0(*(x1)) → *(1(x1))
1(*(x1)) → 0(#(x1))
#(0(x1)) → 0(#(x1))
#(1(x1)) → 1(#(x1))
#($(x1)) → *($(x1))
#(#(x1)) → #(x1)
#(*(x1)) → *(x1)
↳ QTRS
↳ DependencyPairsProof
0(*(x1)) → *(1(x1))
1(*(x1)) → 0(#(x1))
#(0(x1)) → 0(#(x1))
#(1(x1)) → 1(#(x1))
#($(x1)) → *($(x1))
#(#(x1)) → #(x1)
#(*(x1)) → *(x1)
#1(0(x1)) → 01(#(x1))
11(*(x1)) → 01(#(x1))
11(*(x1)) → #1(x1)
#1(1(x1)) → 11(#(x1))
01(*(x1)) → 11(x1)
#1(0(x1)) → #1(x1)
#1(1(x1)) → #1(x1)
0(*(x1)) → *(1(x1))
1(*(x1)) → 0(#(x1))
#(0(x1)) → 0(#(x1))
#(1(x1)) → 1(#(x1))
#($(x1)) → *($(x1))
#(#(x1)) → #(x1)
#(*(x1)) → *(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
#1(0(x1)) → 01(#(x1))
11(*(x1)) → 01(#(x1))
11(*(x1)) → #1(x1)
#1(1(x1)) → 11(#(x1))
01(*(x1)) → 11(x1)
#1(0(x1)) → #1(x1)
#1(1(x1)) → #1(x1)
0(*(x1)) → *(1(x1))
1(*(x1)) → 0(#(x1))
#(0(x1)) → 0(#(x1))
#(1(x1)) → 1(#(x1))
#($(x1)) → *($(x1))
#(#(x1)) → #(x1)
#(*(x1)) → *(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
#1(0(x1)) → 01(#(x1))
11(*(x1)) → 01(#(x1))
01(*(x1)) → 11(x1)
Used ordering: Polynomial interpretation [25,35]:
11(*(x1)) → #1(x1)
#1(1(x1)) → 11(#(x1))
#1(0(x1)) → #1(x1)
#1(1(x1)) → #1(x1)
The value of delta used in the strict ordering is 1/4.
POL(11(x1)) = 1/2 + (1/2)x_1
POL(*(x1)) = 4 + (4)x_1
POL(1(x1)) = x_1
POL(01(x1)) = 1/4 + (1/2)x_1
POL(#1(x1)) = 5/2 + (2)x_1
POL(0(x1)) = x_1
POL(#(x1)) = 4 + (4)x_1
POL($(x1)) = 3/2 + (3/4)x_1
0(*(x1)) → *(1(x1))
1(*(x1)) → 0(#(x1))
#(0(x1)) → 0(#(x1))
#(1(x1)) → 1(#(x1))
#($(x1)) → *($(x1))
#(#(x1)) → #(x1)
#(*(x1)) → *(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
11(*(x1)) → #1(x1)
#1(1(x1)) → 11(#(x1))
#1(0(x1)) → #1(x1)
#1(1(x1)) → #1(x1)
0(*(x1)) → *(1(x1))
1(*(x1)) → 0(#(x1))
#(0(x1)) → 0(#(x1))
#(1(x1)) → 1(#(x1))
#($(x1)) → *($(x1))
#(#(x1)) → #(x1)
#(*(x1)) → *(x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
#1(1(x1)) → 11(#(x1))
#1(0(x1)) → #1(x1)
#1(1(x1)) → #1(x1)
Used ordering: Polynomial interpretation [25,35]:
11(*(x1)) → #1(x1)
The value of delta used in the strict ordering is 1/8.
POL(11(x1)) = 1 + (2)x_1
POL(*(x1)) = x_1
POL(1(x1)) = 1/4 + (4)x_1
POL(#1(x1)) = 1 + (1/2)x_1
POL(0(x1)) = 1/4 + (4)x_1
POL(#(x1)) = x_1
POL($(x1)) = 0
0(*(x1)) → *(1(x1))
1(*(x1)) → 0(#(x1))
#(0(x1)) → 0(#(x1))
#(1(x1)) → 1(#(x1))
#($(x1)) → *($(x1))
#(#(x1)) → #(x1)
#(*(x1)) → *(x1)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
11(*(x1)) → #1(x1)
0(*(x1)) → *(1(x1))
1(*(x1)) → 0(#(x1))
#(0(x1)) → 0(#(x1))
#(1(x1)) → 1(#(x1))
#($(x1)) → *($(x1))
#(#(x1)) → #(x1)
#(*(x1)) → *(x1)