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TRS Relative pair #487081839
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
n150.star.cs.uiowa.edu
space
Mixed_relative_TRS
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
2.38262 seconds
cpu usage
6.02524
user time
5.71386
system time
0.31138
max virtual memory
1.8877136E7
max residence set size
491940.0
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# AProVE Commit ID: 794c25de1cacf0d048858bcd21c9a779e1221865 marcel 20200619 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 41 ms] (2) RelTRS (3) RelTRSRRRProof [EQUIVALENT, 9 ms] (4) RelTRS (5) RelTRSRRRProof [EQUIVALENT, 5 ms] (6) RelTRS (7) RIsEmptyProof [EQUIVALENT, 1 ms] (8) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: f(a, g(y), z) -> f(a, y, g(y)) f(b, g(y), z) -> f(a, y, z) a -> b The relative TRS consists of the following S rules: f(x, y, z) -> f(x, y, g(z)) ---------------------------------------- (1) 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], [1, 0]] * x_1 + [[1, 1], [0, 1]] * x_2 + [[1, 0], [0, 0]] * x_3 >>> <<< POL(a) = [[0], [1]] >>> <<< POL(g(x_1)) = [[0], [1]] + [[1, 0], [1, 1]] * x_1 >>> <<< POL(b) = [[0], [0]] >>> With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: f(a, g(y), z) -> f(a, y, g(y)) Rules from S: none ---------------------------------------- (2) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: f(b, g(y), z) -> f(a, y, z) a -> b The relative TRS consists of the following S rules: f(x, y, z) -> f(x, y, g(z)) ---------------------------------------- (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], [1]] + [[1, 1], [1, 1]] * x_1 + [[1, 1], [1, 1]] * x_2 + [[1, 0], [1, 0]] * x_3 >>> <<< POL(b) = [[0], [1]] >>> <<< POL(g(x_1)) = [[0], [1]] + [[1, 0], [1, 1]] * x_1 >>> <<<
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