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TRS Conditional pair #487562874
details
property
value
status
complete
benchmark
364.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n184.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.73779606819 seconds
cpu usage
3.517249587
max memory
2.18714112E8
stage attributes
key
value
output-size
2171
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 31 ms] (4) QTRS (5) RisEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: even(0) -> true The conditional TRS C consists of the following conditional rules: even(s(x)) -> true <= odd(x) -> true odd(s(x)) -> true <= even(x) -> true ---------------------------------------- (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: even(s(x)) -> U1(odd(x)) U1(true) -> true odd(s(x)) -> U2(even(x)) U2(true) -> true even(0) -> true Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:U2_1 > 0 > even_1 > true > odd_1 > U1_1 > s_1 and weight map: true=3 0=1 even_1=2 s_1=1 U1_1=1 odd_1=2 U2_1=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: even(s(x)) -> U1(odd(x)) U1(true) -> true odd(s(x)) -> U2(even(x)) U2(true) -> true even(0) -> true ---------------------------------------- (4) Obligation: Q restricted rewrite system: R is empty. Q is empty. ---------------------------------------- (5) RisEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (6) YES
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