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TRS Stand 20472 pair #381712379
details
property
value
status
complete
benchmark
025.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n080.star.cs.uiowa.edu
space
AotoYamada_05
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.0200200080872 seconds
cpu usage
0.016372603
max memory
1290240.0
stage attributes
key
value
output-size
1277
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. app : [o * o] --> o apply : [] --> o app(app(apply, X), Y) => app(X, Y) We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): app(app(apply, X), Y) >? app(X, Y) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: app = \y0y1.3 + y0 + 3y1 apply = 3 Using this interpretation, the requirements translate to: [[app(app(apply, _x0), _x1)]] = 9 + 3x0 + 3x1 > 3 + x0 + 3x1 = [[app(_x0, _x1)]] We can thus remove the following rules: app(app(apply, X), Y) => app(X, Y) All rules were succesfully removed. Thus, termination of the original system has been reduced to termination of the beta-rule, which is well-known to hold. +++ Citations +++ [Kop12] C. Kop. Higher Order Termination. PhD Thesis, 2012.
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