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TRS Relat 75837 pair #381725044
details
property
value
status
complete
benchmark
#3.54_rand.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n006.star.cs.uiowa.edu
space
INVY_15
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.67545485497 seconds
cpu usage
7.692675021
max memory
9.38344448E8
stage attributes
key
value
output-size
5261
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 53 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 22 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 19 ms] (6) RelTRS (7) RelTRSRRRProof [EQUIVALENT, 14 ms] (8) RelTRS (9) RIsEmptyProof [EQUIVALENT, 0 ms] (10) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: f(g(x)) -> g(f(f(x))) f(h(x)) -> h(g(x)) 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: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(f(x_1)) = [[0], [2]] + [[1, 0], [0, 0]] * x_1 >>> <<< POL(g(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 >>> <<< POL(h(x_1)) = [[0], [0]] + [[2, 0], [0, 0]] * x_1 >>> <<< POL(f'(x_1, x_2, x_3)) = [[0], [0]] + [[3, 0], [0, 0]] * x_1 + [[2, 0], [0, 0]] * x_2 + [[1, 0], [0, 0]] * x_3 >>> <<< POL(s(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 >>> <<< POL(rand(x_1)) = [[3], [3]] + [[1, 0], [0, 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(g(x)) -> g(f(f(x))) f(h(x)) -> h(g(x)) f'(s(x), y, y) -> f'(y, x, s(x)) The relative TRS consists of the following S rules: rand(x) -> rand(s(x)) ----------------------------------------
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