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TRS_Innermost 2019-03-28 22.12 pair #432270832
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
n034.star.cs.uiowa.edu
space
Transformed_CSR_innermost_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.82273 seconds
cpu usage
3.65508
user time
3.46806
system time
0.187014
max virtual memory
1.8411164E7
max residence set size
231916.0
stage attributes
key
value
starexec-result
YES
output
3.57/1.78 YES 3.57/1.79 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.57/1.79 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.57/1.79 3.57/1.79 3.57/1.79 Termination w.r.t. Q of the given QTRS could be proven: 3.57/1.79 3.57/1.79 (0) QTRS 3.57/1.79 (1) QTRSToCSRProof [SOUND, 0 ms] 3.57/1.79 (2) CSR 3.57/1.79 (3) CSDependencyPairsProof [EQUIVALENT, 0 ms] 3.57/1.79 (4) QCSDP 3.57/1.79 (5) QCSDPForwardInstantiationProcessor [EQUIVALENT, 0 ms] 3.57/1.79 (6) QCSDP 3.57/1.79 (7) PIsEmptyProof [EQUIVALENT, 0 ms] 3.57/1.79 (8) YES 3.57/1.79 3.57/1.79 3.57/1.79 ---------------------------------------- 3.57/1.79 3.57/1.79 (0) 3.57/1.79 Obligation: 3.57/1.79 Q restricted rewrite system: 3.57/1.79 The TRS R consists of the following rules: 3.57/1.79 3.57/1.79 active(f(a, b, X)) -> mark(f(X, X, X)) 3.57/1.79 active(c) -> mark(a) 3.57/1.79 active(c) -> mark(b) 3.57/1.79 active(f(X1, X2, X3)) -> f(active(X1), X2, X3) 3.57/1.79 active(f(X1, X2, X3)) -> f(X1, X2, active(X3)) 3.57/1.79 f(mark(X1), X2, X3) -> mark(f(X1, X2, X3)) 3.57/1.79 f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3)) 3.57/1.79 proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)) 3.57/1.79 proper(a) -> ok(a) 3.57/1.79 proper(b) -> ok(b) 3.57/1.79 proper(c) -> ok(c) 3.57/1.79 f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) 3.57/1.79 top(mark(X)) -> top(proper(X)) 3.57/1.79 top(ok(X)) -> top(active(X)) 3.57/1.79 3.57/1.79 The set Q consists of the following terms: 3.57/1.79 3.57/1.79 active(c) 3.57/1.79 active(f(x0, x1, x2)) 3.57/1.79 f(mark(x0), x1, x2) 3.57/1.79 f(x0, x1, mark(x2)) 3.57/1.79 proper(f(x0, x1, x2)) 3.57/1.79 proper(a) 3.57/1.79 proper(b) 3.57/1.79 proper(c) 3.57/1.79 f(ok(x0), ok(x1), ok(x2)) 3.57/1.79 top(mark(x0)) 3.57/1.79 top(ok(x0)) 3.57/1.79 3.57/1.79 3.57/1.79 ---------------------------------------- 3.57/1.79 3.57/1.79 (1) QTRSToCSRProof (SOUND) 3.57/1.79 The following Q TRS is given: Q restricted rewrite system: 3.57/1.79 The TRS R consists of the following rules: 3.57/1.79 3.57/1.79 active(f(a, b, X)) -> mark(f(X, X, X)) 3.57/1.79 active(c) -> mark(a) 3.57/1.79 active(c) -> mark(b) 3.57/1.79 active(f(X1, X2, X3)) -> f(active(X1), X2, X3) 3.57/1.79 active(f(X1, X2, X3)) -> f(X1, X2, active(X3)) 3.57/1.79 f(mark(X1), X2, X3) -> mark(f(X1, X2, X3)) 3.57/1.79 f(X1, X2, mark(X3)) -> mark(f(X1, X2, X3)) 3.57/1.79 proper(f(X1, X2, X3)) -> f(proper(X1), proper(X2), proper(X3)) 3.57/1.79 proper(a) -> ok(a) 3.57/1.79 proper(b) -> ok(b) 3.57/1.79 proper(c) -> ok(c) 3.57/1.79 f(ok(X1), ok(X2), ok(X3)) -> ok(f(X1, X2, X3)) 3.57/1.79 top(mark(X)) -> top(proper(X)) 3.57/1.79 top(ok(X)) -> top(active(X)) 3.57/1.79 3.57/1.79 The set Q consists of the following terms: 3.57/1.79 3.57/1.79 active(c) 3.57/1.79 active(f(x0, x1, x2)) 3.57/1.79 f(mark(x0), x1, x2) 3.57/1.79 f(x0, x1, mark(x2)) 3.57/1.79 proper(f(x0, x1, x2)) 3.57/1.79 proper(a) 3.57/1.79 proper(b) 3.57/1.79 proper(c) 3.57/1.79 f(ok(x0), ok(x1), ok(x2)) 3.57/1.79 top(mark(x0)) 3.57/1.79 top(ok(x0)) 3.57/1.79 3.57/1.79 Special symbols used for the transformation (see [GM04]): 3.57/1.79 top: top_1, active: active_1, mark: mark_1, ok: ok_1, proper: proper_1 3.57/1.79 The replacement map contains the following entries: 3.57/1.79 3.57/1.79 f: {1, 3} 3.57/1.79 a: empty set 3.57/1.79 b: empty set 3.57/1.79 c: empty set 3.57/1.79 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. 3.57/1.79 ----------------------------------------
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