Termination proof

1: switching to dependency pairs

The following set of initial dependency pairs has been identified.

active#( __( __( X , Y ) , Z ) ) → __#( X , __( Y , Z ) )

active#( __( __( X , Y ) , Z ) ) → __#( Y , Z )

active#( isList( V ) ) → isNeList#( V )

active#( isList( __( V1 , V2 ) ) ) → and#( isList( V1 ) , isList( V2 ) )

active#( isList( __( V1 , V2 ) ) ) → isList#( V1 )

active#( isList( __( V1 , V2 ) ) ) → isList#( V2 )

active#( isNeList( V ) ) → isQid#( V )

active#( isNeList( __( V1 , V2 ) ) ) → and#( isList( V1 ) , isNeList( V2 ) )

active#( isNeList( __( V1 , V2 ) ) ) → isList#( V1 )

active#( isNeList( __( V1 , V2 ) ) ) → isNeList#( V2 )

active#( isNeList( __( V1 , V2 ) ) ) → and#( isNeList( V1 ) , isList( V2 ) )

active#( isNeList( __( V1 , V2 ) ) ) → isNeList#( V1 )

active#( isNeList( __( V1 , V2 ) ) ) → isList#( V2 )

active#( isNePal( V ) ) → isQid#( V )

active#( isNePal( __( I , __( P , I ) ) ) ) → and#( isQid( I ) , isPal( P ) )

active#( isNePal( __( I , __( P , I ) ) ) ) → isQid#( I )

active#( isNePal( __( I , __( P , I ) ) ) ) → isPal#( P )

active#( isPal( V ) ) → isNePal#( V )

active#( __( X1 , X2 ) ) → __#( active( X1 ) , X2 )

active#( __( X1 , X2 ) ) → active#( X1 )

active#( __( X1 , X2 ) ) → __#( X1 , active( X2 ) )

active#( __( X1 , X2 ) ) → active#( X2 )

active#( and( X1 , X2 ) ) → and#( active( X1 ) , X2 )

active#( and( X1 , X2 ) ) → active#( X1 )

__#( mark( X1 ) , X2 ) → __#( X1 , X2 )

__#( X1 , mark( X2 ) ) → __#( X1 , X2 )

and#( mark( X1 ) , X2 ) → and#( X1 , X2 )

proper#( __( X1 , X2 ) ) → __#( proper( X1 ) , proper( X2 ) )

proper#( __( X1 , X2 ) ) → proper#( X1 )

proper#( __( X1 , X2 ) ) → proper#( X2 )

proper#( and( X1 , X2 ) ) → and#( proper( X1 ) , proper( X2 ) )

proper#( and( X1 , X2 ) ) → proper#( X1 )

proper#( and( X1 , X2 ) ) → proper#( X2 )

proper#( isList( X ) ) → isList#( proper( X ) )

proper#( isList( X ) ) → proper#( X )

proper#( isNeList( X ) ) → isNeList#( proper( X ) )

proper#( isNeList( X ) ) → proper#( X )

proper#( isQid( X ) ) → isQid#( proper( X ) )

proper#( isQid( X ) ) → proper#( X )

proper#( isNePal( X ) ) → isNePal#( proper( X ) )

proper#( isNePal( X ) ) → proper#( X )

proper#( isPal( X ) ) → isPal#( proper( X ) )

proper#( isPal( X ) ) → proper#( X )

__#( ok( X1 ) , ok( X2 ) ) → __#( X1 , X2 )

and#( ok( X1 ) , ok( X2 ) ) → and#( X1 , X2 )

isList#( ok( X ) ) → isList#( X )

isNeList#( ok( X ) ) → isNeList#( X )

isQid#( ok( X ) ) → isQid#( X )

isNePal#( ok( X ) ) → isNePal#( X )

isPal#( ok( X ) ) → isPal#( X )

top#( mark( X ) ) → top#( proper( X ) )

top#( mark( X ) ) → proper#( X )

top#( ok( X ) ) → top#( active( X ) )

top#( ok( X ) ) → active#( X )

1.1: dependency graph processor

The dependency pairs are split into 10 component(s).

The 1st component contains the pair(s)

top#( ok( X ) ) → top#( active( X ) )

top#( mark( X ) ) → top#( proper( X ) )

1.1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a] = 2

[mark (x₁) ] = x₁ + 1

[__ (x₁, x₂) ] = 2 x₁ + x₂ + 1

[isNePal (x₁) ] = 2 x₁ + 2

[active (x₁) ] = x₁

[i] = 2

[nil] = 2

[tt] = 2

[o] = 2

[e] = 2

[u] = 2

[and (x₁, x₂) ] = x₁ + x₂

[isNeList (x₁) ] = 3 x₁ + 1

[isQid (x₁) ] = 2 x₁

[isPal (x₁) ] = 2 x₁ + 3

[top# (x₁) ] = x₁

[ok (x₁) ] = x₁

[isList (x₁) ] = 3 x₁ + 2

[top (x₁) ] = 0

[proper (x₁) ] = x₁

[f(x₁, ..., x_n)] = x₁ + ... + x_n + 1 for all other symbols f of arity n

one remains with the following pair(s).

top#( ok( X ) ) → top#( active( X ) )

1.1.1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a] = 2

[__ (x₁, x₂) ] = x₁ + 3 x₂

[mark (x₁) ] = 0

[isNePal (x₁) ] = x₁

[active (x₁) ] = x₁

[i] = 2

[nil] = 2

[tt] = 2

[o] = 2

[e] = 2

[u] = 2

[and (x₁, x₂) ] = 2 x₁

[isNeList (x₁) ] = 2 x₁ + 2

[isQid (x₁) ] = 2 x₁

[isPal (x₁) ] = x₁

[top# (x₁) ] = 3 x₁

[ok (x₁) ] = 2 x₁ + 2

[isList (x₁) ] = 2 x₁

[top (x₁) ] = 0

[proper (x₁) ] = 3 x₁

[f(x₁, ..., x_n)] = x₁ + ... + x_n + 1 for all other symbols f of arity n

one remains with the following pair(s).

none

1.1.1.1.1: P is empty

All dependency pairs have been removed.

The 2nd component contains the pair(s)

active#( __( X1 , X2 ) ) → active#( X2 )

active#( __( X1 , X2 ) ) → active#( X1 )

active#( and( X1 , X2 ) ) → active#( X1 )

1.1.2: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[__ (x₁, x₂) ] = x₁ + x₂ + 2

[mark (x₁) ] = 0

[a] = 2

[active# (x₁) ] = 2 x₁

[isNePal (x₁) ] = 0

[active (x₁) ] = x₁

[i] = 2

[nil] = 0

[tt] = 2

[o] = 2

[e] = 2

[u] = 0

[and (x₁, x₂) ] = 2 x₁ + 3 x₂ + 1

[isNeList (x₁) ] = 3 x₁ + 3

[isQid (x₁) ] = 3 x₁ + 3

[isPal (x₁) ] = 3 x₁ + 1

[ok (x₁) ] = 0

[isList (x₁) ] = 3

[top (x₁) ] = 0

[proper (x₁) ] = 2 x₁

[f(x₁, ..., x_n)] = x₁ + ... + x_n + 1 for all other symbols f of arity n

one remains with the following pair(s).

none

1.1.2.1: P is empty

All dependency pairs have been removed.

The 3rd component contains the pair(s)

proper#( __( X1 , X2 ) ) → proper#( X2 )

proper#( __( X1 , X2 ) ) → proper#( X1 )

proper#( and( X1 , X2 ) ) → proper#( X1 )

proper#( and( X1 , X2 ) ) → proper#( X2 )

proper#( isList( X ) ) → proper#( X )

proper#( isNeList( X ) ) → proper#( X )

proper#( isQid( X ) ) → proper#( X )

proper#( isNePal( X ) ) → proper#( X )

proper#( isPal( X ) ) → proper#( X )

1.1.3: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[__ (x₁, x₂) ] = 2 x₁ + x₂

[mark (x₁) ] = 0

[a] = 3

[isNePal (x₁) ] = 2 x₁ + 1

[active (x₁) ] = 2 x₁

[i] = 3

[nil] = 3

[tt] = 0

[o] = 3

[e] = 3

[u] = 1

[and (x₁, x₂) ] = x₁ + 2 x₂ + 1

[isNeList (x₁) ] = x₁ + 3

[proper# (x₁) ] = x₁

[isQid (x₁) ] = x₁ + 1

[isPal (x₁) ] = x₁ + 1

[ok (x₁) ] = 0

[isList (x₁) ] = x₁ + 3

[top (x₁) ] = 0

[proper (x₁) ] = x₁

[f(x₁, ..., x_n)] = x₁ + ... + x_n + 1 for all other symbols f of arity n

one remains with the following pair(s).

proper#( __( X1 , X2 ) ) → proper#( X2 )

proper#( __( X1 , X2 ) ) → proper#( X1 )

1.1.3.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[__ (x₁, x₂) ] = 2 x₁ + x₂ + 1

[mark (x₁) ] = 0

[a] = 3

[isNePal (x₁) ] = x₁

[active (x₁) ] = 2 x₁

[i] = 3

[nil] = 0

[tt] = 3

[o] = 3

[e] = 3

[u] = 3

[and (x₁, x₂) ] = x₁ + 3 x₂

[isNeList (x₁) ] = 0

[proper# (x₁) ] = 2 x₁

[isQid (x₁) ] = 3 x₁

[isPal (x₁) ] = x₁

[ok (x₁) ] = 0

[isList (x₁) ] = 2 x₁

[top (x₁) ] = 0

[proper (x₁) ] = x₁

[f(x₁, ..., x_n)] = x₁ + ... + x_n + 1 for all other symbols f of arity n

one remains with the following pair(s).

none

1.1.3.1.1: P is empty

All dependency pairs have been removed.

The 4th component contains the pair(s)

__#( X1 , mark( X2 ) ) → __#( X1 , X2 )

__#( mark( X1 ) , X2 ) → __#( X1 , X2 )

__#( ok( X1 ) , ok( X2 ) ) → __#( X1 , X2 )

1.1.4: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a] = 0

[mark (x₁) ] = x₁ + 1

[__ (x₁, x₂) ] = x₁ + x₂

[isNePal (x₁) ] = 0

[active (x₁) ] = x₁ + 1

[__# (x₁, x₂) ] = 3 x₁ + 3 x₂

[i] = 0

[nil] = 0

[tt] = 0

[o] = 0

[e] = 0

[u] = 0

[and (x₁, x₂) ] = x₁ + 2 x₂

[isNeList (x₁) ] = 0

[isQid (x₁) ] = 0

[isPal (x₁) ] = 0

[ok (x₁) ] = x₁

[isList (x₁) ] = 0

[top (x₁) ] = 0

[proper (x₁) ] = 0

[f(x₁, ..., x_n)] = x₁ + ... + x_n + 1 for all other symbols f of arity n

one remains with the following pair(s).

__#( ok( X1 ) , ok( X2 ) ) → __#( X1 , X2 )

1.1.4.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a] = 1

[__ (x₁, x₂) ] = x₁ + 2 x₂

[mark (x₁) ] = 0

[isNePal (x₁) ] = 2 x₁ + 1

[active (x₁) ] = x₁

[__# (x₁, x₂) ] = x₁

[i] = 1

[nil] = 2

[tt] = 3

[o] = 3

[e] = 1

[u] = 3

[and (x₁, x₂) ] = x₁

[isNeList (x₁) ] = 3 x₁ + 2

[isQid (x₁) ] = x₁

[isPal (x₁) ] = 3 x₁ + 1

[ok (x₁) ] = 2 x₁ + 1

[isList (x₁) ] = 2 x₁

[top (x₁) ] = 0

[proper (x₁) ] = 3 x₁

[f(x₁, ..., x_n)] = x₁ + ... + x_n + 1 for all other symbols f of arity n

one remains with the following pair(s).

none

1.1.4.1.1: P is empty

All dependency pairs have been removed.

The 5th component contains the pair(s)

and#( ok( X1 ) , ok( X2 ) ) → and#( X1 , X2 )

and#( mark( X1 ) , X2 ) → and#( X1 , X2 )

1.1.5: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a] = 2

[mark (x₁) ] = 0

[__ (x₁, x₂) ] = 3 x₁

[isNePal (x₁) ] = 2 x₁

[active (x₁) ] = x₁

[i] = 2

[nil] = 2

[tt] = 2

[o] = 2

[e] = 2

[u] = 1

[and (x₁, x₂) ] = 2 x₁ + 1

[isNeList (x₁) ] = x₁

[isQid (x₁) ] = 3 x₁

[isPal (x₁) ] = x₁

[ok (x₁) ] = x₁ + 1

[isList (x₁) ] = 3 x₁ + 1

[and# (x₁, x₂) ] = 2 x₁

[top (x₁) ] = 0

[proper (x₁) ] = 2 x₁

[f(x₁, ..., x_n)] = x₁ + ... + x_n + 1 for all other symbols f of arity n

one remains with the following pair(s).

and#( mark( X1 ) , X2 ) → and#( X1 , X2 )

1.1.5.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[mark (x₁) ] = x₁ + 1

[__ (x₁, x₂) ] = x₁ + x₂

[a] = 0

[isNePal (x₁) ] = 0

[active (x₁) ] = x₁ + 1

[i] = 0

[nil] = 0

[tt] = 0

[o] = 0

[e] = 0

[u] = 0

[and (x₁, x₂) ] = x₁ + x₂

[isNeList (x₁) ] = 0

[isQid (x₁) ] = 0

[isPal (x₁) ] = 0

[ok (x₁) ] = 0

[isList (x₁) ] = 0

[and# (x₁, x₂) ] = x₁

[top (x₁) ] = 0

[proper (x₁) ] = 0

[f(x₁, ..., x_n)] = x₁ + ... + x_n + 1 for all other symbols f of arity n

one remains with the following pair(s).

none

1.1.5.1.1: P is empty

All dependency pairs have been removed.

The 6th component contains the pair(s)

isList#( ok( X ) ) → isList#( X )

1.1.6: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[isList# (x₁) ] = x₁

[a] = 1

[__ (x₁, x₂) ] = x₁ + 2 x₂

[mark (x₁) ] = 0

[isNePal (x₁) ] = x₁

[active (x₁) ] = x₁

[i] = 3

[nil] = 1

[tt] = 2

[o] = 3

[e] = 1

[u] = 2

[and (x₁, x₂) ] = 2 x₁

[isNeList (x₁) ] = 2 x₁

[isQid (x₁) ] = 2 x₁ + 3

[isPal (x₁) ] = 2 x₁

[ok (x₁) ] = x₁ + 1

[isList (x₁) ] = 2 x₁

[top (x₁) ] = 0

[proper (x₁) ] = 2 x₁

[f(x₁, ..., x_n)] = x₁ + ... + x_n + 1 for all other symbols f of arity n

one remains with the following pair(s).

none

1.1.6.1: P is empty

All dependency pairs have been removed.

The 7th component contains the pair(s)

isNeList#( ok( X ) ) → isNeList#( X )

1.1.7: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a] = 1

[__ (x₁, x₂) ] = x₁ + 2 x₂

[mark (x₁) ] = 0

[isNePal (x₁) ] = x₁

[active (x₁) ] = x₁

[i] = 3

[nil] = 1

[tt] = 2

[o] = 3

[e] = 1

[u] = 2

[and (x₁, x₂) ] = 2 x₁

[isNeList# (x₁) ] = x₁

[isNeList (x₁) ] = 2 x₁

[isQid (x₁) ] = 2 x₁ + 3

[isPal (x₁) ] = 2 x₁

[ok (x₁) ] = x₁ + 1

[isList (x₁) ] = 2 x₁

[top (x₁) ] = 0

[proper (x₁) ] = 2 x₁

[f(x₁, ..., x_n)] = x₁ + ... + x_n + 1 for all other symbols f of arity n

one remains with the following pair(s).

none

1.1.7.1: P is empty

All dependency pairs have been removed.

The 8th component contains the pair(s)

isQid#( ok( X ) ) → isQid#( X )

1.1.8: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[isQid# (x₁) ] = x₁

[a] = 1

[__ (x₁, x₂) ] = x₁ + 2 x₂

[mark (x₁) ] = 0

[isNePal (x₁) ] = x₁

[active (x₁) ] = x₁

[i] = 3

[nil] = 1

[tt] = 2

[o] = 3

[e] = 1

[u] = 2

[and (x₁, x₂) ] = 2 x₁

[isNeList (x₁) ] = 2 x₁

[isQid (x₁) ] = 2 x₁ + 3

[isPal (x₁) ] = 2 x₁

[ok (x₁) ] = x₁ + 1

[isList (x₁) ] = 2 x₁

[top (x₁) ] = 0

[proper (x₁) ] = 2 x₁

[f(x₁, ..., x_n)] = x₁ + ... + x_n + 1 for all other symbols f of arity n

one remains with the following pair(s).

none

1.1.8.1: P is empty

All dependency pairs have been removed.

The 9th component contains the pair(s)

isNePal#( ok( X ) ) → isNePal#( X )

1.1.9: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a] = 1

[__ (x₁, x₂) ] = x₁ + 2 x₂

[mark (x₁) ] = 0

[isNePal (x₁) ] = x₁

[active (x₁) ] = x₁

[i] = 3

[nil] = 1

[tt] = 2

[o] = 3

[e] = 1

[u] = 2

[and (x₁, x₂) ] = 2 x₁

[isNeList (x₁) ] = 2 x₁

[isNePal# (x₁) ] = x₁

[isQid (x₁) ] = 2 x₁ + 3

[isPal (x₁) ] = 2 x₁

[ok (x₁) ] = x₁ + 1

[isList (x₁) ] = 2 x₁

[top (x₁) ] = 0

[proper (x₁) ] = 2 x₁

[f(x₁, ..., x_n)] = x₁ + ... + x_n + 1 for all other symbols f of arity n

one remains with the following pair(s).

none

1.1.9.1: P is empty

All dependency pairs have been removed.

The 10th component contains the pair(s)

isPal#( ok( X ) ) → isPal#( X )

1.1.10: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a] = 1

[__ (x₁, x₂) ] = x₁ + 2 x₂

[mark (x₁) ] = 0

[isPal# (x₁) ] = x₁

[isNePal (x₁) ] = x₁

[active (x₁) ] = x₁

[i] = 3

[nil] = 1

[tt] = 2

[o] = 3

[e] = 1

[u] = 2

[and (x₁, x₂) ] = 2 x₁

[isNeList (x₁) ] = 2 x₁

[isQid (x₁) ] = 2 x₁ + 3

[isPal (x₁) ] = 2 x₁

[ok (x₁) ] = x₁ + 1

[isList (x₁) ] = 2 x₁

[top (x₁) ] = 0

[proper (x₁) ] = 2 x₁

[f(x₁, ..., x_n)] = x₁ + ... + x_n + 1 for all other symbols f of arity n

one remains with the following pair(s).

none

1.1.10.1: P is empty

All dependency pairs have been removed.

active#( __( __( X , Y ) , Z ) )	→	__#( X , __( Y , Z ) )
active#( __( __( X , Y ) , Z ) )	→	__#( Y , Z )
active#( isList( V ) )	→	isNeList#( V )
active#( isList( __( V1 , V2 ) ) )	→	and#( isList( V1 ) , isList( V2 ) )
active#( isList( __( V1 , V2 ) ) )	→	isList#( V1 )
active#( isList( __( V1 , V2 ) ) )	→	isList#( V2 )
active#( isNeList( V ) )	→	isQid#( V )
active#( isNeList( __( V1 , V2 ) ) )	→	and#( isList( V1 ) , isNeList( V2 ) )
active#( isNeList( __( V1 , V2 ) ) )	→	isList#( V1 )
active#( isNeList( __( V1 , V2 ) ) )	→	isNeList#( V2 )
active#( isNeList( __( V1 , V2 ) ) )	→	and#( isNeList( V1 ) , isList( V2 ) )
active#( isNeList( __( V1 , V2 ) ) )	→	isNeList#( V1 )
active#( isNeList( __( V1 , V2 ) ) )	→	isList#( V2 )
active#( isNePal( V ) )	→	isQid#( V )
active#( isNePal( __( I , __( P , I ) ) ) )	→	and#( isQid( I ) , isPal( P ) )
active#( isNePal( __( I , __( P , I ) ) ) )	→	isQid#( I )
active#( isNePal( __( I , __( P , I ) ) ) )	→	isPal#( P )
active#( isPal( V ) )	→	isNePal#( V )
active#( __( X1 , X2 ) )	→	__#( active( X1 ) , X2 )
active#( __( X1 , X2 ) )	→	active#( X1 )
active#( __( X1 , X2 ) )	→	__#( X1 , active( X2 ) )
active#( __( X1 , X2 ) )	→	active#( X2 )
active#( and( X1 , X2 ) )	→	and#( active( X1 ) , X2 )
active#( and( X1 , X2 ) )	→	active#( X1 )
__#( mark( X1 ) , X2 )	→	__#( X1 , X2 )
__#( X1 , mark( X2 ) )	→	__#( X1 , X2 )
and#( mark( X1 ) , X2 )	→	and#( X1 , X2 )
proper#( __( X1 , X2 ) )	→	__#( proper( X1 ) , proper( X2 ) )
proper#( __( X1 , X2 ) )	→	proper#( X1 )
proper#( __( X1 , X2 ) )	→	proper#( X2 )
proper#( and( X1 , X2 ) )	→	and#( proper( X1 ) , proper( X2 ) )
proper#( and( X1 , X2 ) )	→	proper#( X1 )
proper#( and( X1 , X2 ) )	→	proper#( X2 )
proper#( isList( X ) )	→	isList#( proper( X ) )
proper#( isList( X ) )	→	proper#( X )
proper#( isNeList( X ) )	→	isNeList#( proper( X ) )
proper#( isNeList( X ) )	→	proper#( X )
proper#( isQid( X ) )	→	isQid#( proper( X ) )
proper#( isQid( X ) )	→	proper#( X )
proper#( isNePal( X ) )	→	isNePal#( proper( X ) )
proper#( isNePal( X ) )	→	proper#( X )
proper#( isPal( X ) )	→	isPal#( proper( X ) )
proper#( isPal( X ) )	→	proper#( X )
__#( ok( X1 ) , ok( X2 ) )	→	__#( X1 , X2 )
and#( ok( X1 ) , ok( X2 ) )	→	and#( X1 , X2 )
isList#( ok( X ) )	→	isList#( X )
isNeList#( ok( X ) )	→	isNeList#( X )
isQid#( ok( X ) )	→	isQid#( X )
isNePal#( ok( X ) )	→	isNePal#( X )
isPal#( ok( X ) )	→	isPal#( X )
top#( mark( X ) )	→	top#( proper( X ) )
top#( mark( X ) )	→	proper#( X )
top#( ok( X ) )	→	top#( active( X ) )
top#( ok( X ) )	→	active#( X )

[a]	=	2
[mark (x₁) ]	=	x₁ + 1
[__ (x₁, x₂) ]	=	2 x₁ + x₂ + 1
[isNePal (x₁) ]	=	2 x₁ + 2
[active (x₁) ]	=	x₁
[i]	=	2
[nil]	=	2
[tt]	=	2
[o]	=	2
[e]	=	2
[u]	=	2
[and (x₁, x₂) ]	=	x₁ + x₂
[isNeList (x₁) ]	=	3 x₁ + 1
[isQid (x₁) ]	=	2 x₁
[isPal (x₁) ]	=	2 x₁ + 3
[top# (x₁) ]	=	x₁
[ok (x₁) ]	=	x₁
[isList (x₁) ]	=	3 x₁ + 2
[top (x₁) ]	=	0
[proper (x₁) ]	=	x₁
[f(x₁, ..., x_n)]	=	x₁ + ... + x_n + 1	for all other symbols f of arity n

[a]	=	2
[__ (x₁, x₂) ]	=	x₁ + 3 x₂
[mark (x₁) ]	=	0
[isNePal (x₁) ]	=	x₁
[active (x₁) ]	=	x₁
[i]	=	2
[nil]	=	2
[tt]	=	2
[o]	=	2
[e]	=	2
[u]	=	2
[and (x₁, x₂) ]	=	2 x₁
[isNeList (x₁) ]	=	2 x₁ + 2
[isQid (x₁) ]	=	2 x₁
[isPal (x₁) ]	=	x₁
[top# (x₁) ]	=	3 x₁
[ok (x₁) ]	=	2 x₁ + 2
[isList (x₁) ]	=	2 x₁
[top (x₁) ]	=	0
[proper (x₁) ]	=	3 x₁
[f(x₁, ..., x_n)]	=	x₁ + ... + x_n + 1	for all other symbols f of arity n

[__ (x₁, x₂) ]	=	x₁ + x₂ + 2
[mark (x₁) ]	=	0
[a]	=	2
[active# (x₁) ]	=	2 x₁
[isNePal (x₁) ]	=	0
[active (x₁) ]	=	x₁
[i]	=	2
[nil]	=	0
[tt]	=	2
[o]	=	2
[e]	=	2
[u]	=	0
[and (x₁, x₂) ]	=	2 x₁ + 3 x₂ + 1
[isNeList (x₁) ]	=	3 x₁ + 3
[isQid (x₁) ]	=	3 x₁ + 3
[isPal (x₁) ]	=	3 x₁ + 1
[ok (x₁) ]	=	0
[isList (x₁) ]	=	3
[top (x₁) ]	=	0
[proper (x₁) ]	=	2 x₁
[f(x₁, ..., x_n)]	=	x₁ + ... + x_n + 1	for all other symbols f of arity n

[__ (x₁, x₂) ]	=	2 x₁ + x₂
[mark (x₁) ]	=	0
[a]	=	3
[isNePal (x₁) ]	=	2 x₁ + 1
[active (x₁) ]	=	2 x₁
[i]	=	3
[nil]	=	3
[tt]	=	0
[o]	=	3
[e]	=	3
[u]	=	1
[and (x₁, x₂) ]	=	x₁ + 2 x₂ + 1
[isNeList (x₁) ]	=	x₁ + 3
[proper# (x₁) ]	=	x₁
[isQid (x₁) ]	=	x₁ + 1
[isPal (x₁) ]	=	x₁ + 1
[ok (x₁) ]	=	0
[isList (x₁) ]	=	x₁ + 3
[top (x₁) ]	=	0
[proper (x₁) ]	=	x₁
[f(x₁, ..., x_n)]	=	x₁ + ... + x_n + 1	for all other symbols f of arity n

[a]	=	1
[__ (x₁, x₂) ]	=	x₁ + 2 x₂
[mark (x₁) ]	=	0
[isNePal (x₁) ]	=	2 x₁ + 1
[active (x₁) ]	=	x₁
[__# (x₁, x₂) ]	=	x₁
[i]	=	1
[nil]	=	2
[tt]	=	3
[o]	=	3
[e]	=	1
[u]	=	3
[and (x₁, x₂) ]	=	x₁
[isNeList (x₁) ]	=	3 x₁ + 2
[isQid (x₁) ]	=	x₁
[isPal (x₁) ]	=	3 x₁ + 1
[ok (x₁) ]	=	2 x₁ + 1
[isList (x₁) ]	=	2 x₁
[top (x₁) ]	=	0
[proper (x₁) ]	=	3 x₁
[f(x₁, ..., x_n)]	=	x₁ + ... + x_n + 1	for all other symbols f of arity n

[isList# (x₁) ]	=	x₁
[a]	=	1
[__ (x₁, x₂) ]	=	x₁ + 2 x₂
[mark (x₁) ]	=	0
[isNePal (x₁) ]	=	x₁
[active (x₁) ]	=	x₁
[i]	=	3
[nil]	=	1
[tt]	=	2
[o]	=	3
[e]	=	1
[u]	=	2
[and (x₁, x₂) ]	=	2 x₁
[isNeList (x₁) ]	=	2 x₁
[isQid (x₁) ]	=	2 x₁ + 3
[isPal (x₁) ]	=	2 x₁
[ok (x₁) ]	=	x₁ + 1
[isList (x₁) ]	=	2 x₁
[top (x₁) ]	=	0
[proper (x₁) ]	=	2 x₁
[f(x₁, ..., x_n)]	=	x₁ + ... + x_n + 1	for all other symbols f of arity n

[isQid# (x₁) ]	=	x₁
[a]	=	1
[__ (x₁, x₂) ]	=	x₁ + 2 x₂
[mark (x₁) ]	=	0
[isNePal (x₁) ]	=	x₁
[active (x₁) ]	=	x₁
[i]	=	3
[nil]	=	1
[tt]	=	2
[o]	=	3
[e]	=	1
[u]	=	2
[and (x₁, x₂) ]	=	2 x₁
[isNeList (x₁) ]	=	2 x₁
[isQid (x₁) ]	=	2 x₁ + 3
[isPal (x₁) ]	=	2 x₁
[ok (x₁) ]	=	x₁ + 1
[isList (x₁) ]	=	2 x₁
[top (x₁) ]	=	0
[proper (x₁) ]	=	2 x₁
[f(x₁, ..., x_n)]	=	x₁ + ... + x_n + 1	for all other symbols f of arity n