details

property	value
status	complete
benchmark	r8.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n146.star.cs.uiowa.edu
space	Waldmann_06_relative

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	6.45526 seconds
cpu usage	21.8588
user time	20.8088
system time	1.04995
max virtual memory	3.8903172E7
max residence set size	2558320.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRS Reverse [EQUIVALENT, 0 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 669 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 0 ms] (6) RelTRS (7) RIsEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: a(b(a(x1))) -> c(c(c(x1))) c(c(c(x1))) -> a(c(a(x1))) The relative TRS consists of the following S rules: a(x1) -> b(c(b(x1))) ---------------------------------------- (1) RelTRS Reverse (EQUIVALENT) We have reversed the following relative TRS [REVERSE]: The set of rules R is a(b(a(x1))) -> c(c(c(x1))) c(c(c(x1))) -> a(c(a(x1))) The set of rules S is a(x1) -> b(c(b(x1))) We have obtained the following relative TRS: The set of rules R is a(b(a(x1))) -> c(c(c(x1))) c(c(c(x1))) -> a(c(a(x1))) The set of rules S is a(x1) -> b(c(b(x1))) ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: a(b(a(x1))) -> c(c(c(x1))) c(c(c(x1))) -> a(c(a(x1))) The relative TRS consists of the following S rules: a(x1) -> b(c(b(x1))) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^6, +, *, >=, >) : <<< POL(a(x_1)) = [[0], [0], [1], [0], [0], [0]] + [[1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0]] * x_1 >>> <<< POL(b(x_1)) = [[0], [0], [0], [0], [0], [0]] + [[1, 0, 0, 0, 0, 0], [0, 0, 1, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]] * x_1 >>> <<< POL(c(x_1)) = [[0], [0], [0], [0], [0], [1]] + [[1, 0, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0]] * x_1 >>> With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: a(b(a(x1))) -> c(c(c(x1))) Rules from S: none ---------------------------------------- (4) Obligation: popout

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

job log

popout

actions

all output return to SRS Relative