Termination proof

1: switching to dependency pairs

The following set of initial dependency pairs has been identified.

a____#( __( X , Y ) , Z ) → a____#( mark( X ) , a____( mark( Y ) , mark( Z ) ) )

a____#( __( X , Y ) , Z ) → mark#( X )

a____#( __( X , Y ) , Z ) → a____#( mark( Y ) , mark( Z ) )

a____#( __( X , Y ) , Z ) → mark#( Y )

a____#( __( X , Y ) , Z ) → mark#( Z )

a____#( X , nil ) → mark#( X )

a____#( nil , X ) → mark#( X )

a__U21#( tt , V2 ) → a__U22#( a__isList( V2 ) )

a__U21#( tt , V2 ) → a__isList#( V2 )

a__U41#( tt , V2 ) → a__U42#( a__isNeList( V2 ) )

a__U41#( tt , V2 ) → a__isNeList#( V2 )

a__U51#( tt , V2 ) → a__U52#( a__isList( V2 ) )

a__U51#( tt , V2 ) → a__isList#( V2 )

a__U71#( tt , P ) → a__U72#( a__isPal( P ) )

a__U71#( tt , P ) → a__isPal#( P )

a__isList#( V ) → a__U11#( a__isNeList( V ) )

a__isList#( V ) → a__isNeList#( V )

a__isList#( __( V1 , V2 ) ) → a__U21#( a__isList( V1 ) , V2 )

a__isList#( __( V1 , V2 ) ) → a__isList#( V1 )

a__isNeList#( V ) → a__U31#( a__isQid( V ) )

a__isNeList#( V ) → a__isQid#( V )

a__isNeList#( __( V1 , V2 ) ) → a__U41#( a__isList( V1 ) , V2 )

a__isNeList#( __( V1 , V2 ) ) → a__isList#( V1 )

a__isNeList#( __( V1 , V2 ) ) → a__U51#( a__isNeList( V1 ) , V2 )

a__isNeList#( __( V1 , V2 ) ) → a__isNeList#( V1 )

a__isNePal#( V ) → a__U61#( a__isQid( V ) )

a__isNePal#( V ) → a__isQid#( V )

a__isNePal#( __( I , __( P , I ) ) ) → a__U71#( a__isQid( I ) , P )

a__isNePal#( __( I , __( P , I ) ) ) → a__isQid#( I )

a__isPal#( V ) → a__U81#( a__isNePal( V ) )

a__isPal#( V ) → a__isNePal#( V )

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

mark#( __( X1 , X2 ) ) → mark#( X1 )

mark#( __( X1 , X2 ) ) → mark#( X2 )

mark#( U11( X ) ) → a__U11#( mark( X ) )

mark#( U11( X ) ) → mark#( X )

mark#( U21( X1 , X2 ) ) → a__U21#( mark( X1 ) , X2 )

mark#( U21( X1 , X2 ) ) → mark#( X1 )

mark#( U22( X ) ) → a__U22#( mark( X ) )

mark#( U22( X ) ) → mark#( X )

mark#( isList( X ) ) → a__isList#( X )

mark#( U31( X ) ) → a__U31#( mark( X ) )

mark#( U31( X ) ) → mark#( X )

mark#( U41( X1 , X2 ) ) → a__U41#( mark( X1 ) , X2 )

mark#( U41( X1 , X2 ) ) → mark#( X1 )

mark#( U42( X ) ) → a__U42#( mark( X ) )

mark#( U42( X ) ) → mark#( X )

mark#( isNeList( X ) ) → a__isNeList#( X )

mark#( U51( X1 , X2 ) ) → a__U51#( mark( X1 ) , X2 )

mark#( U51( X1 , X2 ) ) → mark#( X1 )

mark#( U52( X ) ) → a__U52#( mark( X ) )

mark#( U52( X ) ) → mark#( X )

mark#( U61( X ) ) → a__U61#( mark( X ) )

mark#( U61( X ) ) → mark#( X )

mark#( U71( X1 , X2 ) ) → a__U71#( mark( X1 ) , X2 )

mark#( U71( X1 , X2 ) ) → mark#( X1 )

mark#( U72( X ) ) → a__U72#( mark( X ) )

mark#( U72( X ) ) → mark#( X )

mark#( isPal( X ) ) → a__isPal#( X )

mark#( U81( X ) ) → a__U81#( mark( X ) )

mark#( U81( X ) ) → mark#( X )

mark#( isQid( X ) ) → a__isQid#( X )

mark#( isNePal( X ) ) → a__isNePal#( X )

1.1: dependency graph processor

The dependency pairs are split into 3 component(s).

The 1st component contains the pair(s)

a____#( __( X , Y ) , Z ) → mark#( X )

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

a____#( __( X , Y ) , Z ) → a____#( mark( X ) , a____( mark( Y ) , mark( Z ) ) )

a____#( __( X , Y ) , Z ) → a____#( mark( Y ) , mark( Z ) )

a____#( __( X , Y ) , Z ) → mark#( Y )

mark#( __( X1 , X2 ) ) → mark#( X1 )

mark#( __( X1 , X2 ) ) → mark#( X2 )

mark#( U11( X ) ) → mark#( X )

mark#( U21( X1 , X2 ) ) → mark#( X1 )

mark#( U22( X ) ) → mark#( X )

mark#( U31( X ) ) → mark#( X )

mark#( U41( X1 , X2 ) ) → mark#( X1 )

mark#( U42( X ) ) → mark#( X )

mark#( U51( X1 , X2 ) ) → mark#( X1 )

mark#( U52( X ) ) → mark#( X )

mark#( U61( X ) ) → mark#( X )

mark#( U71( X1 , X2 ) ) → mark#( X1 )

mark#( U72( X ) ) → mark#( X )

mark#( U81( X ) ) → mark#( X )

a____#( __( X , Y ) , Z ) → mark#( Z )

a____#( X , nil ) → mark#( X )

a____#( nil , X ) → mark#( X )

1.1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a__U31 (x₁) ] = 2 x₁

[U81 (x₁) ] = x₁

[__ (x₁, x₂) ] = x₁ + x₂

[a] = 0

[a__isQid (x₁) ] = 0

[isNePal (x₁) ] = 0

[U22 (x₁) ] = x₁

[a__U51 (x₁, x₂) ] = 2 x₁

[a__U22 (x₁) ] = x₁

[a____ (x₁, x₂) ] = x₁ + x₂

[a__U61 (x₁) ] = 2 x₁

[i] = 2

[U21 (x₁, x₂) ] = x₁

[U72 (x₁) ] = x₁

[a__U41 (x₁, x₂) ] = x₁

[u] = 0

[a__U81 (x₁) ] = x₁

[U71 (x₁, x₂) ] = 2 x₁

[a__U11 (x₁) ] = 2 x₁

[isNeList (x₁) ] = 0

[U52 (x₁) ] = 2 x₁

[a__isPal (x₁) ] = 0

[isPal (x₁) ] = 0

[U11 (x₁) ] = 2 x₁

[a____# (x₁, x₂) ] = x₁ + x₂

[isList (x₁) ] = 0

[a__U42 (x₁) ] = x₁

[a__U72 (x₁) ] = x₁

[mark (x₁) ] = x₁

[a__U21 (x₁, x₂) ] = x₁

[U61 (x₁) ] = 2 x₁

[U41 (x₁, x₂) ] = x₁

[U31 (x₁) ] = 2 x₁

[mark# (x₁) ] = x₁

[a__U71 (x₁, x₂) ] = 2 x₁

[U51 (x₁, x₂) ] = 2 x₁

[nil] = 1

[a__isNeList (x₁) ] = 0

[tt] = 0

[o] = 0

[e] = 0

[a__U52 (x₁) ] = 2 x₁

[a__isNePal (x₁) ] = 0

[isQid (x₁) ] = 0

[a__isList (x₁) ] = 0

[U42 (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).

1.1.1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a__U31 (x₁) ] = 2 x₁

[U81 (x₁) ] = x₁

[__ (x₁, x₂) ] = 2 x₁ + x₂ + 2

[a] = 0

[a__isQid (x₁) ] = 0

[isNePal (x₁) ] = 0

[U22 (x₁) ] = x₁

[a__U51 (x₁, x₂) ] = 2 x₁

[a__U22 (x₁) ] = x₁

[a____ (x₁, x₂) ] = 2 x₁ + x₂ + 2

[a__U61 (x₁) ] = x₁

[i] = 0

[U21 (x₁, x₂) ] = x₁

[U72 (x₁) ] = x₁

[a__U41 (x₁, x₂) ] = 2 x₁

[u] = 0

[a__U81 (x₁) ] = x₁

[U71 (x₁, x₂) ] = 2 x₁

[a__U11 (x₁) ] = x₁

[isNeList (x₁) ] = 0

[U52 (x₁) ] = x₁

[a__isPal (x₁) ] = 0

[isPal (x₁) ] = 0

[U11 (x₁) ] = x₁

[a____# (x₁, x₂) ] = 2 x₁ + x₂

[isList (x₁) ] = 0

[a__U42 (x₁) ] = 2 x₁

[a__U72 (x₁) ] = x₁

[mark (x₁) ] = x₁

[a__U21 (x₁, x₂) ] = x₁

[U61 (x₁) ] = x₁

[U41 (x₁, x₂) ] = 2 x₁

[U31 (x₁) ] = 2 x₁

[mark# (x₁) ] = x₁ + 1

[a__U71 (x₁, x₂) ] = 2 x₁

[U51 (x₁, x₂) ] = 2 x₁

[nil] = 0

[a__isNeList (x₁) ] = 0

[tt] = 0

[o] = 3

[e] = 2

[a__U52 (x₁) ] = x₁

[a__isNePal (x₁) ] = 0

[isQid (x₁) ] = 0

[a__isList (x₁) ] = 0

[U42 (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).

mark#( U11( X ) ) → mark#( X )

mark#( U21( X1 , X2 ) ) → mark#( X1 )

mark#( U22( X ) ) → mark#( X )

mark#( U31( X ) ) → mark#( X )

mark#( U41( X1 , X2 ) ) → mark#( X1 )

mark#( U42( X ) ) → mark#( X )

mark#( U51( X1 , X2 ) ) → mark#( X1 )

mark#( U52( X ) ) → mark#( X )

mark#( U61( X ) ) → mark#( X )

mark#( U71( X1 , X2 ) ) → mark#( X1 )

mark#( U72( X ) ) → mark#( X )

mark#( U81( X ) ) → mark#( X )

1.1.1.1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a__U31 (x₁) ] = x₁

[U81 (x₁) ] = x₁

[__ (x₁, x₂) ] = x₁ + x₂

[a] = 0

[a__isQid (x₁) ] = 0

[isNePal (x₁) ] = 1

[U22 (x₁) ] = 2 x₁

[a__U51 (x₁, x₂) ] = x₁

[a__U22 (x₁) ] = 2 x₁

[a____ (x₁, x₂) ] = x₁ + x₂

[a__U61 (x₁) ] = 2 x₁ + 1

[i] = 0

[U72 (x₁) ] = x₁

[U21 (x₁, x₂) ] = x₁

[a__U41 (x₁, x₂) ] = 2 x₁

[u] = 0

[a__U81 (x₁) ] = x₁

[U71 (x₁, x₂) ] = x₁ + 1

[a__U11 (x₁) ] = x₁

[isNeList (x₁) ] = 0

[U52 (x₁) ] = 2 x₁

[a__isPal (x₁) ] = 1

[isPal (x₁) ] = 1

[U11 (x₁) ] = x₁

[isList (x₁) ] = 0

[a__U42 (x₁) ] = x₁

[a__U72 (x₁) ] = x₁

[mark (x₁) ] = x₁

[a__U21 (x₁, x₂) ] = x₁

[U41 (x₁, x₂) ] = 2 x₁

[U61 (x₁) ] = 2 x₁ + 1

[U31 (x₁) ] = x₁

[mark# (x₁) ] = x₁

[a__U71 (x₁, x₂) ] = x₁ + 1

[U51 (x₁, x₂) ] = x₁

[nil] = 0

[a__isNeList (x₁) ] = 0

[tt] = 0

[o] = 0

[e] = 2

[a__U52 (x₁) ] = 2 x₁

[a__isNePal (x₁) ] = 1

[isQid (x₁) ] = 0

[a__isList (x₁) ] = 0

[U42 (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).

mark#( U11( X ) ) → mark#( X )

mark#( U21( X1 , X2 ) ) → mark#( X1 )

mark#( U22( X ) ) → mark#( X )

mark#( U31( X ) ) → mark#( X )

mark#( U41( X1 , X2 ) ) → mark#( X1 )

mark#( U42( X ) ) → mark#( X )

mark#( U51( X1 , X2 ) ) → mark#( X1 )

mark#( U52( X ) ) → mark#( X )

mark#( U72( X ) ) → mark#( X )

mark#( U81( X ) ) → mark#( X )

1.1.1.1.1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a__U31 (x₁) ] = x₁

[U81 (x₁) ] = x₁ + 1

[__ (x₁, x₂) ] = 2 x₁ + x₂ + 2

[a] = 0

[a__isQid (x₁) ] = 0

[isNePal (x₁) ] = 2 x₁

[a__U51 (x₁, x₂) ] = x₁

[U22 (x₁) ] = x₁

[a__U22 (x₁) ] = x₁

[a____ (x₁, x₂) ] = 2 x₁ + x₂ + 2

[a__U61 (x₁) ] = 0

[i] = 2

[U72 (x₁) ] = x₁

[U21 (x₁, x₂) ] = 2 x₁

[a__U41 (x₁, x₂) ] = x₁

[u] = 0

[a__U81 (x₁) ] = x₁ + 1

[U71 (x₁, x₂) ] = 2 x₁ + 1

[a__U11 (x₁) ] = 2 x₁

[isNeList (x₁) ] = 0

[U52 (x₁) ] = 2 x₁

[a__isPal (x₁) ] = 2 x₁ + 1

[isPal (x₁) ] = 2 x₁ + 1

[U11 (x₁) ] = 2 x₁

[isList (x₁) ] = 0

[a__U42 (x₁) ] = 2 x₁

[a__U72 (x₁) ] = x₁

[mark (x₁) ] = x₁

[a__U21 (x₁, x₂) ] = 2 x₁

[U41 (x₁, x₂) ] = x₁

[U61 (x₁) ] = 0

[U31 (x₁) ] = x₁

[mark# (x₁) ] = 2 x₁

[a__U71 (x₁, x₂) ] = 2 x₁ + 1

[U51 (x₁, x₂) ] = x₁

[nil] = 0

[a__isNeList (x₁) ] = 0

[tt] = 0

[o] = 0

[e] = 0

[a__U52 (x₁) ] = 2 x₁

[a__isNePal (x₁) ] = 2 x₁

[isQid (x₁) ] = 0

[a__isList (x₁) ] = 0

[U42 (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).

1.1.1.1.1.1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a__U31 (x₁) ] = 2 x₁

[U81 (x₁) ] = 0

[__ (x₁, x₂) ] = x₁ + x₂ + 2

[a] = 0

[a__isQid (x₁) ] = 0

[isNePal (x₁) ] = x₁ + 1

[a__U51 (x₁, x₂) ] = x₁

[U22 (x₁) ] = 2 x₁

[a__U22 (x₁) ] = 2 x₁

[a____ (x₁, x₂) ] = x₁ + x₂ + 2

[a__U61 (x₁) ] = 0

[i] = 0

[U72 (x₁) ] = x₁ + 1

[U21 (x₁, x₂) ] = x₁

[a__U41 (x₁, x₂) ] = 2 x₁

[u] = 1

[a__U81 (x₁) ] = 0

[U71 (x₁, x₂) ] = x₁ + 3

[a__U11 (x₁) ] = x₁

[isNeList (x₁) ] = 0

[U52 (x₁) ] = x₁

[a__isPal (x₁) ] = 2

[isPal (x₁) ] = 2

[U11 (x₁) ] = x₁

[isList (x₁) ] = 0

[a__U42 (x₁) ] = x₁

[a__U72 (x₁) ] = x₁ + 1

[mark (x₁) ] = x₁

[a__U21 (x₁, x₂) ] = x₁

[U41 (x₁, x₂) ] = 2 x₁

[U61 (x₁) ] = 0

[U31 (x₁) ] = 2 x₁

[mark# (x₁) ] = x₁

[a__U71 (x₁, x₂) ] = x₁ + 3

[U51 (x₁, x₂) ] = x₁

[nil] = 2

[a__isNeList (x₁) ] = 0

[tt] = 0

[o] = 0

[e] = 0

[a__U52 (x₁) ] = x₁

[a__isNePal (x₁) ] = x₁ + 1

[isQid (x₁) ] = 0

[a__isList (x₁) ] = 0

[U42 (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).

1.1.1.1.1.1.1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a__U31 (x₁) ] = x₁

[U81 (x₁) ] = x₁

[__ (x₁, x₂) ] = 2 x₁ + x₂

[a] = 1

[a__isQid (x₁) ] = x₁

[isNePal (x₁) ] = 2 x₁

[a__U51 (x₁, x₂) ] = 2 x₁ + x₂

[U22 (x₁) ] = x₁ + 2

[a__U22 (x₁) ] = x₁ + 2

[a____ (x₁, x₂) ] = 2 x₁ + x₂

[a__U61 (x₁) ] = x₁

[i] = 2

[U72 (x₁) ] = 1

[U21 (x₁, x₂) ] = 2 x₁ + x₂

[a__U41 (x₁, x₂) ] = 2 x₁ + x₂

[u] = 1

[a__U81 (x₁) ] = x₁

[U71 (x₁, x₂) ] = 2 x₁ + 2 x₂

[a__U11 (x₁) ] = x₁

[isNeList (x₁) ] = x₁

[U52 (x₁) ] = x₁ + 1

[a__isPal (x₁) ] = 2 x₁

[isPal (x₁) ] = 2 x₁

[U11 (x₁) ] = x₁

[isList (x₁) ] = x₁

[a__U42 (x₁) ] = x₁ + 2

[a__U72 (x₁) ] = 1

[mark (x₁) ] = x₁

[a__U21 (x₁, x₂) ] = 2 x₁ + x₂

[U41 (x₁, x₂) ] = 2 x₁ + x₂

[U61 (x₁) ] = x₁

[U31 (x₁) ] = x₁

[mark# (x₁) ] = 2 x₁

[a__U71 (x₁, x₂) ] = 2 x₁ + 2 x₂

[U51 (x₁, x₂) ] = 2 x₁ + x₂

[nil] = 2

[a__isNeList (x₁) ] = x₁

[tt] = 1

[o] = 1

[e] = 2

[a__U52 (x₁) ] = x₁ + 1

[a__isNePal (x₁) ] = 2 x₁

[isQid (x₁) ] = x₁

[a__isList (x₁) ] = x₁

[U42 (x₁) ] = x₁ + 2

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

one remains with the following pair(s).

mark#( U11( X ) ) → mark#( X )

mark#( U21( X1 , X2 ) ) → mark#( X1 )

mark#( U31( X ) ) → mark#( X )

mark#( U41( X1 , X2 ) ) → mark#( X1 )

mark#( U51( X1 , X2 ) ) → mark#( X1 )

1.1.1.1.1.1.1.1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a__U31 (x₁) ] = 2 x₁

[U81 (x₁) ] = 0

[__ (x₁, x₂) ] = 3 x₁ + x₂ + 2

[a] = 1

[a__isQid (x₁) ] = 0

[isNePal (x₁) ] = 0

[a__U51 (x₁, x₂) ] = x₁ + x₂ + 2

[U22 (x₁) ] = 0

[a__U22 (x₁) ] = 0

[a____ (x₁, x₂) ] = 3 x₁ + x₂ + 2

[a__U61 (x₁) ] = 0

[i] = 0

[U72 (x₁) ] = 0

[U21 (x₁, x₂) ] = x₁

[a__U41 (x₁, x₂) ] = x₁

[u] = 0

[a__U81 (x₁) ] = 0

[U71 (x₁, x₂) ] = 0

[a__U11 (x₁) ] = 2 x₁

[isNeList (x₁) ] = x₁

[U52 (x₁) ] = 2

[a__isPal (x₁) ] = 0

[isPal (x₁) ] = 0

[U11 (x₁) ] = 2 x₁

[isList (x₁) ] = 2 x₁

[a__U42 (x₁) ] = 0

[a__U72 (x₁) ] = 0

[mark (x₁) ] = x₁

[U41 (x₁, x₂) ] = x₁

[a__U21 (x₁, x₂) ] = x₁

[U61 (x₁) ] = 0

[U31 (x₁) ] = 2 x₁

[mark# (x₁) ] = 2 x₁

[a__U71 (x₁, x₂) ] = 0

[U51 (x₁, x₂) ] = x₁ + x₂ + 2

[nil] = 2

[a__isNeList (x₁) ] = x₁

[tt] = 0

[o] = 0

[e] = 0

[a__U52 (x₁) ] = 2

[a__isNePal (x₁) ] = 0

[isQid (x₁) ] = 0

[a__isList (x₁) ] = 2 x₁

[U42 (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).

mark#( U11( X ) ) → mark#( X )

mark#( U21( X1 , X2 ) ) → mark#( X1 )

mark#( U31( X ) ) → mark#( X )

mark#( U41( X1 , X2 ) ) → mark#( X1 )

1.1.1.1.1.1.1.1.1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a__U31 (x₁) ] = 2 x₁

[U81 (x₁) ] = 0

[__ (x₁, x₂) ] = 2 x₁ + x₂ + 1

[a] = 0

[a__isQid (x₁) ] = x₁

[isNePal (x₁) ] = 0

[a__U51 (x₁, x₂) ] = 0

[U22 (x₁) ] = 0

[a____ (x₁, x₂) ] = 2 x₁ + x₂ + 1

[a__U22 (x₁) ] = 0

[a__U61 (x₁) ] = 0

[i] = 0

[U72 (x₁) ] = 0

[U21 (x₁, x₂) ] = x₁

[a__U41 (x₁, x₂) ] = 2 x₁ + 1

[u] = 0

[a__U81 (x₁) ] = 0

[U71 (x₁, x₂) ] = 0

[a__U11 (x₁) ] = x₁

[isNeList (x₁) ] = 2 x₁

[U52 (x₁) ] = 0

[a__isPal (x₁) ] = 0

[isPal (x₁) ] = 0

[U11 (x₁) ] = x₁

[isList (x₁) ] = 2 x₁

[a__U42 (x₁) ] = 0

[a__U72 (x₁) ] = 0

[mark (x₁) ] = x₁

[U41 (x₁, x₂) ] = 2 x₁ + 1

[a__U21 (x₁, x₂) ] = x₁

[U61 (x₁) ] = 0

[U31 (x₁) ] = 2 x₁

[mark# (x₁) ] = x₁

[a__U71 (x₁, x₂) ] = 0

[U51 (x₁, x₂) ] = 0

[nil] = 0

[a__isNeList (x₁) ] = 2 x₁

[tt] = 0

[o] = 1

[e] = 0

[a__U52 (x₁) ] = 0

[a__isNePal (x₁) ] = 0

[isQid (x₁) ] = x₁

[a__isList (x₁) ] = 2 x₁

[U42 (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).

mark#( U11( X ) ) → mark#( X )

mark#( U21( X1 , X2 ) ) → mark#( X1 )

mark#( U31( X ) ) → mark#( X )

1.1.1.1.1.1.1.1.1.1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a__U31 (x₁) ] = 2 x₁

[U81 (x₁) ] = 0

[__ (x₁, x₂) ] = 2 x₁ + x₂ + 2

[a] = 0

[a__isQid (x₁) ] = 0

[isNePal (x₁) ] = 0

[a__U51 (x₁, x₂) ] = 0

[U22 (x₁) ] = 0

[a____ (x₁, x₂) ] = 2 x₁ + x₂ + 2

[a__U22 (x₁) ] = 0

[a__U61 (x₁) ] = 0

[i] = 0

[U72 (x₁) ] = 0

[U21 (x₁, x₂) ] = 2 x₁ + 2

[a__U41 (x₁, x₂) ] = 0

[u] = 0

[a__U81 (x₁) ] = 0

[U71 (x₁, x₂) ] = 0

[a__U11 (x₁) ] = 2 x₁

[isNeList (x₁) ] = 0

[U52 (x₁) ] = 0

[a__isPal (x₁) ] = 2

[isPal (x₁) ] = 2

[U11 (x₁) ] = 2 x₁

[isList (x₁) ] = x₁

[a__U42 (x₁) ] = 0

[a__U72 (x₁) ] = 0

[mark (x₁) ] = x₁

[a__U21 (x₁, x₂) ] = 2 x₁ + 2

[U41 (x₁, x₂) ] = 0

[U61 (x₁) ] = 0

[U31 (x₁) ] = 2 x₁

[mark# (x₁) ] = x₁

[a__U71 (x₁, x₂) ] = 0

[U51 (x₁, x₂) ] = 0

[nil] = 0

[a__isNeList (x₁) ] = 0

[tt] = 0

[o] = 0

[e] = 0

[a__U52 (x₁) ] = 0

[a__isNePal (x₁) ] = 0

[isQid (x₁) ] = 0

[a__isList (x₁) ] = x₁

[U42 (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).

mark#( U11( X ) ) → mark#( X )

mark#( U31( X ) ) → mark#( X )

1.1.1.1.1.1.1.1.1.1.1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a__U31 (x₁) ] = 2 x₁ + 1

[U81 (x₁) ] = 0

[__ (x₁, x₂) ] = x₁ + x₂

[a] = 0

[a__isQid (x₁) ] = 0

[isNePal (x₁) ] = 0

[a__U51 (x₁, x₂) ] = x₁

[U22 (x₁) ] = 1

[a____ (x₁, x₂) ] = x₁ + x₂

[a__U22 (x₁) ] = 1

[a__U61 (x₁) ] = 0

[i] = 1

[U72 (x₁) ] = 0

[U21 (x₁, x₂) ] = 2

[a__U41 (x₁, x₂) ] = 0

[u] = 0

[a__U81 (x₁) ] = 0

[U71 (x₁, x₂) ] = 0

[a__U11 (x₁) ] = 2 x₁

[isNeList (x₁) ] = 1

[U52 (x₁) ] = 0

[a__isPal (x₁) ] = 0

[isPal (x₁) ] = 0

[U11 (x₁) ] = 2 x₁

[isList (x₁) ] = 2

[a__U42 (x₁) ] = 0

[a__U72 (x₁) ] = 0

[mark (x₁) ] = x₁

[a__U21 (x₁, x₂) ] = 2

[U41 (x₁, x₂) ] = 0

[U61 (x₁) ] = 0

[U31 (x₁) ] = 2 x₁ + 1

[mark# (x₁) ] = x₁

[a__U71 (x₁, x₂) ] = 0

[U51 (x₁, x₂) ] = x₁

[nil] = 0

[a__isNeList (x₁) ] = 1

[tt] = 0

[o] = 0

[e] = 0

[a__isNePal (x₁) ] = 0

[a__U52 (x₁) ] = 0

[isQid (x₁) ] = 0

[a__isList (x₁) ] = 2

[U42 (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).

mark#( U11( X ) ) → mark#( X )

1.1.1.1.1.1.1.1.1.1.1.1.1: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a__U31 (x₁) ] = 0

[U81 (x₁) ] = 0

[a] = 0

[__ (x₁, x₂) ] = 2 x₁ + x₂

[a__isQid (x₁) ] = 2 x₁

[isNePal (x₁) ] = 0

[a__U51 (x₁, x₂) ] = 0

[U22 (x₁) ] = 0

[a____ (x₁, x₂) ] = 2 x₁ + x₂

[a__U22 (x₁) ] = 0

[a__U61 (x₁) ] = 0

[i] = 0

[U72 (x₁) ] = 0

[U21 (x₁, x₂) ] = x₁

[a__U41 (x₁, x₂) ] = 0

[u] = 2

[a__U81 (x₁) ] = 0

[U71 (x₁, x₂) ] = 0

[a__U11 (x₁) ] = 2 x₁ + 1

[isNeList (x₁) ] = 0

[U52 (x₁) ] = 0

[a__isPal (x₁) ] = 0

[isPal (x₁) ] = 0

[U11 (x₁) ] = 2 x₁ + 1

[isList (x₁) ] = 2 x₁ + 2

[a__U42 (x₁) ] = 0

[a__U72 (x₁) ] = 0

[mark (x₁) ] = x₁

[a__U21 (x₁, x₂) ] = x₁

[U41 (x₁, x₂) ] = 0

[U61 (x₁) ] = 0

[U31 (x₁) ] = 0

[mark# (x₁) ] = 2 x₁

[a__U71 (x₁, x₂) ] = 0

[U51 (x₁, x₂) ] = 0

[nil] = 0

[a__isNeList (x₁) ] = 0

[tt] = 0

[o] = 0

[e] = 0

[a__isNePal (x₁) ] = 0

[a__U52 (x₁) ] = 0

[isQid (x₁) ] = 2 x₁

[a__isList (x₁) ] = 2 x₁ + 2

[U42 (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

1.1.1.1.1.1.1.1.1.1.1.1.1.1: P is empty

All dependency pairs have been removed.

The 2nd component contains the pair(s)

a__U21#( tt , V2 ) → a__isList#( V2 )

a__isList#( V ) → a__isNeList#( V )

a__isNeList#( __( V1 , V2 ) ) → a__U41#( a__isList( V1 ) , V2 )

a__U41#( tt , V2 ) → a__isNeList#( V2 )

a__isNeList#( __( V1 , V2 ) ) → a__isList#( V1 )

a__isList#( __( V1 , V2 ) ) → a__U21#( a__isList( V1 ) , V2 )

a__isList#( __( V1 , V2 ) ) → a__isList#( V1 )

a__isNeList#( __( V1 , V2 ) ) → a__U51#( a__isNeList( V1 ) , V2 )

a__U51#( tt , V2 ) → a__isList#( V2 )

a__isNeList#( __( V1 , V2 ) ) → a__isNeList#( V1 )

1.1.2: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[U81 (x₁) ] = 1

[__ (x₁, x₂) ] = x₁ + x₂ + 3

[a] = 1

[isNePal (x₁) ] = x₁

[a__U51 (x₁, x₂) ] = 0

[a__U22 (x₁) ] = 0

[i] = 2

[U21 (x₁, x₂) ] = 0

[U72 (x₁) ] = 0

[a__isNeList# (x₁) ] = 2 x₁

[U71 (x₁, x₂) ] = 3

[isNeList (x₁) ] = 0

[a__isPal (x₁) ] = 1

[isPal (x₁) ] = 1

[U11 (x₁) ] = 0

[a__U51# (x₁, x₂) ] = 2 x₁ + 2

[a__U72 (x₁) ] = 0

[U61 (x₁) ] = 0

[U41 (x₁, x₂) ] = 0

[a__U21 (x₁, x₂) ] = 0

[U31 (x₁) ] = 0

[a__U71 (x₁, x₂) ] = 3

[tt] = 0

[o] = 0

[e] = 0

[a__U21# (x₁, x₂) ] = 2 x₁ + 1

[a__isNePal (x₁) ] = x₁

[a__U31 (x₁) ] = 0

[a__isQid (x₁) ] = 2 x₁

[U22 (x₁) ] = 0

[a____ (x₁, x₂) ] = x₁ + x₂ + 3

[a__U61 (x₁) ] = 0

[a__U41# (x₁, x₂) ] = 2 x₁ + 3

[a__U41 (x₁, x₂) ] = 0

[a__U81 (x₁) ] = 1

[u] = 0

[a__U11 (x₁) ] = 0

[U52 (x₁) ] = 2 x₁

[isList (x₁) ] = 0

[a__U42 (x₁) ] = 0

[mark (x₁) ] = x₁

[a__isList# (x₁) ] = 2 x₁ + 1

[U51 (x₁, x₂) ] = 0

[nil] = 0

[a__isNeList (x₁) ] = 0

[a__U52 (x₁) ] = 2 x₁

[isQid (x₁) ] = 2 x₁

[a__isList (x₁) ] = 0

[U42 (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).

a__U21#( tt , V2 ) → a__isList#( V2 )

1.1.2.1: dependency graph processor

The dependency pairs are split into 0 component(s).

The 3rd component contains the pair(s)

a__U71#( tt , P ) → a__isPal#( P )

a__isPal#( V ) → a__isNePal#( V )

a__isNePal#( __( I , __( P , I ) ) ) → a__U71#( a__isQid( I ) , P )

1.1.3: reduction pair processor

Using the following reduction pair

Linear polynomial interpretation over the naturals

[a__U31 (x₁) ] = 0

[U81 (x₁) ] = 0

[__ (x₁, x₂) ] = x₁ + x₂ + 1

[a] = 0

[a__isQid (x₁) ] = 0

[isNePal (x₁) ] = 2 x₁

[a__U51 (x₁, x₂) ] = 0

[U22 (x₁) ] = 0

[a____ (x₁, x₂) ] = x₁ + x₂ + 1

[a__U22 (x₁) ] = 0

[a__U61 (x₁) ] = 0

[i] = 0

[U72 (x₁) ] = 0

[U21 (x₁, x₂) ] = 0

[a__isPal# (x₁) ] = 2 x₁ + 1

[a__U41 (x₁, x₂) ] = 0

[u] = 2

[a__U81 (x₁) ] = 0

[U71 (x₁, x₂) ] = 0

[a__U11 (x₁) ] = 0

[isNeList (x₁) ] = 0

[U52 (x₁) ] = 0

[a__isPal (x₁) ] = 0

[isPal (x₁) ] = 0

[U11 (x₁) ] = 0

[isList (x₁) ] = 0

[a__U42 (x₁) ] = 0

[a__U72 (x₁) ] = 0

[mark (x₁) ] = x₁

[a__U21 (x₁, x₂) ] = 0

[U41 (x₁, x₂) ] = 0

[U61 (x₁) ] = 0

[U31 (x₁) ] = 0

[a__U71 (x₁, x₂) ] = 0

[U51 (x₁, x₂) ] = 0

[nil] = 0

[a__isNeList (x₁) ] = 0

[tt] = 0

[o] = 0

[e] = 0

[a__isNePal# (x₁) ] = 2 x₁

[a__isNePal (x₁) ] = 2 x₁

[a__U52 (x₁) ] = 0

[a__U71# (x₁, x₂) ] = 2 x₁ + 2

[isQid (x₁) ] = 0

[a__isList (x₁) ] = 0

[U42 (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

1.1.3.1: P is empty

All dependency pairs have been removed.

a____#( __( X , Y ) , Z )	→	a____#( mark( X ) , a____( mark( Y ) , mark( Z ) ) )
a____#( __( X , Y ) , Z )	→	mark#( X )
a____#( __( X , Y ) , Z )	→	a____#( mark( Y ) , mark( Z ) )
a____#( __( X , Y ) , Z )	→	mark#( Y )
a____#( __( X , Y ) , Z )	→	mark#( Z )
a____#( X , nil )	→	mark#( X )
a____#( nil , X )	→	mark#( X )
a__U21#( tt , V2 )	→	a__U22#( a__isList( V2 ) )
a__U21#( tt , V2 )	→	a__isList#( V2 )
a__U41#( tt , V2 )	→	a__U42#( a__isNeList( V2 ) )
a__U41#( tt , V2 )	→	a__isNeList#( V2 )
a__U51#( tt , V2 )	→	a__U52#( a__isList( V2 ) )
a__U51#( tt , V2 )	→	a__isList#( V2 )
a__U71#( tt , P )	→	a__U72#( a__isPal( P ) )
a__U71#( tt , P )	→	a__isPal#( P )
a__isList#( V )	→	a__U11#( a__isNeList( V ) )
a__isList#( V )	→	a__isNeList#( V )
a__isList#( __( V1 , V2 ) )	→	a__U21#( a__isList( V1 ) , V2 )
a__isList#( __( V1 , V2 ) )	→	a__isList#( V1 )
a__isNeList#( V )	→	a__U31#( a__isQid( V ) )
a__isNeList#( V )	→	a__isQid#( V )
a__isNeList#( __( V1 , V2 ) )	→	a__U41#( a__isList( V1 ) , V2 )
a__isNeList#( __( V1 , V2 ) )	→	a__isList#( V1 )
a__isNeList#( __( V1 , V2 ) )	→	a__U51#( a__isNeList( V1 ) , V2 )
a__isNeList#( __( V1 , V2 ) )	→	a__isNeList#( V1 )
a__isNePal#( V )	→	a__U61#( a__isQid( V ) )
a__isNePal#( V )	→	a__isQid#( V )
a__isNePal#( __( I , __( P , I ) ) )	→	a__U71#( a__isQid( I ) , P )
a__isNePal#( __( I , __( P , I ) ) )	→	a__isQid#( I )
a__isPal#( V )	→	a__U81#( a__isNePal( V ) )
a__isPal#( V )	→	a__isNePal#( V )
mark#( __( X1 , X2 ) )	→	a____#( mark( X1 ) , mark( X2 ) )
mark#( __( X1 , X2 ) )	→	mark#( X1 )
mark#( __( X1 , X2 ) )	→	mark#( X2 )
mark#( U11( X ) )	→	a__U11#( mark( X ) )
mark#( U11( X ) )	→	mark#( X )
mark#( U21( X1 , X2 ) )	→	a__U21#( mark( X1 ) , X2 )
mark#( U21( X1 , X2 ) )	→	mark#( X1 )
mark#( U22( X ) )	→	a__U22#( mark( X ) )
mark#( U22( X ) )	→	mark#( X )
mark#( isList( X ) )	→	a__isList#( X )
mark#( U31( X ) )	→	a__U31#( mark( X ) )
mark#( U31( X ) )	→	mark#( X )
mark#( U41( X1 , X2 ) )	→	a__U41#( mark( X1 ) , X2 )
mark#( U41( X1 , X2 ) )	→	mark#( X1 )
mark#( U42( X ) )	→	a__U42#( mark( X ) )
mark#( U42( X ) )	→	mark#( X )
mark#( isNeList( X ) )	→	a__isNeList#( X )
mark#( U51( X1 , X2 ) )	→	a__U51#( mark( X1 ) , X2 )
mark#( U51( X1 , X2 ) )	→	mark#( X1 )
mark#( U52( X ) )	→	a__U52#( mark( X ) )
mark#( U52( X ) )	→	mark#( X )
mark#( U61( X ) )	→	a__U61#( mark( X ) )
mark#( U61( X ) )	→	mark#( X )
mark#( U71( X1 , X2 ) )	→	a__U71#( mark( X1 ) , X2 )
mark#( U71( X1 , X2 ) )	→	mark#( X1 )
mark#( U72( X ) )	→	a__U72#( mark( X ) )
mark#( U72( X ) )	→	mark#( X )
mark#( isPal( X ) )	→	a__isPal#( X )
mark#( U81( X ) )	→	a__U81#( mark( X ) )
mark#( U81( X ) )	→	mark#( X )
mark#( isQid( X ) )	→	a__isQid#( X )
mark#( isNePal( X ) )	→	a__isNePal#( X )

[a__U31 (x₁) ]	=	2 x₁
[U81 (x₁) ]	=	x₁
[__ (x₁, x₂) ]	=	x₁ + x₂
[a]	=	0
[a__isQid (x₁) ]	=	0
[isNePal (x₁) ]	=	0
[U22 (x₁) ]	=	x₁
[a__U51 (x₁, x₂) ]	=	2 x₁
[a__U22 (x₁) ]	=	x₁
[a____ (x₁, x₂) ]	=	x₁ + x₂
[a__U61 (x₁) ]	=	2 x₁
[i]	=	2
[U21 (x₁, x₂) ]	=	x₁
[U72 (x₁) ]	=	x₁
[a__U41 (x₁, x₂) ]	=	x₁
[u]	=	0
[a__U81 (x₁) ]	=	x₁
[U71 (x₁, x₂) ]	=	2 x₁
[a__U11 (x₁) ]	=	2 x₁
[isNeList (x₁) ]	=	0
[U52 (x₁) ]	=	2 x₁
[a__isPal (x₁) ]	=	0
[isPal (x₁) ]	=	0
[U11 (x₁) ]	=	2 x₁
[a____# (x₁, x₂) ]	=	x₁ + x₂
[isList (x₁) ]	=	0
[a__U42 (x₁) ]	=	x₁
[a__U72 (x₁) ]	=	x₁
[mark (x₁) ]	=	x₁
[a__U21 (x₁, x₂) ]	=	x₁
[U61 (x₁) ]	=	2 x₁
[U41 (x₁, x₂) ]	=	x₁
[U31 (x₁) ]	=	2 x₁
[mark# (x₁) ]	=	x₁
[a__U71 (x₁, x₂) ]	=	2 x₁
[U51 (x₁, x₂) ]	=	2 x₁
[nil]	=	1
[a__isNeList (x₁) ]	=	0
[tt]	=	0
[o]	=	0
[e]	=	0
[a__U52 (x₁) ]	=	2 x₁
[a__isNePal (x₁) ]	=	0
[isQid (x₁) ]	=	0
[a__isList (x₁) ]	=	0
[U42 (x₁) ]	=	x₁
[f(x₁, ..., x_n)]	=	x₁ + ... + x_n + 1	for all other symbols f of arity n

[a__U31 (x₁) ]	=	2 x₁ + 1
[U81 (x₁) ]	=	0
[__ (x₁, x₂) ]	=	x₁ + x₂
[a]	=	0
[a__isQid (x₁) ]	=	0
[isNePal (x₁) ]	=	0
[a__U51 (x₁, x₂) ]	=	x₁
[U22 (x₁) ]	=	1
[a____ (x₁, x₂) ]	=	x₁ + x₂
[a__U22 (x₁) ]	=	1
[a__U61 (x₁) ]	=	0
[i]	=	1
[U72 (x₁) ]	=	0
[U21 (x₁, x₂) ]	=	2
[a__U41 (x₁, x₂) ]	=	0
[u]	=	0
[a__U81 (x₁) ]	=	0
[U71 (x₁, x₂) ]	=	0
[a__U11 (x₁) ]	=	2 x₁
[isNeList (x₁) ]	=	1
[U52 (x₁) ]	=	0
[a__isPal (x₁) ]	=	0
[isPal (x₁) ]	=	0
[U11 (x₁) ]	=	2 x₁
[isList (x₁) ]	=	2
[a__U42 (x₁) ]	=	0
[a__U72 (x₁) ]	=	0
[mark (x₁) ]	=	x₁
[a__U21 (x₁, x₂) ]	=	2
[U41 (x₁, x₂) ]	=	0
[U61 (x₁) ]	=	0
[U31 (x₁) ]	=	2 x₁ + 1
[mark# (x₁) ]	=	x₁
[a__U71 (x₁, x₂) ]	=	0
[U51 (x₁, x₂) ]	=	x₁
[nil]	=	0
[a__isNeList (x₁) ]	=	1
[tt]	=	0
[o]	=	0
[e]	=	0
[a__isNePal (x₁) ]	=	0
[a__U52 (x₁) ]	=	0
[isQid (x₁) ]	=	0
[a__isList (x₁) ]	=	2
[U42 (x₁) ]	=	0
[f(x₁, ..., x_n)]	=	x₁ + ... + x_n + 1	for all other symbols f of arity n

[U81 (x₁) ]	=	1
[__ (x₁, x₂) ]	=	x₁ + x₂ + 3
[a]	=	1
[isNePal (x₁) ]	=	x₁
[a__U51 (x₁, x₂) ]	=	0
[a__U22 (x₁) ]	=	0
[i]	=	2
[U21 (x₁, x₂) ]	=	0
[U72 (x₁) ]	=	0
[a__isNeList# (x₁) ]	=	2 x₁
[U71 (x₁, x₂) ]	=	3
[isNeList (x₁) ]	=	0
[a__isPal (x₁) ]	=	1
[isPal (x₁) ]	=	1
[U11 (x₁) ]	=	0
[a__U51# (x₁, x₂) ]	=	2 x₁ + 2
[a__U72 (x₁) ]	=	0
[U61 (x₁) ]	=	0
[U41 (x₁, x₂) ]	=	0
[a__U21 (x₁, x₂) ]	=	0
[U31 (x₁) ]	=	0
[a__U71 (x₁, x₂) ]	=	3
[tt]	=	0
[o]	=	0
[e]	=	0
[a__U21# (x₁, x₂) ]	=	2 x₁ + 1
[a__isNePal (x₁) ]	=	x₁
[a__U31 (x₁) ]	=	0
[a__isQid (x₁) ]	=	2 x₁
[U22 (x₁) ]	=	0
[a____ (x₁, x₂) ]	=	x₁ + x₂ + 3
[a__U61 (x₁) ]	=	0
[a__U41# (x₁, x₂) ]	=	2 x₁ + 3
[a__U41 (x₁, x₂) ]	=	0
[a__U81 (x₁) ]	=	1
[u]	=	0
[a__U11 (x₁) ]	=	0
[U52 (x₁) ]	=	2 x₁
[isList (x₁) ]	=	0
[a__U42 (x₁) ]	=	0
[mark (x₁) ]	=	x₁
[a__isList# (x₁) ]	=	2 x₁ + 1
[U51 (x₁, x₂) ]	=	0
[nil]	=	0
[a__isNeList (x₁) ]	=	0
[a__U52 (x₁) ]	=	2 x₁
[isQid (x₁) ]	=	2 x₁
[a__isList (x₁) ]	=	0
[U42 (x₁) ]	=	0
[f(x₁, ..., x_n)]	=	x₁ + ... + x_n + 1	for all other symbols f of arity n