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TRS_Relative 2019-03-21 03.54 pair #429988758
details
property
value
status
complete
benchmark
rt2-5.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
Relative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.84673 seconds
cpu usage
3.99332
user time
3.7876
system time
0.205714
max virtual memory
3.8036792E7
max residence set size
306512.0
stage attributes
key
value
starexec-result
YES
output
3.86/1.81 YES 3.93/1.81 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 3.93/1.81 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 3.93/1.81 3.93/1.81 3.93/1.81 Termination of the given RelTRS could be proven: 3.93/1.81 3.93/1.81 (0) RelTRS 3.93/1.81 (1) RelTRSRRRProof [EQUIVALENT, 82 ms] 3.93/1.81 (2) RelTRS 3.93/1.81 (3) RIsEmptyProof [EQUIVALENT, 0 ms] 3.93/1.81 (4) YES 3.93/1.81 3.93/1.81 3.93/1.81 ---------------------------------------- 3.93/1.81 3.93/1.81 (0) 3.93/1.81 Obligation: 3.93/1.81 Relative term rewrite system: 3.93/1.81 The relative TRS consists of the following R rules: 3.93/1.81 3.93/1.81 f(f(x)) -> x 3.93/1.81 3.93/1.81 The relative TRS consists of the following S rules: 3.93/1.81 3.93/1.81 f(x) -> g(f(g(f(x)))) 3.93/1.81 3.93/1.81 3.93/1.81 ---------------------------------------- 3.93/1.81 3.93/1.81 (1) RelTRSRRRProof (EQUIVALENT) 3.93/1.81 We used the following monotonic ordering for rule removal: 3.93/1.81 Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : 3.93/1.81 3.93/1.81 <<< 3.93/1.81 POL(f(x_1)) = [[0], [1]] + [[1, 1], [2, 0]] * x_1 3.93/1.81 >>> 3.93/1.81 3.93/1.81 <<< 3.93/1.81 POL(g(x_1)) = [[0], [0]] + [[1, 0], [0, 0]] * x_1 3.93/1.81 >>> 3.93/1.81 3.93/1.81 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 3.93/1.81 Rules from R: 3.93/1.81 3.93/1.81 f(f(x)) -> x 3.93/1.81 Rules from S: 3.93/1.81 none 3.93/1.81 3.93/1.81 3.93/1.81 3.93/1.81 3.93/1.81 ---------------------------------------- 3.93/1.81 3.93/1.81 (2) 3.93/1.81 Obligation: 3.93/1.81 Relative term rewrite system: 3.93/1.81 R is empty. 3.93/1.81 The relative TRS consists of the following S rules: 3.93/1.81 3.93/1.81 f(x) -> g(f(g(f(x)))) 3.93/1.81 3.93/1.81 3.93/1.81 ---------------------------------------- 3.93/1.81 3.93/1.81 (3) RIsEmptyProof (EQUIVALENT) 3.93/1.81 The TRS R is empty. Hence, termination is trivially proven. 3.93/1.81 ---------------------------------------- 3.93/1.81 3.93/1.81 (4) 3.93/1.81 YES 3.95/1.84 EOF
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