0 QTRS
↳1 Overlay + Local Confluence (⇔)
↳2 QTRS
↳3 DependencyPairsProof (⇔)
↳4 QDP
↳5 DependencyGraphProof (⇔)
↳6 AND
↳7 QDP
↳8 QDPOrderProof (⇔)
↳9 QDP
↳10 PisEmptyProof (⇔)
↳11 TRUE
↳12 QDP
↳13 QDPOrderProof (⇔)
↳14 QDP
↳15 PisEmptyProof (⇔)
↳16 TRUE
not(true) → false
not(false) → true
odd(0) → false
odd(s(x)) → not(odd(x))
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(s(x), y) → s(+(x, y))
not(true) → false
not(false) → true
odd(0) → false
odd(s(x)) → not(odd(x))
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(s(x), y) → s(+(x, y))
not(true)
not(false)
odd(0)
odd(s(x0))
+(x0, 0)
+(x0, s(x1))
+(s(x0), x1)
ODD(s(x)) → NOT(odd(x))
ODD(s(x)) → ODD(x)
+1(x, s(y)) → +1(x, y)
+1(s(x), y) → +1(x, y)
not(true) → false
not(false) → true
odd(0) → false
odd(s(x)) → not(odd(x))
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(s(x), y) → s(+(x, y))
not(true)
not(false)
odd(0)
odd(s(x0))
+(x0, 0)
+(x0, s(x1))
+(s(x0), x1)
+1(s(x), y) → +1(x, y)
+1(x, s(y)) → +1(x, y)
not(true) → false
not(false) → true
odd(0) → false
odd(s(x)) → not(odd(x))
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(s(x), y) → s(+(x, y))
not(true)
not(false)
odd(0)
odd(s(x0))
+(x0, 0)
+(x0, s(x1))
+(s(x0), x1)
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)
+1(x, s(y)) → +1(x, y)
[true, false, odd]
+2 > s1
odd: []
true: []
false: []
s1: [1]
0: []
+^12: [2,1]
+2: [2,1]
not(true) → false
not(false) → true
odd(0) → false
odd(s(x)) → not(odd(x))
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(s(x), y) → s(+(x, y))
not(true) → false
not(false) → true
odd(0) → false
odd(s(x)) → not(odd(x))
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(s(x), y) → s(+(x, y))
not(true)
not(false)
odd(0)
odd(s(x0))
+(x0, 0)
+(x0, s(x1))
+(s(x0), x1)
ODD(s(x)) → ODD(x)
not(true) → false
not(false) → true
odd(0) → false
odd(s(x)) → not(odd(x))
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(s(x), y) → s(+(x, y))
not(true)
not(false)
odd(0)
odd(s(x0))
+(x0, 0)
+(x0, s(x1))
+(s(x0), x1)
The following pairs can be oriented strictly and are deleted.
The remaining pairs can at least be oriented weakly.
ODD(s(x)) → ODD(x)
[not, odd] > true > false > [ODD1, s1]
0 > false > [ODD1, s1]
+2 > [ODD1, s1]
ODD1: [1]
odd: []
true: []
not: []
false: []
s1: [1]
0: []
+2: [1,2]
not(true) → false
not(false) → true
odd(0) → false
odd(s(x)) → not(odd(x))
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(s(x), y) → s(+(x, y))
not(true) → false
not(false) → true
odd(0) → false
odd(s(x)) → not(odd(x))
+(x, 0) → x
+(x, s(y)) → s(+(x, y))
+(s(x), y) → s(+(x, y))
not(true)
not(false)
odd(0)
odd(s(x0))
+(x0, 0)
+(x0, s(x1))
+(s(x0), x1)