cond(true, x, y) → cond(gr(x, y), p(x), y)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
p(0) → 0
p(s(x)) → x
↳ QTRS
↳ DependencyPairsProof
cond(true, x, y) → cond(gr(x, y), p(x), y)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
p(0) → 0
p(s(x)) → x
COND(true, x, y) → COND(gr(x, y), p(x), y)
COND(true, x, y) → P(x)
COND(true, x, y) → GR(x, y)
GR(s(x), s(y)) → GR(x, y)
cond(true, x, y) → cond(gr(x, y), p(x), y)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
p(0) → 0
p(s(x)) → x
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
COND(true, x, y) → COND(gr(x, y), p(x), y)
COND(true, x, y) → P(x)
COND(true, x, y) → GR(x, y)
GR(s(x), s(y)) → GR(x, y)
cond(true, x, y) → cond(gr(x, y), p(x), y)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
p(0) → 0
p(s(x)) → x
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
GR(s(x), s(y)) → GR(x, y)
cond(true, x, y) → cond(gr(x, y), p(x), y)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
p(0) → 0
p(s(x)) → x
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
GR(s(x), s(y)) → GR(x, y)
The value of delta used in the strict ordering is 3.
POL(GR(x1, x2)) = (3)x_2
POL(s(x1)) = 1 + (4)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
cond(true, x, y) → cond(gr(x, y), p(x), y)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
p(0) → 0
p(s(x)) → x
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
COND(true, x, y) → COND(gr(x, y), p(x), y)
cond(true, x, y) → cond(gr(x, y), p(x), y)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
p(0) → 0
p(s(x)) → x
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
COND(true, x, y) → COND(gr(x, y), p(x), y)
The value of delta used in the strict ordering is 1/8.
POL(gr(x1, x2)) = 2 + (5/4)x_1
POL(true) = 9/4
POL(false) = 2
POL(p(x1)) = (1/4)x_1
POL(s(x1)) = 7/4 + (4)x_1
POL(COND(x1, x2, x3)) = (1/2)x_1 + (9/4)x_2
POL(0) = 0
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
p(0) → 0
p(s(x)) → x
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
cond(true, x, y) → cond(gr(x, y), p(x), y)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
p(0) → 0
p(s(x)) → x