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TRS Stand 20472 pair #381710910
details
property
value
status
complete
benchmark
7.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n081.star.cs.uiowa.edu
space
Secret_06_TRS
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.0563418865204 seconds
cpu usage
0.053552788
max memory
2969600.0
stage attributes
key
value
output-size
1728
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. 0 : [] --> o a : [o * o] --> o b : [o * o] --> o c : [o] --> o c(c(c(a(X, Y)))) => b(c(c(c(c(Y)))), X) c(c(b(c(X), 0))) => a(0, c(c(a(X, 0)))) c(c(a(a(X, 0), Y))) => c(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]): c(c(c(a(X, Y)))) >? b(c(c(c(c(Y)))), X) c(c(b(c(X), 0))) >? a(0, c(c(a(X, 0)))) c(c(a(a(X, 0), Y))) >? c(X) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: 0 = 0 a = \y0y1.1 + y0 + 2y1 b = \y0y1.3 + y0 + y1 c = \y0.2y0 Using this interpretation, the requirements translate to: [[c(c(c(a(_x0, _x1))))]] = 8 + 8x0 + 16x1 > 3 + x0 + 16x1 = [[b(c(c(c(c(_x1)))), _x0)]] [[c(c(b(c(_x0), 0)))]] = 12 + 8x0 > 9 + 8x0 = [[a(0, c(c(a(_x0, 0))))]] [[c(c(a(a(_x0, 0), _x1)))]] = 8 + 4x0 + 8x1 > 2x0 = [[c(_x0)]] We can thus remove the following rules: c(c(c(a(X, Y)))) => b(c(c(c(c(Y)))), X) c(c(b(c(X), 0))) => a(0, c(c(a(X, 0)))) c(c(a(a(X, 0), Y))) => c(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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