cond(true, x, y, z) → cond(and(gr(x, z), gr(y, z)), p(x), p(y), z)
and(true, true) → true
and(x, false) → false
and(false, x) → false
gr(0, 0) → false
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, z) → cond(and(gr(x, z), gr(y, z)), p(x), p(y), z)
and(true, true) → true
and(x, false) → false
and(false, x) → false
gr(0, 0) → false
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, z) → GR(y, z)
COND(true, x, y, z) → COND(and(gr(x, z), gr(y, z)), p(x), p(y), z)
COND(true, x, y, z) → P(y)
COND(true, x, y, z) → P(x)
COND(true, x, y, z) → GR(x, z)
COND(true, x, y, z) → AND(gr(x, z), gr(y, z))
GR(s(x), s(y)) → GR(x, y)
cond(true, x, y, z) → cond(and(gr(x, z), gr(y, z)), p(x), p(y), z)
and(true, true) → true
and(x, false) → false
and(false, x) → false
gr(0, 0) → false
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, z) → GR(y, z)
COND(true, x, y, z) → COND(and(gr(x, z), gr(y, z)), p(x), p(y), z)
COND(true, x, y, z) → P(y)
COND(true, x, y, z) → P(x)
COND(true, x, y, z) → GR(x, z)
COND(true, x, y, z) → AND(gr(x, z), gr(y, z))
GR(s(x), s(y)) → GR(x, y)
cond(true, x, y, z) → cond(and(gr(x, z), gr(y, z)), p(x), p(y), z)
and(true, true) → true
and(x, false) → false
and(false, x) → false
gr(0, 0) → false
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, z) → cond(and(gr(x, z), gr(y, z)), p(x), p(y), z)
and(true, true) → true
and(x, false) → false
and(false, x) → false
gr(0, 0) → false
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 1.
POL(GR(x1, x2)) = x_2
POL(s(x1)) = 1 + x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
cond(true, x, y, z) → cond(and(gr(x, z), gr(y, z)), p(x), p(y), z)
and(true, true) → true
and(x, false) → false
and(false, x) → false
gr(0, 0) → false
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, z) → COND(and(gr(x, z), gr(y, z)), p(x), p(y), z)
cond(true, x, y, z) → cond(and(gr(x, z), gr(y, z)), p(x), p(y), z)
and(true, true) → true
and(x, false) → false
and(false, x) → false
gr(0, 0) → false
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, z) → COND(and(gr(x, z), gr(y, z)), p(x), p(y), z)
The value of delta used in the strict ordering is 1/16.
POL(COND(x1, x2, x3, x4)) = (1/4)x_1 + x_3
POL(gr(x1, x2)) = (2)x_1
POL(true) = 1/4
POL(false) = 0
POL(p(x1)) = (1/4)x_1
POL(s(x1)) = 4 + (4)x_1
POL(and(x1, x2)) = x_2
POL(0) = 0
p(s(x)) → x
p(0) → 0
and(true, true) → true
and(x, false) → false
and(false, x) → false
gr(0, 0) → false
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
cond(true, x, y, z) → cond(and(gr(x, z), gr(y, z)), p(x), p(y), z)
and(true, true) → true
and(x, false) → false
and(false, x) → false
gr(0, 0) → false
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
p(0) → 0
p(s(x)) → x