cond(true, x) → cond(odd(x), p(x))
odd(0) → false
odd(s(0)) → true
odd(s(s(x))) → odd(x)
p(0) → 0
p(s(x)) → x
↳ QTRS
↳ DependencyPairsProof
cond(true, x) → cond(odd(x), p(x))
odd(0) → false
odd(s(0)) → true
odd(s(s(x))) → odd(x)
p(0) → 0
p(s(x)) → x
ODD(s(s(x))) → ODD(x)
COND(true, x) → P(x)
COND(true, x) → ODD(x)
COND(true, x) → COND(odd(x), p(x))
cond(true, x) → cond(odd(x), p(x))
odd(0) → false
odd(s(0)) → true
odd(s(s(x))) → odd(x)
p(0) → 0
p(s(x)) → x
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
ODD(s(s(x))) → ODD(x)
COND(true, x) → P(x)
COND(true, x) → ODD(x)
COND(true, x) → COND(odd(x), p(x))
cond(true, x) → cond(odd(x), p(x))
odd(0) → false
odd(s(0)) → true
odd(s(s(x))) → odd(x)
p(0) → 0
p(s(x)) → x
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
ODD(s(s(x))) → ODD(x)
cond(true, x) → cond(odd(x), p(x))
odd(0) → false
odd(s(0)) → true
odd(s(s(x))) → odd(x)
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.
ODD(s(s(x))) → ODD(x)
The value of delta used in the strict ordering is 1/4.
POL(ODD(x1)) = (1/2)x_1
POL(s(x1)) = 1/4 + x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
cond(true, x) → cond(odd(x), p(x))
odd(0) → false
odd(s(0)) → true
odd(s(s(x))) → odd(x)
p(0) → 0
p(s(x)) → x
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
COND(true, x) → COND(odd(x), p(x))
cond(true, x) → cond(odd(x), p(x))
odd(0) → false
odd(s(0)) → true
odd(s(s(x))) → odd(x)
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) → COND(odd(x), p(x))
The value of delta used in the strict ordering is 27/16.
POL(odd(x1)) = 3 + (1/4)x_1
POL(true) = 4
POL(false) = 0
POL(p(x1)) = 1/4 + (1/4)x_1
POL(s(x1)) = 4 + (4)x_1
POL(COND(x1, x2)) = (9/4)x_1 + (9/4)x_2
POL(0) = 0
odd(0) → false
odd(s(0)) → true
odd(s(s(x))) → odd(x)
p(0) → 0
p(s(x)) → x
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
cond(true, x) → cond(odd(x), p(x))
odd(0) → false
odd(s(0)) → true
odd(s(s(x))) → odd(x)
p(0) → 0
p(s(x)) → x