/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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished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) CSDependencyPairsProof [EQUIVALENT, 0 ms]
(2) QCSDP
(3) QCSDPForwardInstantiationProcessor [EQUIVALENT, 0 ms]
(4) QCSDP
(5) PIsEmptyProof [EQUIVALENT, 0 ms]
(6) YES


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

   f(a, b, X) -> f(X, X, X)
   c -> a
   c -> b

The replacement map contains the following entries:

f: {1, 3}
a: empty set
b: empty set
c: empty set

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(1) CSDependencyPairsProof (EQUIVALENT)
Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem.
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(2)
Obligation:
Q-restricted context-sensitive dependency pair problem:
For all symbols f in {f_3, F_3} we have mu(f) = {1, 3}.

The ordinary context-sensitive dependency pairs DP_o are:
   F(a, b, X) -> F(X, X, X)

The TRS R consists of the following rules:

   f(a, b, X) -> f(X, X, X)
   c -> a
   c -> b

Q is empty.

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(3) QCSDPForwardInstantiationProcessor (EQUIVALENT)
Using the Context-Sensitive Forward Instantiation[DA_EMMES] Processor

the pair F(a, b, X) -> F(X, X, X)

was transformed to the following new pairs: 
   F(a, b, b) -> F(b, b, b)



----------------------------------------

(4)
Obligation:
Q-restricted context-sensitive dependency pair problem:
For all symbols f in {f_3} we have mu(f) = {1, 3}.

The TRS P consists of the following rules:
none

The TRS R consists of the following rules:

   f(a, b, X) -> f(X, X, X)
   c -> a
   c -> b

Q is empty.

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(5) PIsEmptyProof (EQUIVALENT)
The TRS P is empty. Hence, there is no (P,Q,R,mu)-chain.
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(6)
YES