details

property	value
status	complete
benchmark	carbridge.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	Mixed_relative_TRS

run statistics

property	value
solver	AProVE
configuration	standard
runtime (wallclock)	2.30139 seconds
cpu usage	5.9069
user time	5.63483
system time	0.272077
max virtual memory	1.8546144E7
max residence set size	588388.0

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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 134 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 12 ms] (4) RelTRS (5) RIsEmptyProof [EQUIVALENT, 3 ms] (6) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: top(left(car(x, y), car(old, z))) -> top(right(y, car(old, z))) top(left(car(x, car(old, y)), z)) -> top(right(car(old, y), z)) top(right(x, car(y, car(old, z)))) -> top(left(x, car(old, z))) top(right(car(old, x), car(y, z))) -> top(left(car(old, x), z)) top(left(bot, car(old, x))) -> top(right(bot, car(old, x))) top(right(car(old, x), bot)) -> top(left(car(old, x), bot)) The relative TRS consists of the following S rules: top(left(car(x, y), z)) -> top(left(y, z)) top(right(x, car(y, z))) -> top(right(x, z)) bot -> car(new, bot) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(top(x_1)) = [[0], [1]] + [[1, 1], [1, 0]] * x_1 >>> <<< POL(left(x_1, x_2)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 + [[1, 1], [0, 1]] * x_2 >>> <<< POL(car(x_1, x_2)) = [[0], [0]] + [[1, 0], [1, 1]] * x_1 + [[1, 1], [1, 1]] * x_2 >>> <<< POL(old) = [[0], [1]] >>> <<< POL(right(x_1, x_2)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 + [[1, 1], [0, 0]] * x_2 >>> <<< POL(bot) = [[0], [0]] >>> <<< POL(new) = [[0], [0]] >>> With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: top(left(car(x, y), car(old, z))) -> top(right(y, car(old, z))) top(left(car(x, car(old, y)), z)) -> top(right(car(old, y), z)) top(left(bot, car(old, x))) -> top(right(bot, car(old, x))) Rules from S: none ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: top(right(x, car(y, car(old, z)))) -> top(left(x, car(old, z))) top(right(car(old, x), car(y, z))) -> top(left(car(old, x), z)) top(right(car(old, x), bot)) -> top(left(car(old, x), bot)) The relative TRS consists of the following S rules: top(left(car(x, y), z)) -> top(left(y, z)) top(right(x, car(y, z))) -> top(right(x, z)) bot -> car(new, bot) popout

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

job log

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actions

all output return to TRS Relative