/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination of the given CSR could be proven:

(0) CSR
(1) CSRRRRProof [EQUIVALENT, 35 ms]
(2) CSR
(3) CSDependencyPairsProof [EQUIVALENT, 0 ms]
(4) QCSDP
(5) QCSDependencyGraphProof [EQUIVALENT, 0 ms]
(6) TRUE


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

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

The replacement map contains the following entries:

f: empty set
g: {1}
b: empty set
c: empty set

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

The replacement map contains the following entries:

f: empty set
g: {1}
b: empty set
c: empty set
Used ordering:
Polynomial interpretation [POLO]:

   POL(b) = 1
   POL(c) = 0
   POL(f(x_1, x_2, x_3)) = 0
   POL(g(x_1)) = x_1
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   g(b) -> c
   b -> c




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

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

The replacement map contains the following entries:

f: empty set
g: {1}

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(3) CSDependencyPairsProof (EQUIVALENT)
Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem.
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(4)
Obligation:
Q-restricted context-sensitive dependency pair problem:
The symbols in {g_1} are replacing on all positions.
The symbols in {f_3, F_3} are not replacing on any position.

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

The TRS R consists of the following rules:

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

Q is empty.

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(5) QCSDependencyGraphProof (EQUIVALENT)
The approximation of the Context-Sensitive Dependency Graph [LPAR08] contains 0 SCCs.
The rules F(z0, g(z0), z1) -> F(z1, z1, z1) and F(x0, g(x0), x1) -> F(x1, x1, x1) form no chain, because ECap^mu(F(z1, z1, z1)) = F(z1, z1, z1) does not unify with F(x0, g(x0), x1). 
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(6)
TRUE