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TRS Relative pair #487520601
details
property
value
status
complete
benchmark
#3.47_rand.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n149.star.cs.uiowa.edu
space
INVY_15
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.40395212173 seconds
cpu usage
5.347348534
max memory
4.4517376E8
stage attributes
key
value
output-size
3886
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_standard /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- 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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 50 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 3 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 3 ms] (6) RelTRS (7) RIsEmptyProof [EQUIVALENT, 0 ms] (8) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: f(x, c(y)) -> f(x, s(f(y, y))) f(s(x), y) -> f(x, s(c(y))) The relative TRS consists of the following S rules: rand(x) -> x rand(x) -> rand(s(x)) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(f(x_1, x_2)) = [[1], [0]] + [[1, 0], [1, 0]] * x_1 + [[1, 1], [1, 1]] * x_2 >>> <<< POL(c(x_1)) = [[0], [1]] + [[1, 1], [1, 1]] * x_1 >>> <<< POL(s(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 >>> <<< POL(rand(x_1)) = [[1], [1]] + [[1, 1], [1, 1]] * x_1 >>> With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: none Rules from S: rand(x) -> x ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: f(x, c(y)) -> f(x, s(f(y, y))) f(s(x), y) -> f(x, s(c(y))) The relative TRS consists of the following S rules: rand(x) -> rand(s(x)) ---------------------------------------- (3) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(f(x_1, x_2)) = [[0], [1]] + [[1, 0], [1, 0]] * x_1 + [[1, 1], [0, 0]] * x_2 >>> <<< POL(c(x_1)) = [[0], [1]] + [[1, 1], [1, 1]] * x_1 >>>
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