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TRS Stand 20472 pair #381716640
details
property
value
status
complete
benchmark
PALINDROME_nosorts_noand_iGM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n103.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
0.437361001968 seconds
cpu usage
0.43398769
max memory
8626176.0
stage attributes
key
value
output-size
25195
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 active : [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(U11(tt)) => mark(U12(tt)) active(U12(tt)) => mark(tt) active(isNePal(!6220!6220(X, !6220!6220(Y, X)))) => mark(U11(tt)) mark(!6220!6220(X, Y)) => active(!6220!6220(mark(X), mark(Y))) mark(nil) => active(nil) mark(U11(X)) => active(U11(mark(X))) mark(tt) => active(tt) mark(U12(X)) => active(U12(mark(X))) 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) U11(mark(X)) => U11(X) U11(active(X)) => U11(X) U12(mark(X)) => U12(X) U12(active(X)) => U12(X) 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(U11(tt)) >? mark(U12(tt)) active(U12(tt)) >? mark(tt) active(isNePal(!6220!6220(X, !6220!6220(Y, X)))) >? mark(U11(tt)) mark(!6220!6220(X, Y)) >? active(!6220!6220(mark(X), mark(Y))) mark(nil) >? active(nil) mark(U11(X)) >? active(U11(mark(X))) mark(tt) >? active(tt) mark(U12(X)) >? active(U12(mark(X))) 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) U11(mark(X)) >? U11(X) U11(active(X)) >? U11(X) U12(mark(X)) >? U12(X) U12(active(X)) >? U12(X) 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 U11 = \y0.y0 U12 = \y0.y0 active = \y0.y0 isNePal = \y0.2y0 mark = \y0.y0 nil = 1 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))]] = 1 + x0 > x0 = [[mark(_x0)]] [[active(!6220!6220(nil, _x0))]] = 1 + x0 > x0 = [[mark(_x0)]] [[active(U11(tt))]] = 0 >= 0 = [[mark(U12(tt))]] [[active(U12(tt))]] = 0 >= 0 = [[mark(tt)]] [[active(isNePal(!6220!6220(_x0, !6220!6220(_x1, _x0))))]] = 2x1 + 4x0 >= 0 = [[mark(U11(tt))]] [[mark(!6220!6220(_x0, _x1))]] = x0 + x1 >= x0 + x1 = [[active(!6220!6220(mark(_x0), mark(_x1)))]] [[mark(nil)]] = 1 >= 1 = [[active(nil)]] [[mark(U11(_x0))]] = x0 >= x0 = [[active(U11(mark(_x0)))]] [[mark(tt)]] = 0 >= 0 = [[active(tt)]] [[mark(U12(_x0))]] = x0 >= x0 = [[active(U12(mark(_x0)))]] [[mark(isNePal(_x0))]] = 2x0 >= 2x0 = [[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)]]
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