p(s(x)) → x
fact(0) → s(0)
fact(s(x)) → *(s(x), fact(p(s(x))))
*(0, y) → 0
*(s(x), y) → +(*(x, y), y)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
↳ QTRS
↳ DependencyPairsProof
p(s(x)) → x
fact(0) → s(0)
fact(s(x)) → *(s(x), fact(p(s(x))))
*(0, y) → 0
*(s(x), y) → +(*(x, y), y)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+1(x, s(y)) → +1(x, y)
*1(s(x), y) → +1(*(x, y), y)
FACT(s(x)) → FACT(p(s(x)))
FACT(s(x)) → P(s(x))
FACT(s(x)) → *1(s(x), fact(p(s(x))))
*1(s(x), y) → *1(x, y)
p(s(x)) → x
fact(0) → s(0)
fact(s(x)) → *(s(x), fact(p(s(x))))
*(0, y) → 0
*(s(x), y) → +(*(x, y), y)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
+1(x, s(y)) → +1(x, y)
*1(s(x), y) → +1(*(x, y), y)
FACT(s(x)) → FACT(p(s(x)))
FACT(s(x)) → P(s(x))
FACT(s(x)) → *1(s(x), fact(p(s(x))))
*1(s(x), y) → *1(x, y)
p(s(x)) → x
fact(0) → s(0)
fact(s(x)) → *(s(x), fact(p(s(x))))
*(0, y) → 0
*(s(x), y) → +(*(x, y), y)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
+1(x, s(y)) → +1(x, y)
p(s(x)) → x
fact(0) → s(0)
fact(s(x)) → *(s(x), fact(p(s(x))))
*(0, y) → 0
*(s(x), y) → +(*(x, y), y)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
+1(x, s(y)) → +1(x, y)
The value of delta used in the strict ordering is 1/2.
POL(s(x1)) = 1/4 + (7/2)x_1
POL(+1(x1, x2)) = (2)x_2
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
p(s(x)) → x
fact(0) → s(0)
fact(s(x)) → *(s(x), fact(p(s(x))))
*(0, y) → 0
*(s(x), y) → +(*(x, y), y)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
*1(s(x), y) → *1(x, y)
p(s(x)) → x
fact(0) → s(0)
fact(s(x)) → *(s(x), fact(p(s(x))))
*(0, y) → 0
*(s(x), y) → +(*(x, y), y)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
*1(s(x), y) → *1(x, y)
The value of delta used in the strict ordering is 1/2.
POL(*1(x1, x2)) = (2)x_1
POL(s(x1)) = 1/4 + (7/2)x_1
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
p(s(x)) → x
fact(0) → s(0)
fact(s(x)) → *(s(x), fact(p(s(x))))
*(0, y) → 0
*(s(x), y) → +(*(x, y), y)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
FACT(s(x)) → FACT(p(s(x)))
p(s(x)) → x
fact(0) → s(0)
fact(s(x)) → *(s(x), fact(p(s(x))))
*(0, y) → 0
*(s(x), y) → +(*(x, y), y)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
FACT(s(x)) → FACT(p(s(x)))
The value of delta used in the strict ordering is 1.
POL(FACT(x1)) = (4)x_1
POL(s(x1)) = 4 + (4)x_1
POL(p(x1)) = 7/4 + (1/2)x_1
p(s(x)) → x
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
p(s(x)) → x
fact(0) → s(0)
fact(s(x)) → *(s(x), fact(p(s(x))))
*(0, y) → 0
*(s(x), y) → +(*(x, y), y)
+(x, 0) → x
+(x, s(y)) → s(+(x, y))