Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Innermost pair #487524603
details
property
value
status
complete
benchmark
innermost3.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_innermost
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.95871901512 seconds
cpu usage
4.13340475
max memory
2.940928E8
stage attributes
key
value
output-size
4190
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) UsableRulesProof [EQUIVALENT, 0 ms] (4) QDP (5) QReductionProof [EQUIVALENT, 0 ms] (6) QDP (7) TransformationProof [EQUIVALENT, 0 ms] (8) QDP (9) TransformationProof [EQUIVALENT, 0 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: f(a(x), y) -> g(x, y) g(x, y) -> h(x, y) h(b, y) -> f(y, y) a(b) -> c The set Q consists of the following terms: f(a(x0), x1) g(x0, x1) h(b, x0) a(b) ---------------------------------------- (1) DependencyPairsProof (EQUIVALENT) Using Dependency Pairs [AG00,LPAR04] we result in the following initial DP problem. ---------------------------------------- (2) Obligation: Q DP problem: The TRS P consists of the following rules: F(a(x), y) -> G(x, y) G(x, y) -> H(x, y) H(b, y) -> F(y, y) The TRS R consists of the following rules: f(a(x), y) -> g(x, y) g(x, y) -> h(x, y) h(b, y) -> f(y, y) a(b) -> c The set Q consists of the following terms: f(a(x0), x1) g(x0, x1) h(b, x0) a(b) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) UsableRulesProof (EQUIVALENT) As all Q-normal forms are R-normal forms we are in the innermost case. Hence, by the usable rules processor [LPAR04] we can delete all non-usable rules [FROCOS05] from R. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: F(a(x), y) -> G(x, y) G(x, y) -> H(x, y) H(b, y) -> F(y, y) R is empty. The set Q consists of the following terms: f(a(x0), x1) g(x0, x1) h(b, x0) a(b)
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Innermost