Termination w.r.t. Q of the following Term Rewriting System could be proven:
Q restricted rewrite system:
The TRS R consists of the following rules:
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(V) → isQid(activate(V))
isNePal(n____(I, n____(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
Q is empty.
↳ QTRS
↳ RRRPoloQTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(V) → isQid(activate(V))
isNePal(n____(I, n____(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
Q is empty.
The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(V) → isQid(activate(V))
isNePal(n____(I, n____(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isPal(n__nil) → tt
isQid(n__a) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:
isNePal(V) → isQid(activate(V))
isPal(n__nil) → tt
isQid(n__e) → tt
isQid(n__i) → tt
isQid(n__o) → tt
Used ordering:
Polynomial interpretation [25]:
POL(__(x1, x2)) = 2·x1 + x2
POL(a) = 0
POL(activate(x1)) = x1
POL(and(x1, x2)) = 2·x1 + x2
POL(e) = 2
POL(i) = 1
POL(isList(x1)) = x1
POL(isNeList(x1)) = x1
POL(isNePal(x1)) = 1 + x1
POL(isPal(x1)) = 1 + x1
POL(isQid(x1)) = x1
POL(n____(x1, x2)) = 2·x1 + x2
POL(n__a) = 0
POL(n__e) = 2
POL(n__i) = 1
POL(n__isList(x1)) = x1
POL(n__isNeList(x1)) = x1
POL(n__isPal(x1)) = 1 + x1
POL(n__nil) = 0
POL(n__o) = 1
POL(n__u) = 0
POL(nil) = 0
POL(o) = 1
POL(tt) = 0
POL(u) = 0
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(n____(I, n____(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isQid(n__a) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
Q is empty.
The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(n____(I, n____(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isQid(n__a) → tt
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:
isQid(n__a) → tt
Used ordering:
Polynomial interpretation [25]:
POL(__(x1, x2)) = x1 + x2
POL(a) = 1
POL(activate(x1)) = x1
POL(and(x1, x2)) = x1 + x2
POL(e) = 0
POL(i) = 1
POL(isList(x1)) = 2·x1
POL(isNeList(x1)) = 2·x1
POL(isNePal(x1)) = x1
POL(isPal(x1)) = x1
POL(isQid(x1)) = x1
POL(n____(x1, x2)) = x1 + x2
POL(n__a) = 1
POL(n__e) = 0
POL(n__i) = 1
POL(n__isList(x1)) = 2·x1
POL(n__isNeList(x1)) = 2·x1
POL(n__isPal(x1)) = x1
POL(n__nil) = 0
POL(n__o) = 0
POL(n__u) = 0
POL(nil) = 0
POL(o) = 0
POL(tt) = 0
POL(u) = 0
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(n____(I, n____(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
Q is empty.
The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(V) → isQid(activate(V))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(n____(I, n____(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isPal(V) → isNePal(activate(V))
isQid(n__u) → tt
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:
__(__(X, Y), Z) → __(X, __(Y, Z))
__(X, nil) → X
__(nil, X) → X
isList(n____(V1, V2)) → and(isList(activate(V1)), n__isList(activate(V2)))
isNeList(n____(V1, V2)) → and(isList(activate(V1)), n__isNeList(activate(V2)))
isNeList(n____(V1, V2)) → and(isNeList(activate(V1)), n__isList(activate(V2)))
isNePal(n____(I, n____(P, I))) → and(isQid(activate(I)), n__isPal(activate(P)))
isQid(n__u) → tt
Used ordering:
Polynomial interpretation [25]:
POL(__(x1, x2)) = 2 + 2·x1 + x2
POL(a) = 0
POL(activate(x1)) = x1
POL(and(x1, x2)) = x1 + x2
POL(e) = 0
POL(i) = 0
POL(isList(x1)) = 2·x1
POL(isNeList(x1)) = 2·x1
POL(isNePal(x1)) = 2·x1
POL(isPal(x1)) = 2·x1
POL(isQid(x1)) = x1
POL(n____(x1, x2)) = 2 + 2·x1 + x2
POL(n__a) = 0
POL(n__e) = 0
POL(n__i) = 0
POL(n__isList(x1)) = 2·x1
POL(n__isNeList(x1)) = 2·x1
POL(n__isPal(x1)) = 2·x1
POL(n__nil) = 0
POL(n__o) = 0
POL(n__u) = 2
POL(nil) = 0
POL(o) = 0
POL(tt) = 0
POL(u) = 2
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isNeList(V) → isQid(activate(V))
isPal(V) → isNePal(activate(V))
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
Q is empty.
The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:
and(tt, X) → activate(X)
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isNeList(V) → isQid(activate(V))
isPal(V) → isNePal(activate(V))
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:
and(tt, X) → activate(X)
Used ordering:
Polynomial interpretation [25]:
POL(__(x1, x2)) = 2 + x1 + 2·x2
POL(a) = 2
POL(activate(x1)) = x1
POL(and(x1, x2)) = 2 + x1 + 2·x2
POL(e) = 0
POL(i) = 0
POL(isList(x1)) = x1
POL(isNeList(x1)) = x1
POL(isNePal(x1)) = x1
POL(isPal(x1)) = x1
POL(isQid(x1)) = x1
POL(n____(x1, x2)) = 2 + x1 + 2·x2
POL(n__a) = 2
POL(n__e) = 0
POL(n__i) = 0
POL(n__isList(x1)) = x1
POL(n__isNeList(x1)) = x1
POL(n__isPal(x1)) = x1
POL(n__nil) = 0
POL(n__o) = 0
POL(n__u) = 0
POL(nil) = 0
POL(o) = 0
POL(tt) = 0
POL(u) = 0
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isNeList(V) → isQid(activate(V))
isPal(V) → isNePal(activate(V))
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
Q is empty.
The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isNeList(V) → isQid(activate(V))
isPal(V) → isNePal(activate(V))
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:
isList(V) → isNeList(activate(V))
isList(n__nil) → tt
isPal(V) → isNePal(activate(V))
Used ordering:
Polynomial interpretation [25]:
POL(__(x1, x2)) = x1 + x2
POL(a) = 0
POL(activate(x1)) = x1
POL(e) = 0
POL(i) = 0
POL(isList(x1)) = 2 + x1
POL(isNeList(x1)) = x1
POL(isNePal(x1)) = 1 + x1
POL(isPal(x1)) = 2 + x1
POL(isQid(x1)) = x1
POL(n____(x1, x2)) = x1 + x2
POL(n__a) = 0
POL(n__e) = 0
POL(n__i) = 0
POL(n__isList(x1)) = 2 + x1
POL(n__isNeList(x1)) = x1
POL(n__isPal(x1)) = 2 + x1
POL(n__nil) = 1
POL(n__o) = 0
POL(n__u) = 0
POL(nil) = 1
POL(o) = 0
POL(tt) = 0
POL(u) = 0
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
isNeList(V) → isQid(activate(V))
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
Q is empty.
The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:
isNeList(V) → isQid(activate(V))
nil → n__nil
__(X1, X2) → n____(X1, X2)
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
isPal(X) → n__isPal(X)
a → n__a
e → n__e
i → n__i
o → n__o
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__isList(X)) → isList(X)
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__e) → e
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:
nil → n__nil
isList(X) → n__isList(X)
isNeList(X) → n__isNeList(X)
e → n__e
o → n__o
activate(n__isNeList(X)) → isNeList(X)
activate(n__isPal(X)) → isPal(X)
activate(n__a) → a
activate(n__i) → i
activate(n__o) → o
activate(n__u) → u
activate(X) → X
Used ordering:
Polynomial interpretation [25]:
POL(__(x1, x2)) = 2 + x1 + x2
POL(a) = 2
POL(activate(x1)) = 2 + 2·x1
POL(e) = 2
POL(i) = 1
POL(isList(x1)) = 2 + 2·x1
POL(isNeList(x1)) = 2 + 2·x1
POL(isPal(x1)) = x1
POL(isQid(x1)) = x1
POL(n____(x1, x2)) = 2 + x1 + x2
POL(n__a) = 2
POL(n__e) = 0
POL(n__i) = 1
POL(n__isList(x1)) = x1
POL(n__isNeList(x1)) = 1 + x1
POL(n__isPal(x1)) = x1
POL(n__nil) = 0
POL(n__o) = 1
POL(n__u) = 1
POL(nil) = 2
POL(o) = 2
POL(u) = 1
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
isNeList(V) → isQid(activate(V))
__(X1, X2) → n____(X1, X2)
isPal(X) → n__isPal(X)
a → n__a
i → n__i
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__isList(X)) → isList(X)
activate(n__e) → e
Q is empty.
The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:
isNeList(V) → isQid(activate(V))
__(X1, X2) → n____(X1, X2)
isPal(X) → n__isPal(X)
a → n__a
i → n__i
u → n__u
activate(n__nil) → nil
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__isList(X)) → isList(X)
activate(n__e) → e
Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:
isNeList(V) → isQid(activate(V))
isPal(X) → n__isPal(X)
a → n__a
u → n__u
activate(n__nil) → nil
activate(n__isList(X)) → isList(X)
Used ordering:
Polynomial interpretation [25]:
POL(__(x1, x2)) = x1 + x2
POL(a) = 1
POL(activate(x1)) = x1
POL(e) = 2
POL(i) = 1
POL(isList(x1)) = x1
POL(isNeList(x1)) = 2 + 2·x1
POL(isPal(x1)) = 2 + 2·x1
POL(isQid(x1)) = x1
POL(n____(x1, x2)) = x1 + x2
POL(n__a) = 0
POL(n__e) = 2
POL(n__i) = 1
POL(n__isList(x1)) = 1 + 2·x1
POL(n__isPal(x1)) = x1
POL(n__nil) = 2
POL(n__u) = 1
POL(nil) = 1
POL(u) = 2
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
__(X1, X2) → n____(X1, X2)
i → n__i
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__e) → e
Q is empty.
The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:
__(X1, X2) → n____(X1, X2)
i → n__i
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
activate(n__e) → e
Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:
activate(n__e) → e
Used ordering:
Polynomial interpretation [25]:
POL(__(x1, x2)) = 2·x1 + x2
POL(activate(x1)) = 2·x1
POL(e) = 1
POL(i) = 2
POL(n____(x1, x2)) = 2·x1 + x2
POL(n__e) = 2
POL(n__i) = 2
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
__(X1, X2) → n____(X1, X2)
i → n__i
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
Q is empty.
The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:
__(X1, X2) → n____(X1, X2)
i → n__i
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:
activate(n____(X1, X2)) → __(activate(X1), activate(X2))
Used ordering:
Polynomial interpretation [25]:
POL(__(x1, x2)) = 1 + 2·x1 + 2·x2
POL(activate(x1)) = 2·x1
POL(i) = 2
POL(n____(x1, x2)) = 1 + 2·x1 + 2·x2
POL(n__i) = 2
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
Q restricted rewrite system:
The TRS R consists of the following rules:
__(X1, X2) → n____(X1, X2)
i → n__i
Q is empty.
The following Q TRS is given: Q restricted rewrite system:
The TRS R consists of the following rules:
__(X1, X2) → n____(X1, X2)
i → n__i
Q is empty.
The following rules can be removed by the rule removal processor [15] because they are oriented strictly by a polynomial ordering:
__(X1, X2) → n____(X1, X2)
i → n__i
Used ordering:
Polynomial interpretation [25]:
POL(__(x1, x2)) = 2 + 2·x1 + 2·x2
POL(i) = 2
POL(n____(x1, x2)) = 1 + x1 + x2
POL(n__i) = 1
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RRRPoloQTRSProof
↳ QTRS
↳ RisEmptyProof
Q restricted rewrite system:
R is empty.
Q is empty.
The TRS R is empty. Hence, termination is trivially proven.