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TRS Stand 20472 pair #381715582
details
property
value
status
complete
benchmark
Ex24_GM04_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n005.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.59393000603 seconds
cpu usage
3.525749872
max memory
2.19594752E8
stage attributes
key
value
output-size
4394
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [EQUIVALENT, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 34 ms] (4)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, g(X), Y)) -> mark(f(Y, Y, Y)) active(g(b)) -> mark(c) active(b) -> mark(c) active(g(X)) -> g(active(X)) g(mark(X)) -> mark(g(X)) proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)) proper(g(X)) -> g(proper(X)) proper(b) -> ok(b) proper(c) -> ok(c) f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) g(ok(X)) -> ok(g(X)) 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(X, g(X), Y)) -> mark(f(Y, Y, Y)) active(g(b)) -> mark(c) active(b) -> mark(c) active(g(X)) -> g(active(X)) g(mark(X)) -> mark(g(X)) proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)) proper(g(X)) -> g(proper(X)) proper(b) -> ok(b) proper(c) -> ok(c) f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) g(ok(X)) -> ok(g(X)) 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: empty set g: {1} 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(X, g(X), Y) -> f(Y, Y, Y) g(b) -> c b -> c The replacement map contains the following entries: f: empty set g: {1} b: empty set c: empty set ---------------------------------------- (3) CSRRRRProof (EQUIVALENT) The following CSR is given: Context-sensitive rewrite system: The TRS R consists of the following rules:
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