Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Stand 20472 pair #381712396
details
property
value
status
complete
benchmark
mfp90b.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n035.star.cs.uiowa.edu
space
Rubio_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.0237898826599 seconds
cpu usage
0.020003761
max memory
1523712.0
stage attributes
key
value
output-size
1414
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. a : [] --> o b : [] --> o c : [] --> o f : [o * o] --> o g : [o] --> o a => g(c) g(a) => b f(g(X), b) => f(a, 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]): a >? g(c) g(a) >? b f(g(X), b) >? f(a, X) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: a = 2 b = 3 c = 0 f = \y0y1.2y0 + 3y1 g = \y0.3y0 Using this interpretation, the requirements translate to: [[a]] = 2 > 0 = [[g(c)]] [[g(a)]] = 6 > 3 = [[b]] [[f(g(_x0), b)]] = 9 + 6x0 > 4 + 3x0 = [[f(a, _x0)]] We can thus remove the following rules: a => g(c) g(a) => b f(g(X), b) => f(a, 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.
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Stand 20472