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TRS Relative pair #487520643
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
n148.star.cs.uiowa.edu
space
Mixed_relative_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.13530302048 seconds
cpu usage
5.338356647
max memory
5.01055488E8
stage attributes
key
value
output-size
4007
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_standard /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 123 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 2 ms] (4) RelTRS (5) RIsEmptyProof [EQUIVALENT, 0 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))
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