-(x, 0) → x
-(s(x), s(y)) → -(x, y)
+(0, y) → y
+(s(x), y) → s(+(x, y))
*(x, 0) → 0
*(x, s(y)) → +(x, *(x, y))
p(s(x)) → x
f(s(x)) → f(-(p(*(s(x), s(x))), *(s(x), s(x))))
↳ QTRS
↳ AAECC Innermost
-(x, 0) → x
-(s(x), s(y)) → -(x, y)
+(0, y) → y
+(s(x), y) → s(+(x, y))
*(x, 0) → 0
*(x, s(y)) → +(x, *(x, y))
p(s(x)) → x
f(s(x)) → f(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x, 0) → x
-(s(x), s(y)) → -(x, y)
+(0, y) → y
+(s(x), y) → s(+(x, y))
*(x, 0) → 0
*(x, s(y)) → +(x, *(x, y))
p(s(x)) → x
f(s(x)) → f(-(p(*(s(x), s(x))), *(s(x), s(x))))
↳ QTRS
↳ AAECC Innermost
↳ QTRS
↳ DependencyPairsProof
-(x, 0) → x
-(s(x), s(y)) → -(x, y)
+(0, y) → y
+(s(x), y) → s(+(x, y))
*(x, 0) → 0
*(x, s(y)) → +(x, *(x, y))
p(s(x)) → x
f(s(x)) → f(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x0, 0)
-(s(x0), s(x1))
+(0, x0)
+(s(x0), x1)
*(x0, 0)
*(x0, s(x1))
p(s(x0))
f(s(x0))
*1(x, s(y)) → +1(x, *(x, y))
*1(x, s(y)) → *1(x, y)
-1(s(x), s(y)) → -1(x, y)
+1(s(x), y) → +1(x, y)
F(s(x)) → *1(s(x), s(x))
F(s(x)) → P(*(s(x), s(x)))
F(s(x)) → -1(p(*(s(x), s(x))), *(s(x), s(x)))
F(s(x)) → F(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x, 0) → x
-(s(x), s(y)) → -(x, y)
+(0, y) → y
+(s(x), y) → s(+(x, y))
*(x, 0) → 0
*(x, s(y)) → +(x, *(x, y))
p(s(x)) → x
f(s(x)) → f(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x0, 0)
-(s(x0), s(x1))
+(0, x0)
+(s(x0), x1)
*(x0, 0)
*(x0, s(x1))
p(s(x0))
f(s(x0))
↳ QTRS
↳ AAECC Innermost
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ EdgeDeletionProof
*1(x, s(y)) → +1(x, *(x, y))
*1(x, s(y)) → *1(x, y)
-1(s(x), s(y)) → -1(x, y)
+1(s(x), y) → +1(x, y)
F(s(x)) → *1(s(x), s(x))
F(s(x)) → P(*(s(x), s(x)))
F(s(x)) → -1(p(*(s(x), s(x))), *(s(x), s(x)))
F(s(x)) → F(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x, 0) → x
-(s(x), s(y)) → -(x, y)
+(0, y) → y
+(s(x), y) → s(+(x, y))
*(x, 0) → 0
*(x, s(y)) → +(x, *(x, y))
p(s(x)) → x
f(s(x)) → f(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x0, 0)
-(s(x0), s(x1))
+(0, x0)
+(s(x0), x1)
*(x0, 0)
*(x0, s(x1))
p(s(x0))
f(s(x0))
↳ QTRS
↳ AAECC Innermost
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ EdgeDeletionProof
↳ QDP
↳ DependencyGraphProof
*1(x, s(y)) → +1(x, *(x, y))
*1(x, s(y)) → *1(x, y)
-1(s(x), s(y)) → -1(x, y)
+1(s(x), y) → +1(x, y)
F(s(x)) → *1(s(x), s(x))
F(s(x)) → -1(p(*(s(x), s(x))), *(s(x), s(x)))
F(s(x)) → P(*(s(x), s(x)))
F(s(x)) → F(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x, 0) → x
-(s(x), s(y)) → -(x, y)
+(0, y) → y
+(s(x), y) → s(+(x, y))
*(x, 0) → 0
*(x, s(y)) → +(x, *(x, y))
p(s(x)) → x
f(s(x)) → f(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x0, 0)
-(s(x0), s(x1))
+(0, x0)
+(s(x0), x1)
*(x0, 0)
*(x0, s(x1))
p(s(x0))
f(s(x0))
↳ QTRS
↳ AAECC Innermost
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ EdgeDeletionProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
↳ QDP
+1(s(x), y) → +1(x, y)
-(x, 0) → x
-(s(x), s(y)) → -(x, y)
+(0, y) → y
+(s(x), y) → s(+(x, y))
*(x, 0) → 0
*(x, s(y)) → +(x, *(x, y))
p(s(x)) → x
f(s(x)) → f(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x0, 0)
-(s(x0), s(x1))
+(0, x0)
+(s(x0), x1)
*(x0, 0)
*(x0, s(x1))
p(s(x0))
f(s(x0))
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)
[+^12, s1]
s1: multiset
+^12: multiset
↳ QTRS
↳ AAECC Innermost
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ EdgeDeletionProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
↳ QDP
-(x, 0) → x
-(s(x), s(y)) → -(x, y)
+(0, y) → y
+(s(x), y) → s(+(x, y))
*(x, 0) → 0
*(x, s(y)) → +(x, *(x, y))
p(s(x)) → x
f(s(x)) → f(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x0, 0)
-(s(x0), s(x1))
+(0, x0)
+(s(x0), x1)
*(x0, 0)
*(x0, s(x1))
p(s(x0))
f(s(x0))
↳ QTRS
↳ AAECC Innermost
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ EdgeDeletionProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ QDP
*1(x, s(y)) → *1(x, y)
-(x, 0) → x
-(s(x), s(y)) → -(x, y)
+(0, y) → y
+(s(x), y) → s(+(x, y))
*(x, 0) → 0
*(x, s(y)) → +(x, *(x, y))
p(s(x)) → x
f(s(x)) → f(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x0, 0)
-(s(x0), s(x1))
+(0, x0)
+(s(x0), x1)
*(x0, 0)
*(x0, s(x1))
p(s(x0))
f(s(x0))
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)
[*^12, s1]
*^12: multiset
s1: [1]
↳ QTRS
↳ AAECC Innermost
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ EdgeDeletionProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
↳ QDP
-(x, 0) → x
-(s(x), s(y)) → -(x, y)
+(0, y) → y
+(s(x), y) → s(+(x, y))
*(x, 0) → 0
*(x, s(y)) → +(x, *(x, y))
p(s(x)) → x
f(s(x)) → f(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x0, 0)
-(s(x0), s(x1))
+(0, x0)
+(s(x0), x1)
*(x0, 0)
*(x0, s(x1))
p(s(x0))
f(s(x0))
↳ QTRS
↳ AAECC Innermost
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ EdgeDeletionProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
-1(s(x), s(y)) → -1(x, y)
-(x, 0) → x
-(s(x), s(y)) → -(x, y)
+(0, y) → y
+(s(x), y) → s(+(x, y))
*(x, 0) → 0
*(x, s(y)) → +(x, *(x, y))
p(s(x)) → x
f(s(x)) → f(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x0, 0)
-(s(x0), s(x1))
+(0, x0)
+(s(x0), x1)
*(x0, 0)
*(x0, s(x1))
p(s(x0))
f(s(x0))
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
-1(s(x), s(y)) → -1(x, y)
[-^11, s1]
-^11: multiset
s1: multiset
↳ QTRS
↳ AAECC Innermost
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ EdgeDeletionProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDPOrderProof
↳ QDP
↳ PisEmptyProof
↳ QDP
-(x, 0) → x
-(s(x), s(y)) → -(x, y)
+(0, y) → y
+(s(x), y) → s(+(x, y))
*(x, 0) → 0
*(x, s(y)) → +(x, *(x, y))
p(s(x)) → x
f(s(x)) → f(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x0, 0)
-(s(x0), s(x1))
+(0, x0)
+(s(x0), x1)
*(x0, 0)
*(x0, s(x1))
p(s(x0))
f(s(x0))
↳ QTRS
↳ AAECC Innermost
↳ QTRS
↳ DependencyPairsProof
↳ QDP
↳ EdgeDeletionProof
↳ QDP
↳ DependencyGraphProof
↳ AND
↳ QDP
↳ QDP
↳ QDP
↳ QDP
F(s(x)) → F(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x, 0) → x
-(s(x), s(y)) → -(x, y)
+(0, y) → y
+(s(x), y) → s(+(x, y))
*(x, 0) → 0
*(x, s(y)) → +(x, *(x, y))
p(s(x)) → x
f(s(x)) → f(-(p(*(s(x), s(x))), *(s(x), s(x))))
-(x0, 0)
-(s(x0), s(x1))
+(0, x0)
+(s(x0), x1)
*(x0, 0)
*(x0, s(x1))
p(s(x0))
f(s(x0))