details

property	value
status	complete
benchmark	zr06.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n149.star.cs.uiowa.edu
space	Mixed_relative_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.41889 seconds
cpu usage	6.76884
user time	6.41631
system time	0.352522
max virtual memory	1.9353616E7
max residence set size	596084.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RootLabelingProof [EQUIVALENT, 0 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 89 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 42 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))) -> a(b(b(a(x1)))) The relative TRS consists of the following S rules: b(x1) -> b(b(b(x1))) ---------------------------------------- (1) RootLabelingProof (EQUIVALENT) We used plain root labeling [ROOTLAB] with the following heuristic: LabelAll: All function symbols get labeled ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: a_{b_1}(b_{a_1}(a_{a_1}(x1))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1)))) a_{b_1}(b_{a_1}(a_{b_1}(x1))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) The relative TRS consists of the following S rules: b_{a_1}(x1) -> b_{b_1}(b_{b_1}(b_{a_1}(x1))) b_{b_1}(x1) -> b_{b_1}(b_{b_1}(b_{b_1}(x1))) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(a_{b_1}(x_1)) = [[0], [0]] + [[1, 2], [0, 0]] * x_1 >>> <<< POL(b_{a_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 2]] * x_1 >>> <<< POL(a_{a_1}(x_1)) = [[0], [2]] + [[1, 0], [0, 0]] * x_1 >>> <<< POL(b_{b_1}(x_1)) = [[0], [0]] + [[1, 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_1}(b_{a_1}(a_{a_1}(x1))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1)))) Rules from S: none ---------------------------------------- (4) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: a_{b_1}(b_{a_1}(a_{b_1}(x1))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) The relative TRS consists of the following S rules: b_{a_1}(x1) -> b_{b_1}(b_{b_1}(b_{a_1}(x1))) b_{b_1}(x1) -> b_{b_1}(b_{b_1}(b_{b_1}(x1))) popout

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

job log

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actions

all output return to SRS Relative