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TRS Conditional pair #516978707
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
n183.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
AProVE21
configuration
standard
runtime (wallclock)
2.07847690582 seconds
cpu usage
5.507898201
max memory
4.70564864E8
stage attributes
key
value
output-size
2160
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: c69e44bd14796315568835c1ffa2502984884775 mhark 20210624 unpublished Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 39 ms] (4) QTRS (5)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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