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TRS Stand 20472 pair #381710476
details
property
value
status
complete
benchmark
ack_prolog.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n110.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.65690588951 seconds
cpu usage
3.66305771
max memory
2.2523904E8
stage attributes
key
value
output-size
2547
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) QTRSRRRProof [EQUIVALENT, 64 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 0 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: ack_in(0, n) -> ack_out(s(n)) ack_in(s(m), 0) -> u11(ack_in(m, s(0))) u11(ack_out(n)) -> ack_out(n) ack_in(s(m), s(n)) -> u21(ack_in(s(m), n), m) u21(ack_out(n), m) -> u22(ack_in(m, n)) u22(ack_out(n)) -> ack_out(n) Q is empty. ---------------------------------------- (1) QTRSRRRProof (EQUIVALENT) Used ordering: ack_in/2(YES,YES) 0/0) ack_out/1(YES) s/1(YES) u11/1(YES) u21/2(YES,YES) u22/1)YES( Quasi precedence: [ack_in_2, u21_2] > [0, ack_out_1, s_1] > u11_1 Status: ack_in_2: [1,2] 0: multiset status ack_out_1: multiset status s_1: multiset status u11_1: multiset status u21_2: [2,1] With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: ack_in(0, n) -> ack_out(s(n)) ack_in(s(m), 0) -> u11(ack_in(m, s(0))) u11(ack_out(n)) -> ack_out(n) ack_in(s(m), s(n)) -> u21(ack_in(s(m), n), m) u21(ack_out(n), m) -> u22(ack_in(m, n)) ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: u22(ack_out(n)) -> ack_out(n) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:u22_1 > ack_out_1 and weight map: u22_1=0 ack_out_1=1 The variable weight is 1With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: u22(ack_out(n)) -> ack_out(n)
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