Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Condi 20667 pair #381733187
details
property
value
status
complete
benchmark
406.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n097.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.67843198776 seconds
cpu usage
3.682923312
max memory
1.9113984E8
stage attributes
key
value
output-size
2889
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Quasi decreasingness of the given CTRS could be proven: (0) CTRS (1) CTRSToQTRSProof [SOUND, 0 ms] (2) QTRS (3) QTRSRRRProof [EQUIVALENT, 62 ms] (4) QTRS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: g(s(x)) -> x h(s(x)) -> x The conditional TRS C consists of the following conditional rules: f(x, y) -> g(x) <= c(g(x)) -> c(a) f(x, y) -> h(x) <= c(h(x)) -> c(a) ---------------------------------------- (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, y) -> U1(c(g(x)), x) U1(c(a), x) -> g(x) f(x, y) -> U2(c(h(x)), x) U2(c(a), x) -> h(x) g(s(x)) -> x h(s(x)) -> x Q is empty. ---------------------------------------- (3) QTRSRRRProof (EQUIVALENT) Used ordering: Polynomial interpretation [POLO]: POL(U1(x_1, x_2)) = x_1 + x_2 POL(U2(x_1, x_2)) = x_1 + x_2 POL(a) = 0 POL(c(x_1)) = x_1 POL(f(x_1, x_2)) = 1 + 2*x_1 + x_2 POL(g(x_1)) = x_1 POL(h(x_1)) = x_1 POL(s(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, y) -> U1(c(g(x)), x) f(x, y) -> U2(c(h(x)), x) g(s(x)) -> x h(s(x)) -> x ---------------------------------------- (4) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: U1(c(a), x) -> g(x) U2(c(a), x) -> h(x) Q is empty. ---------------------------------------- (5) QTRSRRRProof (EQUIVALENT) Used ordering:
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Condi 20667