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TRS Conditional pair #487562868
details
property
value
status
complete
benchmark
324.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n022.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.99246311188 seconds
cpu usage
4.121143439
max memory
3.17386752E8
stage attributes
key
value
output-size
5877
starexec-result
MAYBE
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- MAYBE proof of /export/starexec/sandbox/benchmark/theBenchmark.xml # AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Quasi decreasingness of the given CTRS could not be shown: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 33 ms] (4) QTRS (5) AAECC Innermost [EQUIVALENT, 0 ms] (6) QTRS (7) DependencyPairsProof [EQUIVALENT, 0 ms] (8) QDP (9) UsableRulesProof [EQUIVALENT, 0 ms] (10) QDP (11) QReductionProof [EQUIVALENT, 0 ms] (12) QDP (13) TransformationProof [EQUIVALENT, 0 ms] (14) QDP (15) NonTerminationLoopProof [COMPLETE, 0 ms] (16) NO ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: odd(0) -> false even(0) -> true eq(x, x) -> eq(T, T) The conditional TRS C consists of the following conditional rules: odd(s(x)) -> true <= eq(even(x), true) -> eq(T, T) odd(s(x)) -> false <= eq(even(x), false) -> eq(T, T) even(s(x)) -> true <= eq(odd(x), true) -> eq(T, T) even(s(x)) -> false <= eq(odd(x), false) -> eq(T, T) ---------------------------------------- (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: odd(s(x)) -> U1(eq(even(x), true)) U1(eq(T, T)) -> true odd(s(x)) -> U2(eq(even(x), false)) U2(eq(T, T)) -> false even(s(x)) -> U3(eq(odd(x), true)) U3(eq(T, T)) -> true even(s(x)) -> U4(eq(odd(x), false)) U4(eq(T, T)) -> false odd(0) -> false even(0) -> true eq(x, x) -> eq(T, T) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:odd_1 > U1_1 > true > eq_2 > 0 > even_1 > U4_1 > U3_1 > U2_1 > false > s_1 > T and weight map: true=4 T=1 false=3 0=1 odd_1=5 s_1=7 U1_1=2 even_1=6 U2_1=1 U3_1=3 U4_1=1 eq_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: odd(s(x)) -> U1(eq(even(x), true))
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