cond1(true, x, y, z) → cond2(gr(x, 0), x, y, z)
cond2(true, x, y, z) → cond1(or(gr(x, z), gr(y, z)), p(x), y, z)
cond2(false, x, y, z) → cond3(gr(y, 0), x, y, z)
cond3(true, x, y, z) → cond1(or(gr(x, z), gr(y, z)), x, p(y), z)
cond3(false, x, y, z) → cond1(or(gr(x, z), gr(y, z)), x, y, z)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
↳ QTRS
↳ DependencyPairsProof
cond1(true, x, y, z) → cond2(gr(x, 0), x, y, z)
cond2(true, x, y, z) → cond1(or(gr(x, z), gr(y, z)), p(x), y, z)
cond2(false, x, y, z) → cond3(gr(y, 0), x, y, z)
cond3(true, x, y, z) → cond1(or(gr(x, z), gr(y, z)), x, p(y), z)
cond3(false, x, y, z) → cond1(or(gr(x, z), gr(y, z)), x, y, z)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
COND2(true, x, y, z) → COND1(or(gr(x, z), gr(y, z)), p(x), y, z)
COND3(false, x, y, z) → COND1(or(gr(x, z), gr(y, z)), x, y, z)
COND1(true, x, y, z) → GR(x, 0)
COND3(false, x, y, z) → GR(x, z)
COND2(true, x, y, z) → OR(gr(x, z), gr(y, z))
COND2(true, x, y, z) → GR(x, z)
COND1(true, x, y, z) → COND2(gr(x, 0), x, y, z)
COND3(true, x, y, z) → GR(y, z)
COND3(false, x, y, z) → OR(gr(x, z), gr(y, z))
COND2(false, x, y, z) → GR(y, 0)
COND3(true, x, y, z) → COND1(or(gr(x, z), gr(y, z)), x, p(y), z)
COND3(true, x, y, z) → P(y)
COND3(true, x, y, z) → GR(x, z)
COND2(false, x, y, z) → COND3(gr(y, 0), x, y, z)
COND3(true, x, y, z) → OR(gr(x, z), gr(y, z))
COND3(false, x, y, z) → GR(y, z)
COND2(true, x, y, z) → GR(y, z)
COND2(true, x, y, z) → P(x)
GR(s(x), s(y)) → GR(x, y)
cond1(true, x, y, z) → cond2(gr(x, 0), x, y, z)
cond2(true, x, y, z) → cond1(or(gr(x, z), gr(y, z)), p(x), y, z)
cond2(false, x, y, z) → cond3(gr(y, 0), x, y, z)
cond3(true, x, y, z) → cond1(or(gr(x, z), gr(y, z)), x, p(y), z)
cond3(false, x, y, z) → cond1(or(gr(x, z), gr(y, z)), x, y, z)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
COND2(true, x, y, z) → COND1(or(gr(x, z), gr(y, z)), p(x), y, z)
COND3(false, x, y, z) → COND1(or(gr(x, z), gr(y, z)), x, y, z)
COND1(true, x, y, z) → GR(x, 0)
COND3(false, x, y, z) → GR(x, z)
COND2(true, x, y, z) → OR(gr(x, z), gr(y, z))
COND2(true, x, y, z) → GR(x, z)
COND1(true, x, y, z) → COND2(gr(x, 0), x, y, z)
COND3(true, x, y, z) → GR(y, z)
COND3(false, x, y, z) → OR(gr(x, z), gr(y, z))
COND2(false, x, y, z) → GR(y, 0)
COND3(true, x, y, z) → COND1(or(gr(x, z), gr(y, z)), x, p(y), z)
COND3(true, x, y, z) → P(y)
COND3(true, x, y, z) → GR(x, z)
COND2(false, x, y, z) → COND3(gr(y, 0), x, y, z)
COND3(true, x, y, z) → OR(gr(x, z), gr(y, z))
COND3(false, x, y, z) → GR(y, z)
COND2(true, x, y, z) → GR(y, z)
COND2(true, x, y, z) → P(x)
GR(s(x), s(y)) → GR(x, y)
cond1(true, x, y, z) → cond2(gr(x, 0), x, y, z)
cond2(true, x, y, z) → cond1(or(gr(x, z), gr(y, z)), p(x), y, z)
cond2(false, x, y, z) → cond3(gr(y, 0), x, y, z)
cond3(true, x, y, z) → cond1(or(gr(x, z), gr(y, z)), x, p(y), z)
cond3(false, x, y, z) → cond1(or(gr(x, z), gr(y, z)), x, y, z)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
GR(s(x), s(y)) → GR(x, y)
cond1(true, x, y, z) → cond2(gr(x, 0), x, y, z)
cond2(true, x, y, z) → cond1(or(gr(x, z), gr(y, z)), p(x), y, z)
cond2(false, x, y, z) → cond3(gr(y, 0), x, y, z)
cond3(true, x, y, z) → cond1(or(gr(x, z), gr(y, z)), x, p(y), z)
cond3(false, x, y, z) → cond1(or(gr(x, z), gr(y, z)), x, y, z)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
or(false, false) → false
or(true, x) → true
or(x, true) → true
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 12.
POL(GR(x1, x2)) = (3)x_2
POL(s(x1)) = 4 + (2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
cond1(true, x, y, z) → cond2(gr(x, 0), x, y, z)
cond2(true, x, y, z) → cond1(or(gr(x, z), gr(y, z)), p(x), y, z)
cond2(false, x, y, z) → cond3(gr(y, 0), x, y, z)
cond3(true, x, y, z) → cond1(or(gr(x, z), gr(y, z)), x, p(y), z)
cond3(false, x, y, z) → cond1(or(gr(x, z), gr(y, z)), x, y, z)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
COND2(true, x, y, z) → COND1(or(gr(x, z), gr(y, z)), p(x), y, z)
COND3(false, x, y, z) → COND1(or(gr(x, z), gr(y, z)), x, y, z)
COND2(false, x, y, z) → COND3(gr(y, 0), x, y, z)
COND1(true, x, y, z) → COND2(gr(x, 0), x, y, z)
COND3(true, x, y, z) → COND1(or(gr(x, z), gr(y, z)), x, p(y), z)
cond1(true, x, y, z) → cond2(gr(x, 0), x, y, z)
cond2(true, x, y, z) → cond1(or(gr(x, z), gr(y, z)), p(x), y, z)
cond2(false, x, y, z) → cond3(gr(y, 0), x, y, z)
cond3(true, x, y, z) → cond1(or(gr(x, z), gr(y, z)), x, p(y), z)
cond3(false, x, y, z) → cond1(or(gr(x, z), gr(y, z)), x, y, z)
gr(0, x) → false
gr(s(x), 0) → true
gr(s(x), s(y)) → gr(x, y)
or(false, false) → false
or(true, x) → true
or(x, true) → true
p(0) → 0
p(s(x)) → x