/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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YES
proof of /export/starexec/sandbox/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination of the given CSR could be proven:

(0) CSR
(1) CSRRRRProof [EQUIVALENT, 102 ms]
(2) CSR
(3) CSRRRRProof [EQUIVALENT, 10 ms]
(4) CSR
(5) RisEmptyProof [EQUIVALENT, 0 ms]
(6) YES


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(0)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   __(X, nil) -> X
   __(nil, X) -> X
   U11(tt) -> U12(tt)
   U12(tt) -> tt
   isNePal(__(I, __(P, I))) -> U11(tt)

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNePal: {1}

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(1) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   __(X, nil) -> X
   __(nil, X) -> X
   U11(tt) -> U12(tt)
   U12(tt) -> tt
   isNePal(__(I, __(P, I))) -> U11(tt)

The replacement map contains the following entries:

__: {1, 2}
nil: empty set
U11: {1}
tt: empty set
U12: {1}
isNePal: {1}
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1)) = x_1
   POL(U12(x_1)) = x_1
   POL(__(x_1, x_2)) = x_1 + x_2
   POL(isNePal(x_1)) = 1 + x_1
   POL(nil) = 1
   POL(tt) = 1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   __(X, nil) -> X
   __(nil, X) -> X




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(2)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt) -> U12(tt)
   U12(tt) -> tt
   isNePal(__(I, __(P, I))) -> U11(tt)

The replacement map contains the following entries:

__: {1, 2}
U11: {1}
tt: empty set
U12: {1}
isNePal: {1}

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(3) CSRRRRProof (EQUIVALENT)
The following CSR is given: Context-sensitive rewrite system:
The TRS R consists of the following rules:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt) -> U12(tt)
   U12(tt) -> tt
   isNePal(__(I, __(P, I))) -> U11(tt)

The replacement map contains the following entries:

__: {1, 2}
U11: {1}
tt: empty set
U12: {1}
isNePal: {1}
Used ordering:
Polynomial interpretation [POLO]:

   POL(U11(x_1)) = 2 + x_1
   POL(U12(x_1)) = 2*x_1
   POL(__(x_1, x_2)) = 1 + 2*x_1 + x_2
   POL(isNePal(x_1)) = 2*x_1
   POL(tt) = 1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   __(__(X, Y), Z) -> __(X, __(Y, Z))
   U11(tt) -> U12(tt)
   U12(tt) -> tt
   isNePal(__(I, __(P, I))) -> U11(tt)




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(4)
Obligation:
Context-sensitive rewrite system:
R is empty.

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(5) RisEmptyProof (EQUIVALENT)
The CSR R is empty. Hence, termination is trivially proven.
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(6)
YES