details

property	value
status	complete
benchmark	r3.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n033.star.cs.uiowa.edu
space	Waldmann_06_relative

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	10.117 seconds
cpu usage	36.3183
user time	34.7453
system time	1.57295
max virtual memory	7.9175128E7
max residence set size	4003680.0

stage attributes

key	value
starexec-result	YES

output

34.23/9.55 YES 34.23/9.57 proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml 34.23/9.57 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 34.23/9.57 34.23/9.57 34.23/9.57 Termination of the given RelTRS could be proven: 34.23/9.57 34.23/9.57 (0) RelTRS 34.23/9.57 (1) FlatCCProof [EQUIVALENT, 0 ms] 34.23/9.57 (2) RelTRS 34.23/9.57 (3) RootLabelingProof [EQUIVALENT, 0 ms] 34.23/9.57 (4) RelTRS 34.23/9.57 (5) RelTRSRRRProof [EQUIVALENT, 282 ms] 34.23/9.57 (6) RelTRS 34.23/9.57 (7) RelTRSRRRProof [EQUIVALENT, 101 ms] 34.23/9.57 (8) RelTRS 34.23/9.57 (9) RelTRSRRRProof [EQUIVALENT, 8 ms] 34.23/9.57 (10) RelTRS 34.23/9.57 (11) RIsEmptyProof [EQUIVALENT, 0 ms] 34.23/9.57 (12) YES 34.23/9.57 34.23/9.57 34.23/9.57 ---------------------------------------- 34.23/9.57 34.23/9.57 (0) 34.23/9.57 Obligation: 34.23/9.57 Relative term rewrite system: 34.23/9.57 The relative TRS consists of the following R rules: 34.23/9.57 34.23/9.57 a(a(x1)) -> x1 34.23/9.57 34.23/9.57 The relative TRS consists of the following S rules: 34.23/9.57 34.23/9.57 a(a(x1)) -> b(a(a(a(b(x1))))) 34.23/9.57 34.23/9.57 34.23/9.57 ---------------------------------------- 34.23/9.57 34.23/9.57 (1) FlatCCProof (EQUIVALENT) 34.23/9.57 We used flat context closure [ROOTLAB] 34.23/9.57 34.23/9.57 ---------------------------------------- 34.23/9.57 34.23/9.57 (2) 34.23/9.57 Obligation: 34.23/9.57 Relative term rewrite system: 34.23/9.57 The relative TRS consists of the following R rules: 34.23/9.57 34.23/9.57 a(a(a(x1))) -> a(x1) 34.23/9.57 b(a(a(x1))) -> b(x1) 34.23/9.57 34.23/9.57 The relative TRS consists of the following S rules: 34.23/9.57 34.23/9.57 a(a(a(x1))) -> a(b(a(a(a(b(x1)))))) 34.23/9.57 b(a(a(x1))) -> b(b(a(a(a(b(x1)))))) 34.23/9.57 34.23/9.57 34.23/9.57 ---------------------------------------- 34.23/9.57 34.23/9.57 (3) RootLabelingProof (EQUIVALENT) 34.23/9.57 We used plain root labeling [ROOTLAB] with the following heuristic: 34.23/9.57 LabelAll: All function symbols get labeled 34.23/9.57 34.23/9.57 34.23/9.57 ---------------------------------------- 34.23/9.57 34.23/9.57 (4) 34.23/9.57 Obligation: 34.23/9.57 Relative term rewrite system: 34.23/9.57 The relative TRS consists of the following R rules: 34.23/9.57 34.23/9.57 a_{a_1}(a_{a_1}(a_{a_1}(x1))) -> a_{a_1}(x1) 34.23/9.57 a_{a_1}(a_{a_1}(a_{b_1}(x1))) -> a_{b_1}(x1) 34.23/9.57 b_{a_1}(a_{a_1}(a_{a_1}(x1))) -> b_{a_1}(x1) 34.23/9.57 b_{a_1}(a_{a_1}(a_{b_1}(x1))) -> b_{b_1}(x1) 34.23/9.57 34.23/9.57 The relative TRS consists of the following S rules: 34.23/9.57 34.23/9.57 a_{a_1}(a_{a_1}(a_{a_1}(x1))) -> a_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))))) 34.23/9.57 a_{a_1}(a_{a_1}(a_{b_1}(x1))) -> a_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))))) 34.23/9.57 b_{a_1}(a_{a_1}(a_{a_1}(x1))) -> b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(b_{a_1}(x1)))))) 34.23/9.57 b_{a_1}(a_{a_1}(a_{b_1}(x1))) -> b_{b_1}(b_{a_1}(a_{a_1}(a_{a_1}(a_{b_1}(b_{b_1}(x1)))))) 34.23/9.57 34.23/9.57 34.23/9.57 ---------------------------------------- 34.23/9.57 34.23/9.57 (5) RelTRSRRRProof (EQUIVALENT) 34.23/9.57 We used the following monotonic ordering for rule removal: 34.23/9.57 Matrix interpretation [MATRO] to (N^3, +, *, >=, >) : 34.23/9.57 34.23/9.57 <<< 34.23/9.57 POL(a_{a_1}(x_1)) = [[0], [0], [1]] + [[1, 1, 0], [0, 0, 1], [0, 0, 1]] * x_1 34.23/9.57 >>> 34.23/9.57 34.23/9.57 <<< 34.23/9.57 POL(a_{b_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 34.23/9.57 >>> 34.23/9.57 34.23/9.57 <<< 34.23/9.57 POL(b_{a_1}(x_1)) = [[0], [0], [0]] + [[1, 0, 0], [0, 0, 0], [0, 0, 0]] * x_1 popout

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all output return to SRS_Relative 2019-03-29 08.12