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TRS Context Sensitive pair #487523715
details
property
value
status
complete
benchmark
cariboo_ex6.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n143.star.cs.uiowa.edu
space
Transformed_outermost_08
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.60982298851 seconds
cpu usage
3.447222198
max memory
2.04156928E8
stage attributes
key
value
output-size
5295
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given CSR could be proven: (0) CSR (1) CSRRRRProof [EQUIVALENT, 61 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 0 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 0 ms] (6) CSR (7) CSDependencyPairsProof [EQUIVALENT, 5 ms] (8) QCSDP (9) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (10) TRUE ---------------------------------------- (0) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: f_1(x, x) -> f_1(i_0(x), g_1(g_1(x))) f_1(x, y) -> x g_1(x) -> i_0(x) f_1(x, i_0(x)) -> f_1(x, x) f_1(i_0(x), i_0(g_1(x))) -> a_0 The replacement map contains the following entries: f_1: empty set i_0: {1} g_1: empty set a_0: empty set ---------------------------------------- (1) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules: f_1(x, x) -> f_1(i_0(x), g_1(g_1(x))) f_1(x, y) -> x g_1(x) -> i_0(x) f_1(x, i_0(x)) -> f_1(x, x) f_1(i_0(x), i_0(g_1(x))) -> a_0 The replacement map contains the following entries: f_1: empty set i_0: {1} g_1: empty set a_0: empty set Used ordering: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(f_1(x_1, x_2)) = [[1], [1]] + [[1, 0], [0, 1]] * x_1 + [[1, 0], [0, 1]] * x_2 >>> <<< POL(i_0(x_1)) = [[0], [0]] + [[1, 0], [0, 1]] * x_1 >>> <<< POL(g_1(x_1)) = [[0], [0]] + [[1, 0], [0, 1]] * x_1 >>> <<< POL(a_0) = [[0], [1]] >>> With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f_1(x, y) -> x f_1(i_0(x), i_0(g_1(x))) -> a_0 ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: f_1(x, x) -> f_1(i_0(x), g_1(g_1(x))) g_1(x) -> i_0(x)
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