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TRS Relative pair #487081749
details
property
value
status
complete
benchmark
#3.29_rand.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n137.star.cs.uiowa.edu
space
INVY_15
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
3.08077 seconds
cpu usage
5.61134
user time
5.35745
system time
0.253888
max virtual memory
1.8749456E7
max residence set size
420224.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 12 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 9 ms] (4)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: f(s(x), y, y) -> f(y, x, s(x)) 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: Polynomial interpretation [POLO]: POL(f(x_1, x_2, x_3)) = 5*x_1 + 4*x_2 + x_3 POL(rand(x_1)) = 5 + 7*x_1 POL(s(x_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(s(x), y, y) -> f(y, x, s(x)) 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, x_3)) = [[0], [0]] + [[1, 1], [0, 1]] * x_1 + [[1, 1], [0, 0]] * x_2 + [[1, 0], [0, 1]] * x_3 >>> <<< POL(s(x_1)) = [[0], [1]] + [[1, 0], [1, 1]] * x_1 >>> <<< POL(rand(x_1)) = [[1], [1]] + [[1, 0], [1, 0]] * x_1 >>> With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: f(s(x), y, y) -> f(y, x, s(x)) Rules from S: none ---------------------------------------- (4) Obligation: Relative term rewrite system: R is empty. The relative TRS consists of the following S rules:
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