Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Stand 20472 pair #381709617
details
property
value
status
complete
benchmark
zerolist.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n104.star.cs.uiowa.edu
space
AProVE_09_Inductive
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.51021289825 seconds
cpu usage
6.100476781
max memory
3.19377408E8
stage attributes
key
value
output-size
20109
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof [EQUIVALENT, 0 ms] (4) QDP (5) DependencyGraphProof [EQUIVALENT, 0 ms] (6) AND (7) QDP (8) UsableRulesProof [EQUIVALENT, 0 ms] (9) QDP (10) QReductionProof [EQUIVALENT, 0 ms] (11) QDP (12) QDPSizeChangeProof [EQUIVALENT, 0 ms] (13) YES (14) QDP (15) UsableRulesProof [EQUIVALENT, 0 ms] (16) QDP (17) QReductionProof [EQUIVALENT, 0 ms] (18) QDP (19) QDPOrderProof [EQUIVALENT, 17 ms] (20) QDP (21) Induction-Processor [SOUND, 49 ms] (22) AND (23) QDP (24) DependencyGraphProof [EQUIVALENT, 0 ms] (25) TRUE (26) QTRS (27) QTRSRRRProof [EQUIVALENT, 3 ms] (28) QTRS (29) RisEmptyProof [EQUIVALENT, 0 ms] (30) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: sub(0, 0) -> 0 sub(s(x), 0) -> s(x) sub(0, s(x)) -> 0 sub(s(x), s(y)) -> sub(x, y) zero(nil) -> zero2(0, nil) zero(cons(x, xs)) -> zero2(sub(x, x), cons(x, xs)) zero2(0, nil) -> nil zero2(0, cons(x, xs)) -> cons(sub(x, x), zero(xs)) zero2(s(y), nil) -> zero(nil) zero2(s(y), cons(x, xs)) -> zero(cons(x, xs)) Q is empty. ---------------------------------------- (1) Overlay + Local Confluence (EQUIVALENT) The TRS is overlay and locally confluent. By [NOC] we can switch to innermost. ---------------------------------------- (2) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: sub(0, 0) -> 0 sub(s(x), 0) -> s(x) sub(0, s(x)) -> 0 sub(s(x), s(y)) -> sub(x, y) zero(nil) -> zero2(0, nil) zero(cons(x, xs)) -> zero2(sub(x, x), cons(x, xs)) zero2(0, nil) -> nil zero2(0, cons(x, xs)) -> cons(sub(x, x), zero(xs)) zero2(s(y), nil) -> zero(nil) zero2(s(y), cons(x, xs)) -> zero(cons(x, xs)) The set Q consists of the following terms: sub(0, 0) sub(s(x0), 0) sub(0, s(x0)) sub(s(x0), s(x1)) zero(nil) zero(cons(x0, x1)) zero2(0, nil) zero2(0, cons(x0, x1)) zero2(s(x0), nil) zero2(s(x0), cons(x1, x2))
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Stand 20472