/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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, 0 ms]
(2) CSR
(3) RisEmptyProof [EQUIVALENT, 0 ms]
(4) YES


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

   f(g(X), Y) -> f(X, f(g(X), Y))

The replacement map contains the following entries:

f: {1}
g: {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:

   f(g(X), Y) -> f(X, f(g(X), Y))

The replacement map contains the following entries:

f: {1}
g: {1}
Used ordering:
Polynomial interpretation [POLO]:

   POL(f(x_1, x_2)) = x_1
   POL(g(x_1)) = 1 + x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   f(g(X), Y) -> f(X, f(g(X), Y))




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(2)
Obligation:
Context-sensitive rewrite system:
R is empty.

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(3) RisEmptyProof (EQUIVALENT)
The CSR R is empty. Hence, termination is trivially proven.
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(4)
YES