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TRS Relat 75837 pair #381724816
details
property
value
status
complete
benchmark
rt1-4.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n049.star.cs.uiowa.edu
space
Relative_05
run statistics
property
value
solver
AProVE
configuration
standard
runtime (wallclock)
1.85989785194 seconds
cpu usage
4.23993976
max memory
2.3298048E8
stage attributes
key
value
output-size
1996
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# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty Termination of the given RelTRS could be proven: (0) RelTRS (1) RelTRSRRRProof [EQUIVALENT, 82 ms] (2) RelTRS (3) RIsEmptyProof [EQUIVALENT, 0 ms] (4) YES ---------------------------------------- (0) Obligation: Relative term rewrite system: The relative TRS consists of the following R rules: f(el(x), y) -> f(x, el(y)) The relative TRS consists of the following S rules: f(x, y) -> f(l(x), y) f(x, y) -> f(x, r(y)) l(el(x)) -> el(l(x)) el(r(x)) -> r(el(x)) ---------------------------------------- (1) RelTRSRRRProof (EQUIVALENT) We used the following monotonic ordering for rule removal: Matrix interpretation [MATRO] to (N^2, +, *, >=, >) : <<< POL(f(x_1, x_2)) = [[1], [1]] + [[1, 1], [1, 1]] * x_1 + [[1, 0], [1, 0]] * x_2 >>> <<< POL(el(x_1)) = [[1], [1]] + [[1, 0], [1, 1]] * x_1 >>> <<< POL(l(x_1)) = [[0], [0]] + [[1, 0], [0, 1]] * x_1 >>> <<< POL(r(x_1)) = [[0], [1]] + [[1, 0], [0, 1]] * x_1 >>> With this ordering the following rules can be removed [MATRO] because they are oriented strictly: Rules from R: f(el(x), y) -> f(x, el(y)) Rules from S: none ---------------------------------------- (2) Obligation: Relative term rewrite system: R is empty. The relative TRS consists of the following S rules: f(x, y) -> f(l(x), y) f(x, y) -> f(x, r(y)) l(el(x)) -> el(l(x)) el(r(x)) -> r(el(x)) ---------------------------------------- (3) RIsEmptyProof (EQUIVALENT) The TRS R is empty. Hence, termination is trivially proven. ---------------------------------------- (4) YES
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