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TRS Innermost pair #487093455
details
property
value
status
complete
benchmark
Ex24_Luc06_C.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n148.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.69895 seconds
cpu usage
3.70986
user time
3.55248
system time
0.157375
max virtual memory
1.8343604E7
max residence set size
239488.0
stage attributes
key
value
starexec-result
YES
output
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSToCSRProof [SOUND, 0 ms] (2) CSR (3) CSRRRRProof [EQUIVALENT, 29 ms] (4) CSR (5) CSRRRRProof [EQUIVALENT, 0 ms] (6) CSR (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: active(f(b, X, c)) -> mark(f(X, c, X)) active(c) -> mark(b) 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(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)) The set Q consists of the following terms: active(c) active(f(x0, x1, x2)) f(x0, mark(x1), x2) proper(f(x0, x1, x2)) proper(b) proper(c) f(ok(x0), ok(x1), ok(x2)) 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(b, X, c)) -> mark(f(X, c, X)) active(c) -> mark(b) 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(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)) The set Q consists of the following terms: active(c) active(f(x0, x1, x2)) f(x0, mark(x1), x2) proper(f(x0, x1, x2)) proper(b) proper(c) f(ok(x0), ok(x1), ok(x2)) 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: {2} b: empty set c: 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(b, X, c) -> f(X, c, X) c -> b The replacement map contains the following entries: f: {2} b: empty set
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