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


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NO
proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished


Termination of the given CSR could be disproven:

(0) CSR
(1) CSRRRRProof [EQUIVALENT, 54 ms]
(2) CSR
(3) CSRRRRProof [EQUIVALENT, 0 ms]
(4) CSR
(5) CSRRRRProof [EQUIVALENT, 0 ms]
(6) CSR
(7) ContextSensitiveLoopProof [COMPLETE, 0 ms]
(8) NO


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

   zeros -> cons(0, zeros)
   and(tt, X) -> X
   length(nil) -> 0
   length(cons(N, L)) -> s(length(L))
   take(0, IL) -> nil
   take(s(M), cons(N, IL)) -> cons(N, take(M, IL))

The replacement map contains the following entries:

zeros: empty set
cons: {1}
0: empty set
and: {1}
tt: empty set
length: {1}
nil: empty set
s: {1}
take: {1, 2}

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

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

   zeros -> cons(0, zeros)
   and(tt, X) -> X
   length(nil) -> 0
   length(cons(N, L)) -> s(length(L))
   take(0, IL) -> nil
   take(s(M), cons(N, IL)) -> cons(N, take(M, IL))

The replacement map contains the following entries:

zeros: empty set
cons: {1}
0: empty set
and: {1}
tt: empty set
length: {1}
nil: empty set
s: {1}
take: {1, 2}
Used ordering:
Polynomial interpretation [POLO]:

   POL(0) = 0
   POL(and(x_1, x_2)) = 2*x_1 + x_2
   POL(cons(x_1, x_2)) = x_1 + 2*x_2
   POL(length(x_1)) = 2*x_1
   POL(nil) = 0
   POL(s(x_1)) = 2*x_1
   POL(take(x_1, x_2)) = x_1 + 2*x_2
   POL(tt) = 2
   POL(zeros) = 0
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   and(tt, X) -> X




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

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

   zeros -> cons(0, zeros)
   length(nil) -> 0
   length(cons(N, L)) -> s(length(L))
   take(0, IL) -> nil
   take(s(M), cons(N, IL)) -> cons(N, take(M, IL))

The replacement map contains the following entries:

zeros: empty set
cons: {1}
0: empty set
length: {1}
nil: empty set
s: {1}
take: {1, 2}

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

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

   zeros -> cons(0, zeros)
   length(nil) -> 0
   length(cons(N, L)) -> s(length(L))
   take(0, IL) -> nil
   take(s(M), cons(N, IL)) -> cons(N, take(M, IL))

The replacement map contains the following entries:

zeros: empty set
cons: {1}
0: empty set
length: {1}
nil: empty set
s: {1}
take: {1, 2}
Used ordering:
Polynomial interpretation [POLO]:

   POL(0) = 0
   POL(cons(x_1, x_2)) = 2*x_1 + x_2
   POL(length(x_1)) = x_1
   POL(nil) = 2
   POL(s(x_1)) = x_1
   POL(take(x_1, x_2)) = 2 + x_1 + 2*x_2
   POL(zeros) = 0
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   length(nil) -> 0




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

(4)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   zeros -> cons(0, zeros)
   length(cons(N, L)) -> s(length(L))
   take(0, IL) -> nil
   take(s(M), cons(N, IL)) -> cons(N, take(M, IL))

The replacement map contains the following entries:

zeros: empty set
cons: {1}
0: empty set
length: {1}
nil: empty set
s: {1}
take: {1, 2}

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

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

   zeros -> cons(0, zeros)
   length(cons(N, L)) -> s(length(L))
   take(0, IL) -> nil
   take(s(M), cons(N, IL)) -> cons(N, take(M, IL))

The replacement map contains the following entries:

zeros: empty set
cons: {1}
0: empty set
length: {1}
nil: empty set
s: {1}
take: {1, 2}
Used ordering:
Polynomial interpretation [POLO]:

   POL(0) = 0
   POL(cons(x_1, x_2)) = 2*x_1 + x_2
   POL(length(x_1)) = x_1
   POL(nil) = 0
   POL(s(x_1)) = x_1
   POL(take(x_1, x_2)) = 2 + x_1 + 2*x_2
   POL(zeros) = 0
With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly:

   take(0, IL) -> nil




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

(6)
Obligation:
Context-sensitive rewrite system:
The TRS R consists of the following rules:

   zeros -> cons(0, zeros)
   length(cons(N, L)) -> s(length(L))
   take(s(M), cons(N, IL)) -> cons(N, take(M, IL))

The replacement map contains the following entries:

zeros: empty set
cons: {1}
0: empty set
length: {1}
s: {1}
take: {1, 2}

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

(7) ContextSensitiveLoopProof (COMPLETE)

   zeros -> cons(0, zeros)
   length(cons(N, L)) -> s(length(L))
   take(s(M), cons(N, IL)) -> cons(N, take(M, IL))

---------- Loop: ----------

length(zeros) -> length(cons(0, zeros)) with rule zeros -> cons(0, zeros) at position [0] and matcher [ ]

length(cons(0, zeros)) -> s(length(zeros)) with rule length(cons(N, L)) -> s(length(L)) at position [] and matcher [N / 0, L / zeros]

Now an instance of the first term with Matcher [ ] occurs in the last term at position [0].

Context: s([])

We used [[THIEMANN_LOOPS_UNDER_STRATEGIES], Theorem 1] to show that this loop is an context-sensitive loop.
----------------------------------------

(8)
NO