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TRS_Relative 2019-03-21 03.54 pair #429988482
details
property
value
status
complete
benchmark
ijcar2006.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n122.star.cs.uiowa.edu
space
Mixed_relative_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.45533 seconds
cpu usage
6.44065
user time
6.17127
system time
0.269376
max virtual memory
1.9009924E7
max residence set size
570912.0
stage attributes
key
value
starexec-result
YES
output
5.34/2.15 YES 6.36/2.42 proof of /export/starexec/sandbox/benchmark/theBenchmark.xml 6.36/2.42 # AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty 6.36/2.42 6.36/2.42 6.36/2.42 Termination of the given RelTRS could be proven: 6.36/2.42 6.36/2.42 (0) RelTRS 6.36/2.42 (1) RelTRSRRRProof [EQUIVALENT, 35 ms] 6.36/2.42 (2) RelTRS 6.36/2.42 (3) RelTRSRRRProof [EQUIVALENT, 10 ms] 6.36/2.42 (4) RelTRS 6.36/2.42 (5) RelTRSRRRProof [EQUIVALENT, 0 ms] 6.36/2.42 (6) RelTRS 6.36/2.42 (7) RIsEmptyProof [EQUIVALENT, 2 ms] 6.36/2.42 (8) YES 6.36/2.42 6.36/2.42 6.36/2.42 ---------------------------------------- 6.36/2.42 6.36/2.42 (0) 6.36/2.42 Obligation: 6.36/2.42 Relative term rewrite system: 6.36/2.42 The relative TRS consists of the following R rules: 6.36/2.42 6.36/2.42 f(a, g(y), z) -> f(a, y, g(y)) 6.36/2.42 f(b, g(y), z) -> f(a, y, z) 6.36/2.42 a -> b 6.36/2.42 6.36/2.42 The relative TRS consists of the following S rules: 6.36/2.42 6.36/2.42 f(x, y, z) -> f(x, y, g(z)) 6.36/2.42 6.36/2.42 6.36/2.42 ---------------------------------------- 6.36/2.42 6.36/2.42 (1) RelTRSRRRProof (EQUIVALENT) 6.36/2.42 We used the following monotonic ordering for rule removal: 6.36/2.42 Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : 6.36/2.42 6.36/2.42 <<< 6.36/2.42 POL(f(x_1, x_2, x_3)) = [[0], [0]] + [[1, 1], [1, 0]] * x_1 + [[1, 1], [0, 1]] * x_2 + [[1, 0], [0, 0]] * x_3 6.36/2.42 >>> 6.36/2.42 6.36/2.42 <<< 6.36/2.42 POL(a) = [[0], [1]] 6.36/2.42 >>> 6.36/2.42 6.36/2.42 <<< 6.36/2.42 POL(g(x_1)) = [[0], [1]] + [[1, 0], [1, 1]] * x_1 6.36/2.42 >>> 6.36/2.42 6.36/2.42 <<< 6.36/2.42 POL(b) = [[0], [0]] 6.36/2.42 >>> 6.36/2.42 6.36/2.42 With this ordering the following rules can be removed [MATRO] because they are oriented strictly: 6.36/2.42 Rules from R: 6.36/2.42 6.36/2.42 f(a, g(y), z) -> f(a, y, g(y)) 6.36/2.42 Rules from S: 6.36/2.42 none 6.36/2.42 6.36/2.42 6.36/2.42 6.36/2.42 6.36/2.42 ---------------------------------------- 6.36/2.42 6.36/2.42 (2) 6.36/2.42 Obligation: 6.36/2.42 Relative term rewrite system: 6.36/2.42 The relative TRS consists of the following R rules: 6.36/2.42 6.36/2.42 f(b, g(y), z) -> f(a, y, z) 6.36/2.42 a -> b 6.36/2.42 6.36/2.42 The relative TRS consists of the following S rules: 6.36/2.42 6.36/2.42 f(x, y, z) -> f(x, y, g(z)) 6.36/2.42 6.36/2.42 6.36/2.42 ---------------------------------------- 6.36/2.42 6.36/2.42 (3) RelTRSRRRProof (EQUIVALENT) 6.36/2.42 We used the following monotonic ordering for rule removal: 6.36/2.42 Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : 6.36/2.42 6.36/2.42 <<< 6.36/2.42 POL(f(x_1, x_2, x_3)) = [[0], [1]] + [[1, 1], [1, 1]] * x_1 + [[1, 1], [1, 1]] * x_2 + [[1, 0], [1, 0]] * x_3 6.36/2.42 >>> 6.36/2.42 6.36/2.42 <<< 6.36/2.42 POL(b) = [[0], [1]] 6.36/2.42 >>> 6.36/2.42 6.36/2.42 <<< 6.36/2.42 POL(g(x_1)) = [[0], [1]] + [[1, 0], [1, 1]] * x_1 6.36/2.42 >>> 6.36/2.42 6.36/2.42 <<<
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