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TRS Conditional pair #487563018
details
property
value
status
complete
benchmark
ohl196.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n101.star.cs.uiowa.edu
space
Mixed_CTRS_2014
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.78325200081 seconds
cpu usage
3.660328741
max memory
2.33132032E8
stage attributes
key
value
output-size
3228
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 47 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) QTRSRRRProof [EQUIVALENT, 0 ms] (8) QTRS (9) RisEmptyProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: a -> b a -> c The conditional TRS C consists of the following conditional rules: f(x) -> x <= x -> c g(x) -> x <= x -> c ---------------------------------------- (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: f(x) -> U1(x, x) U1(c, x) -> x g(x) -> U2(x, x) U2(c, x) -> x a -> b a -> c Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(U1(x_1, x_2)) = 1 + x_1 + x_2 POL(U2(x_1, x_2)) = 2 + x_1 + x_2 POL(a) = 1 POL(b) = 0 POL(c) = 0 POL(f(x_1)) = 1 + 2*x_1 POL(g(x_1)) = 2 + 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: U1(c, x) -> x U2(c, x) -> x a -> b a -> c ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(x) -> U1(x, x) g(x) -> U2(x, x) Q is empty. ---------------------------------------- (5) QTRSRRRProof (EQUIVALENT)
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