Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Stand 20472 pair #381710971
details
property
value
status
complete
benchmark
append.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n028.star.cs.uiowa.edu
space
CiME_04
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.59891605377 seconds
cpu usage
3.551902788
max memory
2.2380544E8
stage attributes
key
value
output-size
4951
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) AAECC Innermost [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) UsableRulesProof [EQUIVALENT, 0 ms] (6) QDP (7) QReductionProof [EQUIVALENT, 0 ms] (8) QDP (9) QDPSizeChangeProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: is_empty(nil) -> true is_empty(cons(x, l)) -> false hd(cons(x, l)) -> x tl(cons(x, l)) -> l append(l1, l2) -> ifappend(l1, l2, l1) ifappend(l1, l2, nil) -> l2 ifappend(l1, l2, cons(x, l)) -> cons(x, append(l, l2)) Q is empty. ---------------------------------------- (1) AAECC Innermost (EQUIVALENT) We have applied [NOC,AAECCNOC] to switch to innermost. The TRS R 1 is hd(cons(x, l)) -> x tl(cons(x, l)) -> l ifappend(l1, l2, nil) -> l2 ifappend(l1, l2, cons(x, l)) -> cons(x, append(l, l2)) append(l1, l2) -> ifappend(l1, l2, l1) The TRS R 2 is is_empty(nil) -> true is_empty(cons(x, l)) -> false The signature Sigma is {is_empty_1, true, false} ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: is_empty(nil) -> true is_empty(cons(x, l)) -> false hd(cons(x, l)) -> x tl(cons(x, l)) -> l append(l1, l2) -> ifappend(l1, l2, l1) ifappend(l1, l2, nil) -> l2 ifappend(l1, l2, cons(x, l)) -> cons(x, append(l, l2)) The set Q consists of the following terms: is_empty(nil) is_empty(cons(x0, x1)) hd(cons(x0, x1)) tl(cons(x0, x1)) append(x0, x1) ifappend(x0, x1, nil) ifappend(x0, x1, cons(x2, x3)) ---------------------------------------- (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: APPEND(l1, l2) -> IFAPPEND(l1, l2, l1) IFAPPEND(l1, l2, cons(x, l)) -> APPEND(l, l2) The TRS R consists of the following rules:
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Stand 20472