details

property	value
status	complete
benchmark	zr10.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n037.star.cs.uiowa.edu
space	Mixed_relative_SRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	4.11185 seconds
cpu usage	12.7463
user time	11.9299
system time	0.816444
max virtual memory	3.817356E7
max residence set size	1595812.0

stage attributes

key	value
starexec-result	YES

output

12.29/4.02 YES 12.29/4.04 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 12.29/4.04 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 12.29/4.04 12.29/4.04 12.29/4.04 Termination of the given RelTRS could be proven: 12.29/4.04 12.29/4.04 (0) RelTRS 12.29/4.04 (1) RootLabelingProof [EQUIVALENT, 0 ms] 12.29/4.04 (2) RelTRS 12.29/4.04 (3) RelTRSRRRProof [EQUIVALENT, 133 ms] 12.29/4.04 (4) RelTRS 12.29/4.04 (5) RelTRSRRRProof [EQUIVALENT, 101 ms] 12.29/4.04 (6) RelTRS 12.29/4.04 (7) RelTRSRRRProof [EQUIVALENT, 10 ms] 12.29/4.04 (8) RelTRS 12.29/4.04 (9) RelTRSRRRProof [EQUIVALENT, 0 ms] 12.29/4.04 (10) RelTRS 12.29/4.04 (11) RIsEmptyProof [EQUIVALENT, 0 ms] 12.29/4.04 (12) YES 12.29/4.04 12.29/4.04 12.29/4.04 ---------------------------------------- 12.29/4.04 12.29/4.04 (0) 12.29/4.04 Obligation: 12.29/4.04 Relative term rewrite system: 12.29/4.04 The relative TRS consists of the following R rules: 12.29/4.04 12.29/4.04 a(b(a(x1))) -> a(b(b(a(x1)))) 12.29/4.04 b(a(b(x1))) -> b(a(a(b(x1)))) 12.29/4.04 12.29/4.04 The relative TRS consists of the following S rules: 12.29/4.04 12.29/4.04 a(x1) -> a(a(a(x1))) 12.29/4.04 b(x1) -> b(b(b(x1))) 12.29/4.04 12.29/4.04 12.29/4.04 ---------------------------------------- 12.29/4.04 12.29/4.04 (1) RootLabelingProof (EQUIVALENT) 12.29/4.04 We used plain root labeling [ROOTLAB] with the following heuristic: 12.29/4.04 LabelAll: All function symbols get labeled 12.29/4.04 12.29/4.04 12.29/4.04 ---------------------------------------- 12.29/4.04 12.29/4.04 (2) 12.29/4.04 Obligation: 12.29/4.04 Relative term rewrite system: 12.29/4.04 The relative TRS consists of the following R rules: 12.29/4.04 12.29/4.04 a_{b_1}(b_{a_1}(a_{a_1}(x1))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{a_1}(x1)))) 12.29/4.04 a_{b_1}(b_{a_1}(a_{b_1}(x1))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) 12.29/4.04 b_{a_1}(a_{b_1}(b_{a_1}(x1))) -> b_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))) 12.29/4.04 b_{a_1}(a_{b_1}(b_{b_1}(x1))) -> b_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))) 12.29/4.04 12.29/4.04 The relative TRS consists of the following S rules: 12.29/4.04 12.29/4.04 a_{a_1}(x1) -> a_{a_1}(a_{a_1}(a_{a_1}(x1))) 12.29/4.04 a_{b_1}(x1) -> a_{a_1}(a_{a_1}(a_{b_1}(x1))) 12.29/4.04 b_{a_1}(x1) -> b_{b_1}(b_{b_1}(b_{a_1}(x1))) 12.29/4.04 b_{b_1}(x1) -> b_{b_1}(b_{b_1}(b_{b_1}(x1))) 12.29/4.04 12.29/4.04 12.29/4.04 ---------------------------------------- 12.29/4.04 12.29/4.04 (3) RelTRSRRRProof (EQUIVALENT) 12.29/4.04 We used the following monotonic ordering for rule removal: 12.29/4.04 Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : 12.29/4.04 12.29/4.04 <<< 12.29/4.04 POL(a_{b_1}(x_1)) = [[0], [1]] + [[1, 2], [2, 0]] * x_1 12.29/4.04 >>> 12.29/4.04 12.29/4.04 <<< 12.29/4.04 POL(b_{a_1}(x_1)) = [[0], [0]] + [[2, 0], [1, 1]] * x_1 12.29/4.04 >>> 12.29/4.04 12.29/4.04 <<< 12.29/4.04 POL(a_{a_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 12.29/4.04 >>> 12.29/4.04 12.29/4.04 <<< 12.29/4.04 POL(b_{b_1}(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 12.29/4.04 >>> 12.29/4.04 12.29/4.04 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 12.29/4.04 Rules from R: 12.29/4.04 12.29/4.04 a_{b_1}(b_{a_1}(a_{b_1}(x1))) -> a_{b_1}(b_{b_1}(b_{a_1}(a_{b_1}(x1)))) 12.29/4.04 Rules from S: 12.29/4.04 none 12.29/4.04 12.29/4.04 12.29/4.04 12.29/4.04 12.29/4.04 ---------------------------------------- 12.29/4.04 12.29/4.04 (4) popout

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all output return to SRS_Relative 2019-03-29 08.12