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TRS Stand 20472 pair #381714738
details
property
value
status
complete
benchmark
MYNAT_nosorts_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n023.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.59417796135 seconds
cpu usage
3.420533219
max memory
2.204672E8
stage attributes
key
value
output-size
1796
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 59 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: and(tt, X) -> activate(X) plus(N, 0) -> N plus(N, s(M)) -> s(plus(N, M)) x(N, 0) -> 0 x(N, s(M)) -> plus(x(N, M), N) activate(X) -> X Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Quasi precedence: and_2 > [activate_1, 0, s_1] tt > [activate_1, 0, s_1] x_2 > plus_2 > [activate_1, 0, s_1] Status: and_2: multiset status tt: multiset status activate_1: multiset status plus_2: [1,2] 0: multiset status s_1: multiset status x_2: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: and(tt, X) -> activate(X) plus(N, 0) -> N plus(N, s(M)) -> s(plus(N, M)) x(N, 0) -> 0 x(N, s(M)) -> plus(x(N, M), N) activate(X) -> X ---------------------------------------- (2) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (3) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES
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