0(1(x1))) → 11(q1(x1))
11(q4(x1)) → 11(x1)
11(q0(0(x1))) → 01(0(q1(x1)))
01(q1(h(x1))) → 01(0(q2(h(x1))))
11(q1(0(x1))) → 01(q1(x1))
H(q3(x1)) → H(0(q3(x1)))
H(q0(x1)) → 01(q0(x1))
01(q4(1(x1))) → 11(1(q5(x1)))
01(q0(1(x1))) → 01(1(q0(x1)))
H(q4(x1)) → H(0(q4(x1)))
H(q4(x1)) → 01(q4(x1))
11(q5(1(x1))) → 11(q1(x1))
11(q1(h(x1))) → 11(0(q1(h(x1))))
H(q2(x1)) → 01(q2(x1))
H(q1(x1)) → 01(q1(x1))
H(q0(x1)) → H(0(q0(x1)))
H(q5(x1)) → 01(q5(x1))
01(q4(0(x1))) → 11(0(q5(x1)))
11(q0(h(x1))) → 01(0(q1(h(x1))))
01(q1(1(x1))) → 11(q2(x1))
11(q5(0(x1))) → 01(q1(x1))
11(q0(h(x1))) → 01(q1(h(x1)))
11(q5(h(x1))) → 01(0(q1(h(x1))))
11(q5(1(x1))) → 01(1(q1(x1)))
01(q1(0(x1))) → 01(0(q2(x1)))
11(q2(1(x1))) → 11(q2(x1))
01(q4(h(x1))) → 01(q5(h(x1)))
11(q1(1(x1))) → 11(1(q1(x1)))
11(q1(h(x1))) → 01(q1(h(x1)))
01(q4(0(x1))) → 01(q5(x1))
01(q1(h(x1))) → 01(q2(h(x1)))
01(q4(1(x1))) → 11(q5(x1))
H(q2(x1)) → H(0(q2(x1)))
01(q0(0(x1))) → 01(0(q0(x1)))
0(q0(0(x1))) → 0(0(q0(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(1(x1))) → 0(1(q0(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
1(q1(1(x1))) → 1(1(q1(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
0(q1(h(x1))) → 0(0(q2(h(x1))))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q2(0(x1))) → 1(0(q2(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q4(1(x1))) → 1(1(q5(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
1(q5(1(x1))) → 0(1(q1(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q4(x1)) → h(0(q4(x1)))
h(q5(x1)) → h(0(q5(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
11(q1(0(x1))) → 01(q1(x1))
11(q0(0(x1))) → 01(q1(x1))
01(q4(1(x1))) → 11(1(q5(x1)))
01(q0(1(x1))) → 01(1(q0(x1)))
01(q1(0(x1))) → 01(q2(x1))
01(q3(x1)) → 01(x1)
11(q1(1(x1))) → 11(q1(x1))
11(q5(1(x1))) → 11(q1(x1))
11(q5(0(x1))) → 01(0(q1(x1)))
11(q1(0(x1))) → 11(0(q1(x1)))
11(q1(h(x1))) → 11(0(q1(h(x1))))
01(q2(x1)) → 11(x1)
11(q2(0(x1))) → 01(q2(x1))
11(q2(h(x1))) → 01(q2(h(x1)))
01(q0(h(x1))) → 01(q0(h(x1)))
11(q0(h(x1))) → 01(0(q1(h(x1))))
01(q0(h(x1))) → 01(0(q0(h(x1))))
11(q5(0(x1))) → 01(q1(x1))
01(q1(1(x1))) → 11(q2(x1))
11(q2(0(x1))) → 11(0(q2(x1)))
01(q1(1(x1))) → 01(1(q2(x1)))
11(q5(h(x1))) → 01(0(q1(h(x1))))
11(q0(h(x1))) → 01(q1(h(x1)))
11(q5(1(x1))) → 01(1(q1(x1)))
11(q3(x1)) → 11(x1)
01(q0(1(x1))) → 11(q0(x1))
01(q1(0(x1))) → 01(0(q2(x1)))
11(q2(1(x1))) → 11(q2(x1))
11(q2(h(x1))) → 11(0(q2(h(x1))))
11(q1(1(x1))) → 11(1(q1(x1)))
11(q1(h(x1))) → 01(q1(h(x1)))
11(q2(1(x1))) → 11(1(q2(x1)))
01(q0(0(x1))) → 01(q0(x1))
11(q5(h(x1))) → 01(q1(h(x1)))
01(q4(1(x1))) → 11(q5(x1))
01(q1(h(x1))) → 01(q2(h(x1)))
11(q0(1(x1))) → 01(1(q1(x1)))
11(q4(x1)) → 11(x1)
11(q0(1(x1))) → 11(q1(x1))
11(q0(0(x1))) → 01(0(q1(x1)))
01(q1(h(x1))) → 01(0(q2(h(x1))))
01(q0(0(x1))) → 01(0(q0(x1)))
0(q0(0(x1))) → 0(0(q0(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(1(x1))) → 0(1(q0(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
1(q1(1(x1))) → 1(1(q1(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
0(q1(h(x1))) → 0(0(q2(h(x1))))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q2(0(x1))) → 1(0(q2(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q4(1(x1))) → 1(1(q5(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
1(q5(1(x1))) → 0(1(q1(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q4(x1)) → h(0(q4(x1)))
h(q5(x1)) → h(0(q5(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
01(q0(1(x1))) → 01(1(q0(x1)))
01(q0(h(x1))) → 01(0(q0(h(x1))))
01(q0(1(x1))) → 11(q0(x1))
01(q0(0(x1))) → 01(0(q0(x1)))
Used ordering: Polynomial interpretation [25,35]:
11(q1(0(x1))) → 01(q1(x1))
11(q0(0(x1))) → 01(q1(x1))
01(q4(1(x1))) → 11(1(q5(x1)))
01(q1(0(x1))) → 01(q2(x1))
01(q3(x1)) → 01(x1)
11(q1(1(x1))) → 11(q1(x1))
11(q5(1(x1))) → 11(q1(x1))
11(q5(0(x1))) → 01(0(q1(x1)))
11(q1(0(x1))) → 11(0(q1(x1)))
11(q1(h(x1))) → 11(0(q1(h(x1))))
01(q2(x1)) → 11(x1)
11(q2(0(x1))) → 01(q2(x1))
11(q2(h(x1))) → 01(q2(h(x1)))
01(q0(h(x1))) → 01(q0(h(x1)))
11(q0(h(x1))) → 01(0(q1(h(x1))))
11(q5(0(x1))) → 01(q1(x1))
01(q1(1(x1))) → 11(q2(x1))
11(q2(0(x1))) → 11(0(q2(x1)))
01(q1(1(x1))) → 01(1(q2(x1)))
11(q5(h(x1))) → 01(0(q1(h(x1))))
11(q0(h(x1))) → 01(q1(h(x1)))
11(q5(1(x1))) → 01(1(q1(x1)))
11(q3(x1)) → 11(x1)
01(q1(0(x1))) → 01(0(q2(x1)))
11(q2(1(x1))) → 11(q2(x1))
11(q2(h(x1))) → 11(0(q2(h(x1))))
11(q1(1(x1))) → 11(1(q1(x1)))
11(q1(h(x1))) → 01(q1(h(x1)))
11(q2(1(x1))) → 11(1(q2(x1)))
01(q0(0(x1))) → 01(q0(x1))
11(q5(h(x1))) → 01(q1(h(x1)))
01(q4(1(x1))) → 11(q5(x1))
01(q1(h(x1))) → 01(q2(h(x1)))
11(q0(1(x1))) → 01(1(q1(x1)))
11(q4(x1)) → 11(x1)
11(q0(1(x1))) → 11(q1(x1))
11(q0(0(x1))) → 01(0(q1(x1)))
01(q1(h(x1))) → 01(0(q2(h(x1))))
The value of delta used in the strict ordering is 12.
POL(q1(x1)) = 0
POL(11(x1)) = 0
POL(1(x1)) = 0
POL(01(x1)) = (4)x_1
POL(q0(x1)) = 3
POL(q5(x1)) = 9/4 + x_1
POL(q4(x1)) = 0
POL(h(x1)) = 1/2
POL(q2(x1)) = 0
POL(0(x1)) = 0
POL(q3(x1)) = (4)x_1
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
h(q4(x1)) → h(0(q4(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q5(x1)) → h(0(q5(x1)))
1(q1(1(x1))) → 1(1(q1(x1)))
1(q5(1(x1))) → 0(1(q1(x1)))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(0(x1))) → 0(0(q0(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(0(x1))) → 1(0(q2(x1)))
0(q4(1(x1))) → 1(1(q5(x1)))
0(q0(1(x1))) → 0(1(q0(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
0(q1(h(x1))) → 0(0(q2(h(x1))))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
11(q1(0(x1))) → 01(q1(x1))
11(q0(0(x1))) → 01(q1(x1))
01(q4(1(x1))) → 11(1(q5(x1)))
01(q3(x1)) → 01(x1)
01(q1(0(x1))) → 01(q2(x1))
11(q1(1(x1))) → 11(q1(x1))
11(q1(0(x1))) → 11(0(q1(x1)))
11(q5(0(x1))) → 01(0(q1(x1)))
11(q5(1(x1))) → 11(q1(x1))
11(q1(h(x1))) → 11(0(q1(h(x1))))
01(q2(x1)) → 11(x1)
11(q2(0(x1))) → 01(q2(x1))
11(q2(h(x1))) → 01(q2(h(x1)))
01(q0(h(x1))) → 01(q0(h(x1)))
11(q0(h(x1))) → 01(0(q1(h(x1))))
11(q5(0(x1))) → 01(q1(x1))
01(q1(1(x1))) → 11(q2(x1))
11(q2(0(x1))) → 11(0(q2(x1)))
01(q1(1(x1))) → 01(1(q2(x1)))
11(q5(h(x1))) → 01(0(q1(h(x1))))
11(q0(h(x1))) → 01(q1(h(x1)))
11(q5(1(x1))) → 01(1(q1(x1)))
11(q3(x1)) → 11(x1)
01(q1(0(x1))) → 01(0(q2(x1)))
11(q2(h(x1))) → 11(0(q2(h(x1))))
11(q2(1(x1))) → 11(q2(x1))
11(q1(h(x1))) → 01(q1(h(x1)))
11(q1(1(x1))) → 11(1(q1(x1)))
11(q2(1(x1))) → 11(1(q2(x1)))
01(q0(0(x1))) → 01(q0(x1))
11(q5(h(x1))) → 01(q1(h(x1)))
11(q0(1(x1))) → 01(1(q1(x1)))
01(q1(h(x1))) → 01(q2(h(x1)))
01(q4(1(x1))) → 11(q5(x1))
11(q0(1(x1))) → 11(q1(x1))
11(q4(x1)) → 11(x1)
11(q0(0(x1))) → 01(0(q1(x1)))
01(q1(h(x1))) → 01(0(q2(h(x1))))
0(q0(0(x1))) → 0(0(q0(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(1(x1))) → 0(1(q0(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
1(q1(1(x1))) → 1(1(q1(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
0(q1(h(x1))) → 0(0(q2(h(x1))))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q2(0(x1))) → 1(0(q2(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q4(1(x1))) → 1(1(q5(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
1(q5(1(x1))) → 0(1(q1(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q4(x1)) → h(0(q4(x1)))
h(q5(x1)) → h(0(q5(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
01(q0(h(x1))) → 01(q0(h(x1)))
01(q0(0(x1))) → 01(q0(x1))
0(q0(0(x1))) → 0(0(q0(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(1(x1))) → 0(1(q0(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
1(q1(1(x1))) → 1(1(q1(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
0(q1(h(x1))) → 0(0(q2(h(x1))))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q2(0(x1))) → 1(0(q2(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q4(1(x1))) → 1(1(q5(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
1(q5(1(x1))) → 0(1(q1(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q4(x1)) → h(0(q4(x1)))
h(q5(x1)) → h(0(q5(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
11(q1(0(x1))) → 01(q1(x1))
11(q0(0(x1))) → 01(q1(x1))
01(q4(1(x1))) → 11(1(q5(x1)))
01(q1(0(x1))) → 01(q2(x1))
01(q3(x1)) → 01(x1)
11(q1(1(x1))) → 11(q1(x1))
11(q5(1(x1))) → 11(q1(x1))
11(q5(0(x1))) → 01(0(q1(x1)))
11(q1(0(x1))) → 11(0(q1(x1)))
11(q1(h(x1))) → 11(0(q1(h(x1))))
01(q2(x1)) → 11(x1)
11(q2(0(x1))) → 01(q2(x1))
11(q2(h(x1))) → 01(q2(h(x1)))
11(q0(h(x1))) → 01(0(q1(h(x1))))
11(q5(0(x1))) → 01(q1(x1))
01(q1(1(x1))) → 11(q2(x1))
11(q2(0(x1))) → 11(0(q2(x1)))
01(q1(1(x1))) → 01(1(q2(x1)))
11(q5(h(x1))) → 01(0(q1(h(x1))))
11(q0(h(x1))) → 01(q1(h(x1)))
11(q5(1(x1))) → 01(1(q1(x1)))
11(q3(x1)) → 11(x1)
01(q1(0(x1))) → 01(0(q2(x1)))
11(q2(1(x1))) → 11(q2(x1))
11(q2(h(x1))) → 11(0(q2(h(x1))))
11(q1(1(x1))) → 11(1(q1(x1)))
11(q1(h(x1))) → 01(q1(h(x1)))
11(q2(1(x1))) → 11(1(q2(x1)))
11(q5(h(x1))) → 01(q1(h(x1)))
01(q1(h(x1))) → 01(q2(h(x1)))
01(q4(1(x1))) → 11(q5(x1))
11(q0(1(x1))) → 01(1(q1(x1)))
11(q4(x1)) → 11(x1)
11(q0(1(x1))) → 11(q1(x1))
11(q0(0(x1))) → 01(0(q1(x1)))
01(q1(h(x1))) → 01(0(q2(h(x1))))
0(q0(0(x1))) → 0(0(q0(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(1(x1))) → 0(1(q0(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
1(q1(1(x1))) → 1(1(q1(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
0(q1(h(x1))) → 0(0(q2(h(x1))))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q2(0(x1))) → 1(0(q2(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q4(1(x1))) → 1(1(q5(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
1(q5(1(x1))) → 0(1(q1(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q4(x1)) → h(0(q4(x1)))
h(q5(x1)) → h(0(q5(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
11(q0(0(x1))) → 01(q1(x1))
11(q0(h(x1))) → 01(0(q1(h(x1))))
11(q0(h(x1))) → 01(q1(h(x1)))
11(q0(1(x1))) → 01(1(q1(x1)))
11(q0(1(x1))) → 11(q1(x1))
11(q0(0(x1))) → 01(0(q1(x1)))
Used ordering: Polynomial interpretation [25,35]:
11(q1(0(x1))) → 01(q1(x1))
01(q4(1(x1))) → 11(1(q5(x1)))
01(q1(0(x1))) → 01(q2(x1))
01(q3(x1)) → 01(x1)
11(q1(1(x1))) → 11(q1(x1))
11(q5(1(x1))) → 11(q1(x1))
11(q5(0(x1))) → 01(0(q1(x1)))
11(q1(0(x1))) → 11(0(q1(x1)))
11(q1(h(x1))) → 11(0(q1(h(x1))))
01(q2(x1)) → 11(x1)
11(q2(0(x1))) → 01(q2(x1))
11(q2(h(x1))) → 01(q2(h(x1)))
11(q5(0(x1))) → 01(q1(x1))
01(q1(1(x1))) → 11(q2(x1))
11(q2(0(x1))) → 11(0(q2(x1)))
01(q1(1(x1))) → 01(1(q2(x1)))
11(q5(h(x1))) → 01(0(q1(h(x1))))
11(q5(1(x1))) → 01(1(q1(x1)))
11(q3(x1)) → 11(x1)
01(q1(0(x1))) → 01(0(q2(x1)))
11(q2(1(x1))) → 11(q2(x1))
11(q2(h(x1))) → 11(0(q2(h(x1))))
11(q1(1(x1))) → 11(1(q1(x1)))
11(q1(h(x1))) → 01(q1(h(x1)))
11(q2(1(x1))) → 11(1(q2(x1)))
11(q5(h(x1))) → 01(q1(h(x1)))
01(q1(h(x1))) → 01(q2(h(x1)))
01(q4(1(x1))) → 11(q5(x1))
11(q4(x1)) → 11(x1)
01(q1(h(x1))) → 01(0(q2(h(x1))))
The value of delta used in the strict ordering is 1/8.
POL(q1(x1)) = (4)x_1
POL(11(x1)) = (1/2)x_1
POL(1(x1)) = x_1
POL(01(x1)) = (1/2)x_1
POL(q0(x1)) = 1/4 + (4)x_1
POL(q5(x1)) = (4)x_1
POL(q4(x1)) = (4)x_1
POL(h(x1)) = 0
POL(q2(x1)) = (4)x_1
POL(0(x1)) = x_1
POL(q3(x1)) = (4)x_1
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
h(q4(x1)) → h(0(q4(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q5(x1)) → h(0(q5(x1)))
1(q1(1(x1))) → 1(1(q1(x1)))
1(q5(1(x1))) → 0(1(q1(x1)))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(0(x1))) → 0(0(q0(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(0(x1))) → 1(0(q2(x1)))
0(q4(1(x1))) → 1(1(q5(x1)))
0(q0(1(x1))) → 0(1(q0(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
0(q1(h(x1))) → 0(0(q2(h(x1))))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
11(q1(0(x1))) → 01(q1(x1))
01(q4(1(x1))) → 11(1(q5(x1)))
01(q3(x1)) → 01(x1)
01(q1(0(x1))) → 01(q2(x1))
11(q1(1(x1))) → 11(q1(x1))
11(q1(0(x1))) → 11(0(q1(x1)))
11(q5(0(x1))) → 01(0(q1(x1)))
11(q5(1(x1))) → 11(q1(x1))
11(q1(h(x1))) → 11(0(q1(h(x1))))
01(q2(x1)) → 11(x1)
11(q2(0(x1))) → 01(q2(x1))
11(q2(h(x1))) → 01(q2(h(x1)))
11(q5(0(x1))) → 01(q1(x1))
01(q1(1(x1))) → 11(q2(x1))
11(q2(0(x1))) → 11(0(q2(x1)))
01(q1(1(x1))) → 01(1(q2(x1)))
11(q5(h(x1))) → 01(0(q1(h(x1))))
11(q5(1(x1))) → 01(1(q1(x1)))
11(q3(x1)) → 11(x1)
01(q1(0(x1))) → 01(0(q2(x1)))
11(q2(1(x1))) → 11(q2(x1))
11(q2(h(x1))) → 11(0(q2(h(x1))))
11(q1(1(x1))) → 11(1(q1(x1)))
11(q1(h(x1))) → 01(q1(h(x1)))
11(q2(1(x1))) → 11(1(q2(x1)))
11(q5(h(x1))) → 01(q1(h(x1)))
01(q4(1(x1))) → 11(q5(x1))
01(q1(h(x1))) → 01(q2(h(x1)))
11(q4(x1)) → 11(x1)
01(q1(h(x1))) → 01(0(q2(h(x1))))
0(q0(0(x1))) → 0(0(q0(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(1(x1))) → 0(1(q0(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
1(q1(1(x1))) → 1(1(q1(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
0(q1(h(x1))) → 0(0(q2(h(x1))))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q2(0(x1))) → 1(0(q2(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q4(1(x1))) → 1(1(q5(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
1(q5(1(x1))) → 0(1(q1(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q4(x1)) → h(0(q4(x1)))
h(q5(x1)) → h(0(q5(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
01(q3(x1)) → 01(x1)
01(q2(x1)) → 11(x1)
11(q3(x1)) → 11(x1)
11(q4(x1)) → 11(x1)
Used ordering: Polynomial interpretation [25,35]:
11(q1(0(x1))) → 01(q1(x1))
01(q4(1(x1))) → 11(1(q5(x1)))
01(q1(0(x1))) → 01(q2(x1))
11(q1(1(x1))) → 11(q1(x1))
11(q1(0(x1))) → 11(0(q1(x1)))
11(q5(0(x1))) → 01(0(q1(x1)))
11(q5(1(x1))) → 11(q1(x1))
11(q1(h(x1))) → 11(0(q1(h(x1))))
11(q2(0(x1))) → 01(q2(x1))
11(q2(h(x1))) → 01(q2(h(x1)))
11(q5(0(x1))) → 01(q1(x1))
01(q1(1(x1))) → 11(q2(x1))
11(q2(0(x1))) → 11(0(q2(x1)))
01(q1(1(x1))) → 01(1(q2(x1)))
11(q5(h(x1))) → 01(0(q1(h(x1))))
11(q5(1(x1))) → 01(1(q1(x1)))
01(q1(0(x1))) → 01(0(q2(x1)))
11(q2(1(x1))) → 11(q2(x1))
11(q2(h(x1))) → 11(0(q2(h(x1))))
11(q1(1(x1))) → 11(1(q1(x1)))
11(q1(h(x1))) → 01(q1(h(x1)))
11(q2(1(x1))) → 11(1(q2(x1)))
11(q5(h(x1))) → 01(q1(h(x1)))
01(q4(1(x1))) → 11(q5(x1))
01(q1(h(x1))) → 01(q2(h(x1)))
01(q1(h(x1))) → 01(0(q2(h(x1))))
The value of delta used in the strict ordering is 1.
POL(q1(x1)) = 1/4 + (4)x_1
POL(11(x1)) = (4)x_1
POL(1(x1)) = x_1
POL(01(x1)) = (4)x_1
POL(q0(x1)) = 4 + (4)x_1
POL(q5(x1)) = 1/4 + (4)x_1
POL(q4(x1)) = 1/4 + (4)x_1
POL(h(x1)) = 0
POL(q2(x1)) = 1/4 + (4)x_1
POL(0(x1)) = x_1
POL(q3(x1)) = 1/4 + (4)x_1
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
h(q4(x1)) → h(0(q4(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q5(x1)) → h(0(q5(x1)))
1(q1(1(x1))) → 1(1(q1(x1)))
1(q5(1(x1))) → 0(1(q1(x1)))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(0(x1))) → 0(0(q0(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(0(x1))) → 1(0(q2(x1)))
0(q4(1(x1))) → 1(1(q5(x1)))
0(q0(1(x1))) → 0(1(q0(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
0(q1(h(x1))) → 0(0(q2(h(x1))))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ QDP
11(q1(0(x1))) → 01(q1(x1))
01(q4(1(x1))) → 11(1(q5(x1)))
01(q1(0(x1))) → 01(q2(x1))
11(q1(1(x1))) → 11(q1(x1))
11(q5(1(x1))) → 11(q1(x1))
11(q5(0(x1))) → 01(0(q1(x1)))
11(q1(0(x1))) → 11(0(q1(x1)))
11(q1(h(x1))) → 11(0(q1(h(x1))))
11(q2(0(x1))) → 01(q2(x1))
11(q2(h(x1))) → 01(q2(h(x1)))
01(q1(1(x1))) → 11(q2(x1))
11(q5(0(x1))) → 01(q1(x1))
11(q2(0(x1))) → 11(0(q2(x1)))
01(q1(1(x1))) → 01(1(q2(x1)))
11(q5(h(x1))) → 01(0(q1(h(x1))))
11(q5(1(x1))) → 01(1(q1(x1)))
01(q1(0(x1))) → 01(0(q2(x1)))
11(q2(1(x1))) → 11(q2(x1))
11(q2(h(x1))) → 11(0(q2(h(x1))))
11(q1(1(x1))) → 11(1(q1(x1)))
11(q1(h(x1))) → 01(q1(h(x1)))
11(q2(1(x1))) → 11(1(q2(x1)))
11(q5(h(x1))) → 01(q1(h(x1)))
01(q4(1(x1))) → 11(q5(x1))
01(q1(h(x1))) → 01(q2(h(x1)))
01(q1(h(x1))) → 01(0(q2(h(x1))))
0(q0(0(x1))) → 0(0(q0(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(1(x1))) → 0(1(q0(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
1(q1(1(x1))) → 1(1(q1(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
0(q1(h(x1))) → 0(0(q2(h(x1))))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q2(0(x1))) → 1(0(q2(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q4(1(x1))) → 1(1(q5(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
1(q5(1(x1))) → 0(1(q1(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q4(x1)) → h(0(q4(x1)))
h(q5(x1)) → h(0(q5(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
11(q2(1(x1))) → 11(q2(x1))
0(q0(0(x1))) → 0(0(q0(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(1(x1))) → 0(1(q0(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
1(q1(1(x1))) → 1(1(q1(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
0(q1(h(x1))) → 0(0(q2(h(x1))))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q2(0(x1))) → 1(0(q2(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q4(1(x1))) → 1(1(q5(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
1(q5(1(x1))) → 0(1(q1(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q4(x1)) → h(0(q4(x1)))
h(q5(x1)) → h(0(q5(x1)))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
11(q2(1(x1))) → 11(q2(x1))
The value of delta used in the strict ordering is 2.
POL(11(x1)) = (2)x_1
POL(1(x1)) = 1 + (4)x_1
POL(q2(x1)) = x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
0(q0(0(x1))) → 0(0(q0(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(1(x1))) → 0(1(q0(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
1(q1(1(x1))) → 1(1(q1(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
0(q1(h(x1))) → 0(0(q2(h(x1))))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q2(0(x1))) → 1(0(q2(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q4(1(x1))) → 1(1(q5(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
1(q5(1(x1))) → 0(1(q1(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q4(x1)) → h(0(q4(x1)))
h(q5(x1)) → h(0(q5(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
11(q5(0(x1))) → 01(q1(x1))
11(q1(0(x1))) → 01(q1(x1))
01(q1(1(x1))) → 01(1(q2(x1)))
11(q5(h(x1))) → 01(0(q1(h(x1))))
11(q5(1(x1))) → 01(1(q1(x1)))
01(q1(0(x1))) → 01(0(q2(x1)))
11(q1(1(x1))) → 11(q1(x1))
11(q1(h(x1))) → 01(q1(h(x1)))
11(q5(0(x1))) → 01(0(q1(x1)))
11(q5(1(x1))) → 11(q1(x1))
11(q5(h(x1))) → 01(q1(h(x1)))
01(q4(1(x1))) → 11(q5(x1))
01(q1(h(x1))) → 01(0(q2(h(x1))))
0(q0(0(x1))) → 0(0(q0(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(1(x1))) → 0(1(q0(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
1(q1(1(x1))) → 1(1(q1(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
0(q1(h(x1))) → 0(0(q2(h(x1))))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q2(0(x1))) → 1(0(q2(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q4(1(x1))) → 1(1(q5(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
1(q5(1(x1))) → 0(1(q1(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q4(x1)) → h(0(q4(x1)))
h(q5(x1)) → h(0(q5(x1)))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
H(q3(x1)) → H(0(q3(x1)))
H(q4(x1)) → H(0(q4(x1)))
0(q0(0(x1))) → 0(0(q0(x1)))
0(q0(h(x1))) → 0(0(q0(h(x1))))
0(q0(1(x1))) → 0(1(q0(x1)))
1(q0(0(x1))) → 0(0(q1(x1)))
1(q0(h(x1))) → 0(0(q1(h(x1))))
1(q0(1(x1))) → 0(1(q1(x1)))
1(q1(0(x1))) → 1(0(q1(x1)))
1(q1(h(x1))) → 1(0(q1(h(x1))))
1(q1(1(x1))) → 1(1(q1(x1)))
0(q1(0(x1))) → 0(0(q2(x1)))
0(q1(h(x1))) → 0(0(q2(h(x1))))
0(q1(1(x1))) → 0(1(q2(x1)))
1(q2(0(x1))) → 1(0(q2(x1)))
1(q2(h(x1))) → 1(0(q2(h(x1))))
1(q2(1(x1))) → 1(1(q2(x1)))
0(q2(x1)) → q3(1(x1))
1(q3(x1)) → q3(1(x1))
0(q3(x1)) → q4(0(x1))
1(q4(x1)) → q4(1(x1))
0(q4(0(x1))) → 1(0(q5(x1)))
0(q4(h(x1))) → 1(0(q5(h(x1))))
0(q4(1(x1))) → 1(1(q5(x1)))
1(q5(0(x1))) → 0(0(q1(x1)))
1(q5(h(x1))) → 0(0(q1(h(x1))))
1(q5(1(x1))) → 0(1(q1(x1)))
h(q0(x1)) → h(0(q0(x1)))
h(q1(x1)) → h(0(q1(x1)))
h(q2(x1)) → h(0(q2(x1)))
h(q3(x1)) → h(0(q3(x1)))
h(q4(x1)) → h(0(q4(x1)))
h(q5(x1)) → h(0(q5(x1)))