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TRS Stand 20472 pair #381715972
details
property
value
status
complete
benchmark
PEANO_nosorts_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n072.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.03693699837 seconds
cpu usage
3.66395191
max memory
2.28040704E8
stage attributes
key
value
output-size
2132
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 31 ms] (2) QTRS (3) RisEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a__and(tt, X) -> mark(X) a__plus(N, 0) -> mark(N) a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(0) -> 0 mark(s(X)) -> s(mark(X)) a__and(X1, X2) -> and(X1, X2) a__plus(X1, X2) -> plus(X1, X2) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:mark_1 > a__and_2 > and_2 > a__plus_2 > plus_2 > s_1 > 0 > tt and weight map: tt=1 0=1 mark_1=0 s_1=1 a__and_2=0 a__plus_2=0 and_2=0 plus_2=0 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: a__and(tt, X) -> mark(X) a__plus(N, 0) -> mark(N) a__plus(N, s(M)) -> s(a__plus(mark(N), mark(M))) mark(and(X1, X2)) -> a__and(mark(X1), X2) mark(plus(X1, X2)) -> a__plus(mark(X1), mark(X2)) mark(tt) -> tt mark(0) -> 0 mark(s(X)) -> s(mark(X)) a__and(X1, X2) -> and(X1, X2) a__plus(X1, X2) -> plus(X1, X2) ---------------------------------------- (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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