details

property	value
status	complete
benchmark	thiemann23.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n181.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	3.02417 seconds
cpu usage	7.44626
user time	7.17817
system time	0.268083
max virtual memory	1.849042E7
max residence set size	379744.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) Overlay + Local Confluence [EQUIVALENT, 0 ms] (2) QTRS (3) DependencyPairsProof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) RemovalProof [SOUND, 0 ms] (20) QDP (21) NonInfProof [EQUIVALENT, 4 ms] (22) QDP (23) DependencyGraphProof [EQUIVALENT, 0 ms] (24) TRUE ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: digits -> d(0) d(x) -> if(le(x, s(s(s(s(s(s(s(s(s(0)))))))))), x) if(true, x) -> cons(x, d(s(x))) if(false, x) -> nil le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) 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: digits -> d(0) d(x) -> if(le(x, s(s(s(s(s(s(s(s(s(0)))))))))), x) if(true, x) -> cons(x, d(s(x))) if(false, x) -> nil le(0, y) -> true le(s(x), 0) -> false le(s(x), s(y)) -> le(x, y) The set Q consists of the following terms: digits d(x0) if(true, x0) if(false, x0) le(0, x0) le(s(x0), 0) le(s(x0), s(x1)) ---------------------------------------- (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: DIGITS -> D(0) D(x) -> IF(le(x, s(s(s(s(s(s(s(s(s(0)))))))))), x) D(x) -> LE(x, s(s(s(s(s(s(s(s(s(0)))))))))) IF(true, x) -> D(s(x)) LE(s(x), s(y)) -> LE(x, y) 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 Standard