Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Standard pair #487068733
details
property
value
status
complete
benchmark
z02.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n180.star.cs.uiowa.edu
space
Zantema_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.67948 seconds
cpu usage
6.75626
user time
6.45355
system time
0.302708
max virtual memory
1.8544316E7
max residence set size
461996.0
stage attributes
key
value
starexec-result
YES
output
YES proof of /export/starexec/sandbox2/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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) DependencyGraphProof [EQUIVALENT, 0 ms] (4) QDP (5) TransformationProof [EQUIVALENT, 0 ms] (6) QDP (7) DependencyGraphProof [EQUIVALENT, 0 ms] (8) QDP (9) SemLabProof [SOUND, 47 ms] (10) QDP (11) DependencyGraphProof [EQUIVALENT, 0 ms] (12) QDP (13) UsableRulesReductionPairsProof [EQUIVALENT, 6 ms] (14) QDP (15) DependencyGraphProof [EQUIVALENT, 0 ms] (16) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: a(f, a(f, x)) -> a(x, g) a(x, g) -> a(f, a(g, a(f, x))) Q is empty. ---------------------------------------- (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: A(f, a(f, x)) -> A(x, g) A(x, g) -> A(f, a(g, a(f, x))) A(x, g) -> A(g, a(f, x)) A(x, g) -> A(f, x) The TRS R consists of the following rules: a(f, a(f, x)) -> a(x, g) a(x, g) -> a(f, a(g, a(f, x))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (3) DependencyGraphProof (EQUIVALENT) The approximation of the Dependency Graph [LPAR04,FROCOS05,EDGSTAR] contains 1 SCC with 1 less node. ---------------------------------------- (4) Obligation: Q DP problem: The TRS P consists of the following rules: A(x, g) -> A(f, a(g, a(f, x))) A(f, a(f, x)) -> A(x, g) A(x, g) -> A(f, x) The TRS R consists of the following rules: a(f, a(f, x)) -> a(x, g) a(x, g) -> a(f, a(g, a(f, x))) Q is empty. We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) TransformationProof (EQUIVALENT) By narrowing [LPAR04] the rule A(x, g) -> A(f, a(g, a(f, x))) at position [1] we obtained the following new rules [LPAR04]: (A(a(f, x0), g) -> A(f, a(g, a(x0, g))),A(a(f, x0), g) -> A(f, a(g, a(x0, g)))) (A(g, g) -> A(f, a(g, a(f, a(g, a(f, f))))),A(g, g) -> A(f, a(g, a(f, a(g, a(f, f)))))) ---------------------------------------- (6) Obligation: Q DP problem: The TRS P consists of the following rules: A(f, a(f, x)) -> A(x, g)
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Standard