TRS Stand 20472 pair #381714684

details

property	value
status	complete
benchmark	PALINDROME_nosorts_noand_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n013.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.313899040222 seconds
cpu usage	0.309688926
max memory	7069696.0

stage attributes

key	value
output-size	18959
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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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 
  ok : [o] --> o 
  proper : [o] --> o 
  top : [o] --> 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)) 
  active(!6220!6220(X, Y)) => !6220!6220(active(X), Y) 
  active(!6220!6220(X, Y)) => !6220!6220(X, active(Y)) 
  active(U11(X)) => U11(active(X)) 
  active(U12(X)) => U12(active(X)) 
  active(isNePal(X)) => isNePal(active(X)) 
  !6220!6220(mark(X), Y) => mark(!6220!6220(X, Y)) 
  !6220!6220(X, mark(Y)) => mark(!6220!6220(X, Y)) 
  U11(mark(X)) => mark(U11(X)) 
  U12(mark(X)) => mark(U12(X)) 
  isNePal(mark(X)) => mark(isNePal(X)) 
  proper(!6220!6220(X, Y)) => !6220!6220(proper(X), proper(Y)) 
  proper(nil) => ok(nil) 
  proper(U11(X)) => U11(proper(X)) 
  proper(tt) => ok(tt) 
  proper(U12(X)) => U12(proper(X)) 
  proper(isNePal(X)) => isNePal(proper(X)) 
  !6220!6220(ok(X), ok(Y)) => ok(!6220!6220(X, Y)) 
  U11(ok(X)) => ok(U11(X)) 
  U12(ok(X)) => ok(U12(X)) 
  isNePal(ok(X)) => ok(isNePal(X)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(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)) 
  active(!6220!6220(X, Y)) >? !6220!6220(active(X), Y) 
  active(!6220!6220(X, Y)) >? !6220!6220(X, active(Y)) 
  active(U11(X)) >? U11(active(X)) 
  active(U12(X)) >? U12(active(X)) 
  active(isNePal(X)) >? isNePal(active(X)) 
  !6220!6220(mark(X), Y) >? mark(!6220!6220(X, Y)) 
  !6220!6220(X, mark(Y)) >? mark(!6220!6220(X, Y)) 
  U11(mark(X)) >? mark(U11(X)) 
  U12(mark(X)) >? mark(U12(X)) 
  isNePal(mark(X)) >? mark(isNePal(X)) 
  proper(!6220!6220(X, Y)) >? !6220!6220(proper(X), proper(Y)) 
  proper(nil) >? ok(nil) 
  proper(U11(X)) >? U11(proper(X)) 
  proper(tt) >? ok(tt) 
  proper(U12(X)) >? U12(proper(X)) 
  proper(isNePal(X)) >? isNePal(proper(X)) 
  !6220!6220(ok(X), ok(Y)) >? ok(!6220!6220(X, Y)) 
  U11(ok(X)) >? ok(U11(X)) 
  U12(ok(X)) >? ok(U12(X)) 
  isNePal(ok(X)) >? ok(isNePal(X)) 
  top(mark(X)) >? top(proper(X)) 
  top(ok(X)) >? top(active(X)) 

We orient these requirements with a polynomial interpretation in the natural numbers.

The following interpretation satisfies the requirements:

  !6220!6220 = \y0y1.y1 + 2y0 
  U11 = \y0.y0 
  U12 = \y0.2y0 
  active = \y0.y0 
  isNePal = \y0.y0 
  mark = \y0.y0 
  nil = 1 
  ok = \y0.y0 
  proper = \y0.y0 
  top = \y0.y0 
  tt = 0

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