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TRS Relative pair #487520559
details
property
value
status
complete
benchmark
ex4.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
INVY_15
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.88458299637 seconds
cpu usage
4.270313138
max memory
2.8915712E8
stage attributes
key
value
output-size
1950
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 56 ms] (2) RelTRS (3) RIsEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: a -> b The relative TRS consists of the following S rules: f(s(x)) -> c(x, f(x)) c(x, c(y, z)) -> c(y, c(x, z)) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(a) = [[1], [1]] >>> <<< POL(b) = [[0], [1]] >>> <<< POL(f(x_1)) = [[0], [0]] + [[1, 1], [0, 0]] * x_1 >>> <<< POL(s(x_1)) = [[0], [0]] + [[1, 1], [1, 1]] * x_1 >>> <<< POL(c(x_1, x_2)) = [[0], [0]] + [[1, 1], [0, 0]] * x_1 + [[1, 0], [0, 0]] * x_2 >>> <<< POL(y) = [[0], [0]] >>> <<< POL(z) = [[0], [1]] >>> With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: a -> b Rules from S: none ---------------------------------------- (2) Obligation: Relative term rewrite system: R is empty. The relative TRS consists of the following S rules: f(s(x)) -> c(x, f(x)) c(x, c(y, z)) -> c(y, c(x, z)) ---------------------------------------- (3) RIsEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES
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