Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Stand 20472 pair #381716365
details
property
value
status
complete
benchmark
PALINDROME_nosorts_noand_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n051.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.186450004578 seconds
cpu usage
0.183164934
max memory
4206592.0
stage attributes
key
value
output-size
16219
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 U11 : [o] --> o U12 : [o] --> o a!6220!6220!6220!6220 : [o * o] --> o a!6220!6220U11 : [o] --> o a!6220!6220U12 : [o] --> o a!6220!6220isNePal : [o] --> o isNePal : [o] --> o mark : [o] --> o nil : [] --> o tt : [] --> o a!6220!6220!6220!6220(!6220!6220(X, Y), Z) => a!6220!6220!6220!6220(mark(X), a!6220!6220!6220!6220(mark(Y), mark(Z))) a!6220!6220!6220!6220(X, nil) => mark(X) a!6220!6220!6220!6220(nil, X) => mark(X) a!6220!6220U11(tt) => a!6220!6220U12(tt) a!6220!6220U12(tt) => tt a!6220!6220isNePal(!6220!6220(X, !6220!6220(Y, X))) => a!6220!6220U11(tt) mark(!6220!6220(X, Y)) => a!6220!6220!6220!6220(mark(X), mark(Y)) mark(U11(X)) => a!6220!6220U11(mark(X)) mark(U12(X)) => a!6220!6220U12(mark(X)) mark(isNePal(X)) => a!6220!6220isNePal(mark(X)) mark(nil) => nil mark(tt) => tt a!6220!6220!6220!6220(X, Y) => !6220!6220(X, Y) a!6220!6220U11(X) => U11(X) a!6220!6220U12(X) => U12(X) a!6220!6220isNePal(X) => isNePal(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!6220!6220!6220!6220(!6220!6220(X, Y), Z) >? a!6220!6220!6220!6220(mark(X), a!6220!6220!6220!6220(mark(Y), mark(Z))) a!6220!6220!6220!6220(X, nil) >? mark(X) a!6220!6220!6220!6220(nil, X) >? mark(X) a!6220!6220U11(tt) >? a!6220!6220U12(tt) a!6220!6220U12(tt) >? tt a!6220!6220isNePal(!6220!6220(X, !6220!6220(Y, X))) >? a!6220!6220U11(tt) mark(!6220!6220(X, Y)) >? a!6220!6220!6220!6220(mark(X), mark(Y)) mark(U11(X)) >? a!6220!6220U11(mark(X)) mark(U12(X)) >? a!6220!6220U12(mark(X)) mark(isNePal(X)) >? a!6220!6220isNePal(mark(X)) mark(nil) >? nil mark(tt) >? tt a!6220!6220!6220!6220(X, Y) >? !6220!6220(X, Y) a!6220!6220U11(X) >? U11(X) a!6220!6220U12(X) >? U12(X) a!6220!6220isNePal(X) >? isNePal(X) We orient these requirements with a polynomial interpretation in the natural numbers. The following interpretation satisfies the requirements: !6220!6220 = \y0y1.y0 + y1 U11 = \y0.y0 U12 = \y0.y0 a!6220!6220!6220!6220 = \y0y1.y0 + y1 a!6220!6220U11 = \y0.y0 a!6220!6220U12 = \y0.y0 a!6220!6220isNePal = \y0.1 + 2y0 isNePal = \y0.1 + 2y0 mark = \y0.y0 nil = 0 tt = 0 Using this interpretation, the requirements translate to: [[a!6220!6220!6220!6220(!6220!6220(_x0, _x1), _x2)]] = x0 + x1 + x2 >= x0 + x1 + x2 = [[a!6220!6220!6220!6220(mark(_x0), a!6220!6220!6220!6220(mark(_x1), mark(_x2)))]] [[a!6220!6220!6220!6220(_x0, nil)]] = x0 >= x0 = [[mark(_x0)]] [[a!6220!6220!6220!6220(nil, _x0)]] = x0 >= x0 = [[mark(_x0)]] [[a!6220!6220U11(tt)]] = 0 >= 0 = [[a!6220!6220U12(tt)]] [[a!6220!6220U12(tt)]] = 0 >= 0 = [[tt]] [[a!6220!6220isNePal(!6220!6220(_x0, !6220!6220(_x1, _x0)))]] = 1 + 2x1 + 4x0 > 0 = [[a!6220!6220U11(tt)]] [[mark(!6220!6220(_x0, _x1))]] = x0 + x1 >= x0 + x1 = [[a!6220!6220!6220!6220(mark(_x0), mark(_x1))]] [[mark(U11(_x0))]] = x0 >= x0 = [[a!6220!6220U11(mark(_x0))]] [[mark(U12(_x0))]] = x0 >= x0 = [[a!6220!6220U12(mark(_x0))]] [[mark(isNePal(_x0))]] = 1 + 2x0 >= 1 + 2x0 = [[a!6220!6220isNePal(mark(_x0))]] [[mark(nil)]] = 0 >= 0 = [[nil]] [[mark(tt)]] = 0 >= 0 = [[tt]] [[a!6220!6220!6220!6220(_x0, _x1)]] = x0 + x1 >= x0 + x1 = [[!6220!6220(_x0, _x1)]] [[a!6220!6220U11(_x0)]] = x0 >= x0 = [[U11(_x0)]] [[a!6220!6220U12(_x0)]] = x0 >= x0 = [[U12(_x0)]] [[a!6220!6220isNePal(_x0)]] = 1 + 2x0 >= 1 + 2x0 = [[isNePal(_x0)]] We can thus remove the following rules: a!6220!6220isNePal(!6220!6220(X, !6220!6220(Y, X))) => a!6220!6220U11(tt)
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Stand 20472