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TRS Stand 20472 pair #381716690
details
property
value
status
complete
benchmark
PALINDROME_nosorts_FR.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n111.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.0403590202332 seconds
cpu usage
0.029809324
max memory
1306624.0
stage attributes
key
value
output-size
2835
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. !6220!6220 : [o * o] --> o activate : [o] --> o and : [o * o] --> o isNePal : [o] --> o nil : [] --> o tt : [] --> o !6220!6220(!6220!6220(X, Y), Z) => !6220!6220(X, !6220!6220(Y, Z)) !6220!6220(X, nil) => X !6220!6220(nil, X) => X and(tt, X) => activate(X) isNePal(!6220!6220(X, !6220!6220(Y, X))) => tt activate(X) => X We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): !6220!6220(!6220!6220(X, Y), Z) >? !6220!6220(X, !6220!6220(Y, Z)) !6220!6220(X, nil) >? X !6220!6220(nil, X) >? X and(tt, X) >? activate(X) isNePal(!6220!6220(X, !6220!6220(Y, X))) >? tt activate(X) >? X We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: !6220!6220 = \y0y1.3 + y1 + 3y0 activate = \y0.y0 and = \y0y1.3 + 3y0 + 3y1 isNePal = \y0.3 + 3y0 nil = 3 tt = 0 Using this interpretation, the requirements translate to: [[!6220!6220(!6220!6220(_x0, _x1), _x2)]] = 12 + x2 + 3x1 + 9x0 > 6 + x2 + 3x0 + 3x1 = [[!6220!6220(_x0, !6220!6220(_x1, _x2))]] [[!6220!6220(_x0, nil)]] = 6 + 3x0 > x0 = [[_x0]] [[!6220!6220(nil, _x0)]] = 12 + x0 > x0 = [[_x0]] [[and(tt, _x0)]] = 3 + 3x0 > x0 = [[activate(_x0)]] [[isNePal(!6220!6220(_x0, !6220!6220(_x1, _x0)))]] = 21 + 9x1 + 12x0 > 0 = [[tt]] [[activate(_x0)]] = x0 >= x0 = [[_x0]] We can thus remove the following rules: !6220!6220(!6220!6220(X, Y), Z) => !6220!6220(X, !6220!6220(Y, Z)) !6220!6220(X, nil) => X !6220!6220(nil, X) => X and(tt, X) => activate(X) isNePal(!6220!6220(X, !6220!6220(Y, X))) => tt We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): activate(X) >? X We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: activate = \y0.1 + y0 Using this interpretation, the requirements translate to: [[activate(_x0)]] = 1 + x0 > x0 = [[_x0]] We can thus remove the following rules: activate(X) => X 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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