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TRS Stand 20472 pair #381715627
details
property
value
status
complete
benchmark
Ex9_Luc06_GM.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)
1.7017660141 seconds
cpu usage
3.933212565
max memory
2.53026304E8
stage attributes
key
value
output-size
4328
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 67 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 0 ms] (8) QTRS (9) QTRSRRRProof [EQUIVALENT, 0 ms] (10) QTRS (11) RisEmptyProof [EQUIVALENT, 0 ms] (12) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(a, X, X) -> a__f(X, a__b, b) a__b -> a mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) mark(b) -> a__b mark(a) -> a a__f(X1, X2, X3) -> f(X1, X2, X3) a__b -> b Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a) = 1 POL(a__b) = 1 POL(a__f(x_1, x_2, x_3)) = 2 + 2*x_1 + 2*x_2 + 2*x_3 POL(b) = 0 POL(f(x_1, x_2, x_3)) = 2 + 2*x_1 + 2*x_2 + 2*x_3 POL(mark(x_1)) = 1 + 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: mark(f(X1, X2, X3)) -> a__f(X1, mark(X2), X3) mark(a) -> a a__b -> b ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__f(a, X, X) -> a__f(X, a__b, b) a__b -> a mark(b) -> a__b a__f(X1, X2, X3) -> f(X1, X2, X3) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(a) = 0 POL(a__b) = 0 POL(a__f(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + 2*x_3 POL(b) = 0 POL(f(x_1, x_2, x_3)) = 1 + x_1 + 2*x_2 + x_3 POL(mark(x_1)) = 2 + 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: mark(b) -> a__b ----------------------------------------
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