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TRS Standard pair #516962670
details
property
value
status
complete
benchmark
Ex9_Luc04_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n118.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.20750498772 seconds
cpu usage
5.834790266
max memory
4.77847552E8
stage attributes
key
value
output-size
4046
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# AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [EQUIVALENT, 0 ms] (2) CSR (3) CSDependencyPairsProof [EQUIVALENT, 0 ms] (4) QCSDP (5) QCSDPForwardInstantiationProcessor [EQUIVALENT, 0 ms] (6) QCSDP (7) PIsEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(f(a, b, X)) -> mark(f(X, X, X)) active(c) -> mark(a) active(c) -> mark(b) active(f(X1, X2, X3)) -> f(active(X1), X2, X3) active(f(X1, X2, X3)) -> f(X1, X2, active(X3)) f(mark(X1), X2, X3) -> mark(f(X1, X2, X3)) f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3)) proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)) proper(a) -> ok(a) proper(b) -> ok(b) proper(c) -> ok(c) f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Q is empty. ---------------------------------------- (1) QTRSToCSRProof (EQUIVALENT) The following Q TRS is given: Q restricted rewrite system: The TRS R consists of the following rules: active(f(a, b, X)) -> mark(f(X, X, X)) active(c) -> mark(a) active(c) -> mark(b) active(f(X1, X2, X3)) -> f(active(X1), X2, X3) active(f(X1, X2, X3)) -> f(X1, X2, active(X3)) f(mark(X1), X2, X3) -> mark(f(X1, X2, X3)) f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3)) proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)) proper(a) -> ok(a) proper(b) -> ok(b) proper(c) -> ok(c) f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) top(mark(X)) -> top(proper(X)) top(ok(X)) -> top(active(X)) Q is empty. 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, 3} a: empty set b: empty set c: empty set The QTRS contained all rules created by the complete Giesl-Middeldorp transformation. Therefore, the inverse transformation is complete (and sound). ---------------------------------------- (2) 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 ---------------------------------------- (3) CSDependencyPairsProof (EQUIVALENT)
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