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TRS Standard pair #487070253
details
property
value
status
complete
benchmark
Ex9_Luc06_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n178.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.80852 seconds
cpu usage
3.84605
user time
3.65231
system time
0.193739
max virtual memory
1.8476724E7
max residence set size
249968.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [EQUIVALENT, 0 ms] (2) CSR (3) CSDependencyPairsProof [EQUIVALENT, 0 ms] (4) QCSDP (5) QCSDependencyGraphProof [EQUIVALENT, 0 ms] (6) QCSDP (7) QCSUsableRulesProof [EQUIVALENT, 0 ms] (8) QCSDP (9) QCSDPInstantiationProcessor [EQUIVALENT, 0 ms] (10) QCSDP (11) PIsEmptyProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(f(a, X, X)) -> mark(f(X, b, b)) active(b) -> mark(a) active(f(X1, X2, X3)) -> f(X1, active(X2), X3) f(X1, mark(X2), 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) 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, X, X)) -> mark(f(X, b, b)) active(b) -> mark(a) active(f(X1, X2, X3)) -> f(X1, active(X2), X3) f(X1, mark(X2), 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) 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: {2} a: empty set b: 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, X, X) -> f(X, b, b) b -> a The replacement map contains the following entries: f: {2} a: empty set b: empty set ---------------------------------------- (3) CSDependencyPairsProof (EQUIVALENT) Using Improved CS-DPs [LPAR08] we result in the following initial Q-CSDP problem. ---------------------------------------- (4) Obligation: Q-restricted context-sensitive dependency pair problem: For all symbols f in {f_3, F_3} we have mu(f) = {2}. The ordinary context-sensitive dependency pairs DP_o are: F(a, X, X) -> F(X, b, b) F(a, X, X) -> B The TRS R consists of the following rules:
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