details

property	value
status	complete
benchmark	#4.22.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n138.star.cs.uiowa.edu
space	AG01_innermost

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	1.65738 seconds
cpu usage	3.59191
user time	3.44149
system time	0.150419
max virtual memory	1.8343376E7
max residence set size	230600.0

stage attributes

key	value
starexec-result	YES

output

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination w.r.t. Q of the given QTRS could be proven: (0) QTRS (1) DependencyPairsProof [EQUIVALENT, 0 ms] (2) QDP (3) UsableRulesProof [EQUIVALENT, 0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) QDPSizeChangeProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Q restricted rewrite system: The TRS R consists of the following rules: quot(0, s(y), s(z)) -> 0 quot(s(x), s(y), z) -> quot(x, y, z) quot(x, 0, s(z)) -> s(quot(x, s(z), s(z))) The set Q consists of the following terms: quot(0, s(x0), s(x1)) quot(s(x0), s(x1), x2) quot(x0, 0, s(x1)) ---------------------------------------- (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: QUOT(s(x), s(y), z) -> QUOT(x, y, z) QUOT(x, 0, s(z)) -> QUOT(x, s(z), s(z)) The TRS R consists of the following rules: quot(0, s(y), s(z)) -> 0 quot(s(x), s(y), z) -> quot(x, y, z) quot(x, 0, s(z)) -> s(quot(x, s(z), s(z))) The set Q consists of the following terms: quot(0, s(x0), s(x1)) quot(s(x0), s(x1), x2) quot(x0, 0, s(x1)) 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: QUOT(s(x), s(y), z) -> QUOT(x, y, z) QUOT(x, 0, s(z)) -> QUOT(x, s(z), s(z)) R is empty. The set Q consists of the following terms: quot(0, s(x0), s(x1)) quot(s(x0), s(x1), x2) quot(x0, 0, s(x1)) We have to consider all minimal (P,Q,R)-chains. ---------------------------------------- (5) QReductionProof (EQUIVALENT) We deleted the following terms from Q as each root-symbol of these terms does neither occur in P nor in R.[THIEMANN]. quot(0, s(x0), s(x1)) quot(s(x0), s(x1), x2) quot(x0, 0, s(x1)) ---------------------------------------- (6) Obligation: Q DP problem: popout

output may be truncated. 'popout' for the full output.

job log

popout

actions

all output return to TRS Innermost