Spaces
Explore
Communities
Statistics
Reports
Cluster
Status
Help
TRS Stand 20472 pair #381715285
details
property
value
status
complete
benchmark
PALINDROME_nosorts_iGM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n110.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.382479190826 seconds
cpu usage
0.379138213
max memory
7319552.0
stage attributes
key
value
output-size
23259
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. !6220!6220 : [o * o] --> o active : [o] --> o and : [o * o] --> o isNePal : [o] --> o mark : [o] --> o nil : [] --> o tt : [] --> o active(!6220!6220(!6220!6220(X, Y), Z)) => mark(!6220!6220(X, !6220!6220(Y, Z))) active(!6220!6220(X, nil)) => mark(X) active(!6220!6220(nil, X)) => mark(X) active(and(tt, X)) => mark(X) active(isNePal(!6220!6220(X, !6220!6220(Y, X)))) => mark(tt) mark(!6220!6220(X, Y)) => active(!6220!6220(mark(X), mark(Y))) mark(nil) => active(nil) mark(and(X, Y)) => active(and(mark(X), Y)) mark(tt) => active(tt) mark(isNePal(X)) => active(isNePal(mark(X))) !6220!6220(mark(X), Y) => !6220!6220(X, Y) !6220!6220(X, mark(Y)) => !6220!6220(X, Y) !6220!6220(active(X), Y) => !6220!6220(X, Y) !6220!6220(X, active(Y)) => !6220!6220(X, Y) and(mark(X), Y) => and(X, Y) and(X, mark(Y)) => and(X, Y) and(active(X), Y) => and(X, Y) and(X, active(Y)) => and(X, Y) isNePal(mark(X)) => isNePal(X) isNePal(active(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]): active(!6220!6220(!6220!6220(X, Y), Z)) >? mark(!6220!6220(X, !6220!6220(Y, Z))) active(!6220!6220(X, nil)) >? mark(X) active(!6220!6220(nil, X)) >? mark(X) active(and(tt, X)) >? mark(X) active(isNePal(!6220!6220(X, !6220!6220(Y, X)))) >? mark(tt) mark(!6220!6220(X, Y)) >? active(!6220!6220(mark(X), mark(Y))) mark(nil) >? active(nil) mark(and(X, Y)) >? active(and(mark(X), Y)) mark(tt) >? active(tt) mark(isNePal(X)) >? active(isNePal(mark(X))) !6220!6220(mark(X), Y) >? !6220!6220(X, Y) !6220!6220(X, mark(Y)) >? !6220!6220(X, Y) !6220!6220(active(X), Y) >? !6220!6220(X, Y) !6220!6220(X, active(Y)) >? !6220!6220(X, Y) and(mark(X), Y) >? and(X, Y) and(X, mark(Y)) >? and(X, Y) and(active(X), Y) >? and(X, Y) and(X, active(Y)) >? and(X, Y) isNePal(mark(X)) >? isNePal(X) isNePal(active(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 active = \y0.y0 and = \y0y1.2 + y0 + y1 isNePal = \y0.y0 mark = \y0.y0 nil = 0 tt = 0 Using this interpretation, the requirements translate to: [[active(!6220!6220(!6220!6220(_x0, _x1), _x2))]] = x0 + x1 + x2 >= x0 + x1 + x2 = [[mark(!6220!6220(_x0, !6220!6220(_x1, _x2)))]] [[active(!6220!6220(_x0, nil))]] = x0 >= x0 = [[mark(_x0)]] [[active(!6220!6220(nil, _x0))]] = x0 >= x0 = [[mark(_x0)]] [[active(and(tt, _x0))]] = 2 + x0 > x0 = [[mark(_x0)]] [[active(isNePal(!6220!6220(_x0, !6220!6220(_x1, _x0))))]] = x1 + 2x0 >= 0 = [[mark(tt)]] [[mark(!6220!6220(_x0, _x1))]] = x0 + x1 >= x0 + x1 = [[active(!6220!6220(mark(_x0), mark(_x1)))]] [[mark(nil)]] = 0 >= 0 = [[active(nil)]] [[mark(and(_x0, _x1))]] = 2 + x0 + x1 >= 2 + x0 + x1 = [[active(and(mark(_x0), _x1))]] [[mark(tt)]] = 0 >= 0 = [[active(tt)]] [[mark(isNePal(_x0))]] = x0 >= x0 = [[active(isNePal(mark(_x0)))]] [[!6220!6220(mark(_x0), _x1)]] = x0 + x1 >= x0 + x1 = [[!6220!6220(_x0, _x1)]] [[!6220!6220(_x0, mark(_x1))]] = x0 + x1 >= x0 + x1 = [[!6220!6220(_x0, _x1)]] [[!6220!6220(active(_x0), _x1)]] = x0 + x1 >= x0 + x1 = [[!6220!6220(_x0, _x1)]] [[!6220!6220(_x0, active(_x1))]] = x0 + x1 >= x0 + x1 = [[!6220!6220(_x0, _x1)]] [[and(mark(_x0), _x1)]] = 2 + x0 + x1 >= 2 + x0 + x1 = [[and(_x0, _x1)]] [[and(_x0, mark(_x1))]] = 2 + x0 + x1 >= 2 + x0 + x1 = [[and(_x0, _x1)]] [[and(active(_x0), _x1)]] = 2 + x0 + x1 >= 2 + x0 + x1 = [[and(_x0, _x1)]] [[and(_x0, active(_x1))]] = 2 + x0 + x1 >= 2 + x0 + x1 = [[and(_x0, _x1)]] [[isNePal(mark(_x0))]] = x0 >= x0 = [[isNePal(_x0)]] [[isNePal(active(_x0))]] = x0 >= x0 = [[isNePal(_x0)]]
popout
output may be truncated. 'popout' for the full output.
job log
popout
actions
all output
return to TRS Stand 20472