details

property	value
status	complete
benchmark	r10.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n141.star.cs.uiowa.edu
space	Waldmann_06_relative

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	124.068 seconds
cpu usage	487.04
user time	480.784
system time	6.2555
max virtual memory	3.9701852E7
max residence set size	9087300.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRS Reverse [EQUIVALENT, 0 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 66.7 s] (4) RelTRS (5) RIsEmptyProof [EQUIVALENT, 0 ms] (6) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: b(a(a(b(x1)))) -> a(a(a(a(x1)))) a(b(b(a(x1)))) -> b(b(b(b(x1)))) The relative TRS consists of the following S rules: b(x1) -> b(b(b(x1))) ---------------------------------------- (1) RelTRS Reverse (EQUIVALENT) We have reversed the following relative TRS [REVERSE]: The set of rules R is b(a(a(b(x1)))) -> a(a(a(a(x1)))) a(b(b(a(x1)))) -> b(b(b(b(x1)))) The set of rules S is b(x1) -> b(b(b(x1))) We have obtained the following relative TRS: The set of rules R is b(a(a(b(x1)))) -> a(a(a(a(x1)))) a(b(b(a(x1)))) -> b(b(b(b(x1)))) The set of rules S is b(x1) -> b(b(b(x1))) ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: b(a(a(b(x1)))) -> a(a(a(a(x1)))) a(b(b(a(x1)))) -> b(b(b(b(x1)))) The relative TRS consists of the following S rules: b(x1) -> b(b(b(x1))) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^6, +, *, >=, >) : <<< POL(b(x_1)) = [[0], [0], [1], [0], [0], [0]] + [[1, 0, 0, 1, 0, 0], [0, 0, 0, 1, 0, 1], [0, 1, 0, 0, 1, 0], [0, 0, 0, 0, 0, 0], [0, 0, 0, 1, 0, 0], [0, 0, 0, 0, 1, 0]] * x_1 >>> <<< POL(a(x_1)) = [[0], [0], [0], [0], [1], [0]] + [[1, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 0], [0, 1, 0, 0, 0, 0], [0, 0, 0, 0, 0, 1], [0, 0, 0, 1, 0, 0], [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: b(a(a(b(x1)))) -> a(a(a(a(x1)))) a(b(b(a(x1)))) -> b(b(b(b(x1)))) Rules from S: none ---------------------------------------- (4) Obligation: Relative term rewrite system: R is empty. The relative TRS consists of the following S rules: b(x1) -> b(b(b(x1))) popout

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all output return to SRS Relative