TRS Stand 20472 pair #381715370

details

property	value
status	complete
benchmark	Ex2_Luc02a_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n105.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	1.48178505898 seconds
cpu usage	1.478794788
max memory	3.975168E7

stage attributes

key	value
output-size	46251
starexec-result	YES

output

/export/starexec/sandbox/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/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.

  0 : [] --> o 
  active : [o] --> o 
  add : [o * o] --> o 
  cons : [o * o] --> o 
  dbl : [o] --> o 
  first : [o * o] --> o 
  mark : [o] --> o 
  nil : [] --> o 
  ok : [o] --> o 
  proper : [o] --> o 
  recip : [o] --> o 
  s : [o] --> o 
  sqr : [o] --> o 
  terms : [o] --> o 
  top : [o] --> o 

  active(terms(X)) => mark(cons(recip(sqr(X)), terms(s(X)))) 
  active(sqr(0)) => mark(0) 
  active(sqr(s(X))) => mark(s(add(sqr(X), dbl(X)))) 
  active(dbl(0)) => mark(0) 
  active(dbl(s(X))) => mark(s(s(dbl(X)))) 
  active(add(0, X)) => mark(X) 
  active(add(s(X), Y)) => mark(s(add(X, Y))) 
  active(first(0, X)) => mark(nil) 
  active(first(s(X), cons(Y, Z))) => mark(cons(Y, first(X, Z))) 
  active(terms(X)) => terms(active(X)) 
  active(cons(X, Y)) => cons(active(X), Y) 
  active(recip(X)) => recip(active(X)) 
  active(sqr(X)) => sqr(active(X)) 
  active(s(X)) => s(active(X)) 
  active(add(X, Y)) => add(active(X), Y) 
  active(add(X, Y)) => add(X, active(Y)) 
  active(dbl(X)) => dbl(active(X)) 
  active(first(X, Y)) => first(active(X), Y) 
  active(first(X, Y)) => first(X, active(Y)) 
  terms(mark(X)) => mark(terms(X)) 
  cons(mark(X), Y) => mark(cons(X, Y)) 
  recip(mark(X)) => mark(recip(X)) 
  sqr(mark(X)) => mark(sqr(X)) 
  s(mark(X)) => mark(s(X)) 
  add(mark(X), Y) => mark(add(X, Y)) 
  add(X, mark(Y)) => mark(add(X, Y)) 
  dbl(mark(X)) => mark(dbl(X)) 
  first(mark(X), Y) => mark(first(X, Y)) 
  first(X, mark(Y)) => mark(first(X, Y)) 
  proper(terms(X)) => terms(proper(X)) 
  proper(cons(X, Y)) => cons(proper(X), proper(Y)) 
  proper(recip(X)) => recip(proper(X)) 
  proper(sqr(X)) => sqr(proper(X)) 
  proper(s(X)) => s(proper(X)) 
  proper(0) => ok(0) 
  proper(add(X, Y)) => add(proper(X), proper(Y)) 
  proper(dbl(X)) => dbl(proper(X)) 
  proper(first(X, Y)) => first(proper(X), proper(Y)) 
  proper(nil) => ok(nil) 
  terms(ok(X)) => ok(terms(X)) 
  cons(ok(X), ok(Y)) => ok(cons(X, Y)) 
  recip(ok(X)) => ok(recip(X)) 
  sqr(ok(X)) => ok(sqr(X)) 
  s(ok(X)) => ok(s(X)) 
  add(ok(X), ok(Y)) => ok(add(X, Y)) 
  dbl(ok(X)) => ok(dbl(X)) 
  first(ok(X), ok(Y)) => ok(first(X, Y)) 
  top(mark(X)) => top(proper(X)) 
  top(ok(X)) => top(active(X)) 

We use the dependency pair framework as described in [Kop12, Ch. 6/7], with static dependency pairs (see [KusIsoSakBla09] and the adaptation for AFSMs in [Kop12, Ch. 7.8]).

We thus obtain the following dependency pair problem (P_0, R_0, minimal, formative):

  Dependency Pairs P_0:

    0] active#(terms(X)) =#> cons#(recip(sqr(X)), terms(s(X)))   
    1] active#(terms(X)) =#> recip#(sqr(X))   
    2] active#(terms(X)) =#> sqr#(X)   
    3] active#(terms(X)) =#> terms#(s(X))   
    4] active#(terms(X)) =#> s#(X)   
    5] active#(sqr(s(X))) =#> s#(add(sqr(X), dbl(X)))   
    6] active#(sqr(s(X))) =#> add#(sqr(X), dbl(X))   
    7] active#(sqr(s(X))) =#> sqr#(X)   
    8] active#(sqr(s(X))) =#> dbl#(X)   
    9] active#(dbl(s(X))) =#> s#(s(dbl(X)))   
    10] active#(dbl(s(X))) =#> s#(dbl(X))   
    11] active#(dbl(s(X))) =#> dbl#(X)   
    12] active#(add(s(X), Y)) =#> s#(add(X, Y))   
    13] active#(add(s(X), Y)) =#> add#(X, Y)   
    14] active#(first(s(X), cons(Y, Z))) =#> cons#(Y, first(X, Z))   
    15] active#(first(s(X), cons(Y, Z))) =#> first#(X, Z)   
    16] active#(terms(X)) =#> terms#(active(X))

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