Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Conditional pair #487562850
details
property
value
status
complete
benchmark
263.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)
1.61367201805 seconds
cpu usage
3.644015175
max memory
2.38518272E8
stage attributes
key
value
output-size
2676
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 55 ms] (4) QTRS (5) QTRSRRRProof [EQUIVALENT, 0 ms] (6) QTRS (7) RisEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Conditional term rewrite system: The TRS R consists of the following rules: a -> c g(a) -> h(b) h(b) -> g(c) The conditional TRS C consists of the following conditional rules: f(x) -> z <= g(x) -> h(z) ---------------------------------------- (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(g(x)) U1(h(z)) -> z a -> c g(a) -> h(b) h(b) -> g(c) Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(U1(x_1)) = 2*x_1 POL(a) = 0 POL(b) = 0 POL(c) = 0 POL(f(x_1)) = 2 + 2*x_1 POL(g(x_1)) = x_1 POL(h(x_1)) = 2*x_1 With this ordering the following rules can be removed by the rule removal processor [LPAR04] because they are oriented strictly: f(x) -> U1(g(x)) ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: U1(h(z)) -> z a -> c g(a) -> h(b) h(b) -> g(c) Q is empty. ---------------------------------------- (5) QTRSRRRProof (EQUIVALENT) Used ordering: Knuth-Bendix order [KBO] with precedence:b > h_1 > g_1 > c > a > U1_1 and weight map:
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Conditional