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TRS Innermost pair #487524551
details
property
value
status
complete
benchmark
Ex16_Luc06_C.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_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.72888898849 seconds
cpu usage
3.686913703
max memory
2.27110912E8
stage attributes
key
value
output-size
4338
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [SOUND, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 53 ms] (4) CSR (5) CSDependencyPairsProof [EQUIVALENT, 0 ms] (6) QCSDP (7) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (8) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(f(X, X)) -> mark(f(a, b)) active(b) -> mark(a) active(f(X1, X2)) -> f(active(X1), X2) f(mark(X1), X2) -> mark(f(X1, X2)) proper(f(X1, X2)) -> f(proper(X1), proper(X2)) proper(a) -> ok(a) proper(b) -> ok(b) f(ok(X1), ok(X2)) -> ok(f(X1, X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) The set Q consists of the following terms: active(b) active(f(x0, x1)) f(mark(x0), x1) proper(f(x0, x1)) proper(a) proper(b) f(ok(x0), ok(x1)) top(mark(x0)) top(ok(x0)) ---------------------------------------- (1) QTRSToCSRProof (SOUND) The following Q TRS is given: Q restricted rewrite system: The TRS R consists of the following rules: active(f(X, X)) -> mark(f(a, b)) active(b) -> mark(a) active(f(X1, X2)) -> f(active(X1), X2) f(mark(X1), X2) -> mark(f(X1, X2)) proper(f(X1, X2)) -> f(proper(X1), proper(X2)) proper(a) -> ok(a) proper(b) -> ok(b) f(ok(X1), ok(X2)) -> ok(f(X1, X2)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) The set Q consists of the following terms: active(b) active(f(x0, x1)) f(mark(x0), x1) proper(f(x0, x1)) proper(a) proper(b) f(ok(x0), ok(x1)) top(mark(x0)) top(ok(x0)) Special symbols used for the transformation (see [GM04]): top: top_1, active: active_1, mark: mark_1, ok: ok_1, proper: proper_1 The replacement map contains the following entries: f: {1} a: empty set b: empty set The QTRS contained just a subset of rules created by the complete Giesl-Middeldorp transformation. Therefore, the inverse transformation is sound, but not necessarily complete. ---------------------------------------- (2) Obligation: Context-sensitive rewrite system: The TRS R consists of the following rules: f(X, X) -> f(a, b)
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