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TRS Conditional pair #487562982
details
property
value
status
complete
benchmark
ohl230.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n144.star.cs.uiowa.edu
space
Mixed_CTRS_2014
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.37876009941 seconds
cpu usage
5.262207266
max memory
3.5667968E8
stage attributes
key
value
output-size
4416
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Quasi decreasingness of the given CTRS could not be shown: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) QDP (7) UsableRulesProof [EQUIVALENT, 0 ms] (8) QDP (9) MRRProof [EQUIVALENT, 0 ms] (10) QDP (11) NonTerminationLoopProof [COMPLETE, 0 ms] (12) NO ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: a -> b c -> f(a) f(a) -> c c -> g(b) The conditional TRS C consists of the following conditional rules: f(x) -> g(x) <= f(x) -> g(b) ---------------------------------------- (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(f(x), x) U1(g(b), x) -> g(x) a -> b c -> f(a) f(a) -> c c -> g(b) Q is empty. ---------------------------------------- (3) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: F(x) -> U1^1(f(x), x) F(x) -> F(x) C -> F(a) C -> A F(a) -> C The TRS R consists of the following rules: f(x) -> U1(f(x), x) U1(g(b), x) -> g(x) a -> b c -> f(a) f(a) -> c c -> g(b) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 2 less nodes. ---------------------------------------- (6)
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