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TRS Conditional pair #487562820
details
property
value
status
complete
benchmark
388.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.68415212631 seconds
cpu usage
3.60698343
max memory
2.32292352E8
stage attributes
key
value
output-size
2780
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 56 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: add(x, 0) -> x add(x, s(y)) -> s(add(x, y)) The conditional TRS C consists of the following conditional rules: quad(x) -> z <= add(x, x) -> y, add(y, y) -> z ---------------------------------------- (1) CTRSToQTRSProof (SOUND) The conditional rules have been transormed into unconditional rules according to [CTRS,AAECCNOC]. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: quad(x) -> U1(add(x, x)) U1(y) -> U2(add(y, y)) U2(z) -> z add(x, 0) -> x add(x, s(y)) -> s(add(x, y)) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: quad/1(YES) U1/1(YES) add/2(YES,YES) U2/1)YES( 0/0) s/1)YES( Quasi precedence: quad_1 > U1_1 > add_2 0 > add_2 Status: quad_1: multiset status U1_1: multiset status add_2: multiset status 0: multiset status With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: quad(x) -> U1(add(x, x)) U1(y) -> U2(add(y, y)) add(x, 0) -> x ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: U2(z) -> z add(x, s(y)) -> s(add(x, y)) Q is empty.
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