p(0) → 0
p(s(x)) → x
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
minus(x, y) → if(le(x, y), x, y)
if(true, x, y) → 0
if(false, x, y) → s(minus(p(x), y))
↳ QTRS
↳ DependencyPairsProof
p(0) → 0
p(s(x)) → x
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
minus(x, y) → if(le(x, y), x, y)
if(true, x, y) → 0
if(false, x, y) → s(minus(p(x), y))
IF(false, x, y) → P(x)
MINUS(x, y) → LE(x, y)
IF(false, x, y) → MINUS(p(x), y)
MINUS(x, y) → IF(le(x, y), x, y)
LE(s(x), s(y)) → LE(x, y)
p(0) → 0
p(s(x)) → x
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
minus(x, y) → if(le(x, y), x, y)
if(true, x, y) → 0
if(false, x, y) → s(minus(p(x), y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
IF(false, x, y) → P(x)
MINUS(x, y) → LE(x, y)
IF(false, x, y) → MINUS(p(x), y)
MINUS(x, y) → IF(le(x, y), x, y)
LE(s(x), s(y)) → LE(x, y)
p(0) → 0
p(s(x)) → x
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
minus(x, y) → if(le(x, y), x, y)
if(true, x, y) → 0
if(false, x, y) → s(minus(p(x), y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
LE(s(x), s(y)) → LE(x, y)
p(0) → 0
p(s(x)) → x
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
minus(x, y) → if(le(x, y), x, y)
if(true, x, y) → 0
if(false, x, y) → s(minus(p(x), y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
LE(s(x), s(y)) → LE(x, y)
The value of delta used in the strict ordering is 15/8.
POL(s(x1)) = 1/2 + (13/4)x_1
POL(LE(x1, x2)) = (15/4)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
p(0) → 0
p(s(x)) → x
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
minus(x, y) → if(le(x, y), x, y)
if(true, x, y) → 0
if(false, x, y) → s(minus(p(x), y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
IF(false, x, y) → MINUS(p(x), y)
MINUS(x, y) → IF(le(x, y), x, y)
p(0) → 0
p(s(x)) → x
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
minus(x, y) → if(le(x, y), x, y)
if(true, x, y) → 0
if(false, x, y) → s(minus(p(x), y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
IF(false, x, y) → MINUS(p(x), y)
MINUS(x, y) → IF(le(x, y), x, y)
The value of delta used in the strict ordering is 1/8.
POL(le(x1, x2)) = 1/2 + x_1
POL(true) = 1/2
POL(false) = 9/4
POL(MINUS(x1, x2)) = 2 + x_1
POL(p(x1)) = (1/4)x_1
POL(s(x1)) = 2 + (4)x_1
POL(IF(x1, x2, x3)) = 7/4 + (1/4)x_1 + (1/2)x_2
POL(0) = 0
p(0) → 0
p(s(x)) → x
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
p(0) → 0
p(s(x)) → x
le(0, y) → true
le(s(x), 0) → false
le(s(x), s(y)) → le(x, y)
minus(x, y) → if(le(x, y), x, y)
if(true, x, y) → 0
if(false, x, y) → s(minus(p(x), y))