half(0) → 0
half(s(0)) → 0
half(s(s(x))) → s(half(x))
lastbit(0) → 0
lastbit(s(0)) → s(0)
lastbit(s(s(x))) → lastbit(x)
zero(0) → true
zero(s(x)) → false
conv(x) → conviter(x, cons(0, nil))
conviter(x, l) → if(zero(x), x, l)
if(true, x, l) → l
if(false, x, l) → conviter(half(x), cons(lastbit(x), l))
↳ QTRS
↳ DependencyPairsProof
half(0) → 0
half(s(0)) → 0
half(s(s(x))) → s(half(x))
lastbit(0) → 0
lastbit(s(0)) → s(0)
lastbit(s(s(x))) → lastbit(x)
zero(0) → true
zero(s(x)) → false
conv(x) → conviter(x, cons(0, nil))
conviter(x, l) → if(zero(x), x, l)
if(true, x, l) → l
if(false, x, l) → conviter(half(x), cons(lastbit(x), l))
IF(false, x, l) → HALF(x)
HALF(s(s(x))) → HALF(x)
CONVITER(x, l) → ZERO(x)
LASTBIT(s(s(x))) → LASTBIT(x)
IF(false, x, l) → LASTBIT(x)
CONV(x) → CONVITER(x, cons(0, nil))
IF(false, x, l) → CONVITER(half(x), cons(lastbit(x), l))
CONVITER(x, l) → IF(zero(x), x, l)
half(0) → 0
half(s(0)) → 0
half(s(s(x))) → s(half(x))
lastbit(0) → 0
lastbit(s(0)) → s(0)
lastbit(s(s(x))) → lastbit(x)
zero(0) → true
zero(s(x)) → false
conv(x) → conviter(x, cons(0, nil))
conviter(x, l) → if(zero(x), x, l)
if(true, x, l) → l
if(false, x, l) → conviter(half(x), cons(lastbit(x), l))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
IF(false, x, l) → HALF(x)
HALF(s(s(x))) → HALF(x)
CONVITER(x, l) → ZERO(x)
LASTBIT(s(s(x))) → LASTBIT(x)
IF(false, x, l) → LASTBIT(x)
CONV(x) → CONVITER(x, cons(0, nil))
IF(false, x, l) → CONVITER(half(x), cons(lastbit(x), l))
CONVITER(x, l) → IF(zero(x), x, l)
half(0) → 0
half(s(0)) → 0
half(s(s(x))) → s(half(x))
lastbit(0) → 0
lastbit(s(0)) → s(0)
lastbit(s(s(x))) → lastbit(x)
zero(0) → true
zero(s(x)) → false
conv(x) → conviter(x, cons(0, nil))
conviter(x, l) → if(zero(x), x, l)
if(true, x, l) → l
if(false, x, l) → conviter(half(x), cons(lastbit(x), l))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
LASTBIT(s(s(x))) → LASTBIT(x)
half(0) → 0
half(s(0)) → 0
half(s(s(x))) → s(half(x))
lastbit(0) → 0
lastbit(s(0)) → s(0)
lastbit(s(s(x))) → lastbit(x)
zero(0) → true
zero(s(x)) → false
conv(x) → conviter(x, cons(0, nil))
conviter(x, l) → if(zero(x), x, l)
if(true, x, l) → l
if(false, x, l) → conviter(half(x), cons(lastbit(x), l))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
LASTBIT(s(s(x))) → LASTBIT(x)
The value of delta used in the strict ordering is 4.
POL(LASTBIT(x1)) = (2)x_1
POL(s(x1)) = 1 + x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
half(0) → 0
half(s(0)) → 0
half(s(s(x))) → s(half(x))
lastbit(0) → 0
lastbit(s(0)) → s(0)
lastbit(s(s(x))) → lastbit(x)
zero(0) → true
zero(s(x)) → false
conv(x) → conviter(x, cons(0, nil))
conviter(x, l) → if(zero(x), x, l)
if(true, x, l) → l
if(false, x, l) → conviter(half(x), cons(lastbit(x), l))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
HALF(s(s(x))) → HALF(x)
half(0) → 0
half(s(0)) → 0
half(s(s(x))) → s(half(x))
lastbit(0) → 0
lastbit(s(0)) → s(0)
lastbit(s(s(x))) → lastbit(x)
zero(0) → true
zero(s(x)) → false
conv(x) → conviter(x, cons(0, nil))
conviter(x, l) → if(zero(x), x, l)
if(true, x, l) → l
if(false, x, l) → conviter(half(x), cons(lastbit(x), l))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
HALF(s(s(x))) → HALF(x)
The value of delta used in the strict ordering is 4.
POL(HALF(x1)) = (2)x_1
POL(s(x1)) = 1 + x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
half(0) → 0
half(s(0)) → 0
half(s(s(x))) → s(half(x))
lastbit(0) → 0
lastbit(s(0)) → s(0)
lastbit(s(s(x))) → lastbit(x)
zero(0) → true
zero(s(x)) → false
conv(x) → conviter(x, cons(0, nil))
conviter(x, l) → if(zero(x), x, l)
if(true, x, l) → l
if(false, x, l) → conviter(half(x), cons(lastbit(x), l))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
CONVITER(x, l) → IF(zero(x), x, l)
IF(false, x, l) → CONVITER(half(x), cons(lastbit(x), l))
half(0) → 0
half(s(0)) → 0
half(s(s(x))) → s(half(x))
lastbit(0) → 0
lastbit(s(0)) → s(0)
lastbit(s(s(x))) → lastbit(x)
zero(0) → true
zero(s(x)) → false
conv(x) → conviter(x, cons(0, nil))
conviter(x, l) → if(zero(x), x, l)
if(true, x, l) → l
if(false, x, l) → conviter(half(x), cons(lastbit(x), l))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
IF(false, x, l) → CONVITER(half(x), cons(lastbit(x), l))
Used ordering: Polynomial interpretation [25,35]:
CONVITER(x, l) → IF(zero(x), x, l)
The value of delta used in the strict ordering is 1/16.
POL(zero(x1)) = 2 + x_1
POL(cons(x1, x2)) = (4)x_1 + (4)x_2
POL(half(x1)) = (1/4)x_1
POL(true) = 0
POL(false) = 9/4
POL(s(x1)) = 1/4 + (3)x_1
POL(CONVITER(x1, x2)) = 1/2 + x_1
POL(IF(x1, x2, x3)) = (1/4)x_1 + (1/2)x_2
POL(lastbit(x1)) = 0
POL(0) = 0
zero(s(x)) → false
half(0) → 0
half(s(0)) → 0
half(s(s(x))) → s(half(x))
zero(0) → true
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ DependencyGraphProof
CONVITER(x, l) → IF(zero(x), x, l)
half(0) → 0
half(s(0)) → 0
half(s(s(x))) → s(half(x))
lastbit(0) → 0
lastbit(s(0)) → s(0)
lastbit(s(s(x))) → lastbit(x)
zero(0) → true
zero(s(x)) → false
conv(x) → conviter(x, cons(0, nil))
conviter(x, l) → if(zero(x), x, l)
if(true, x, l) → l
if(false, x, l) → conviter(half(x), cons(lastbit(x), l))