TRS Stand 20472 pair #381716165

details

property	value
status	complete
benchmark	Ex49_GM04_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n082.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	1.11823511124 seconds
cpu usage	0.995907336
max memory	3.2198656E7

stage attributes

key	value
output-size	27826
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 
  div : [o * o] --> o 
  false : [] --> o 
  geq : [o * o] --> o 
  if : [o * o * o] --> o 
  mark : [o] --> o 
  minus : [o * o] --> o 
  ok : [o] --> o 
  proper : [o] --> o 
  s : [o] --> o 
  top : [o] --> o 
  true : [] --> o 

  active(minus(0, X)) => mark(0) 
  active(minus(s(X), s(Y))) => mark(minus(X, Y)) 
  active(geq(X, 0)) => mark(true) 
  active(geq(0, s(X))) => mark(false) 
  active(geq(s(X), s(Y))) => mark(geq(X, Y)) 
  active(div(0, s(X))) => mark(0) 
  active(div(s(X), s(Y))) => mark(if(geq(X, Y), s(div(minus(X, Y), s(Y))), 0)) 
  active(if(true, X, Y)) => mark(X) 
  active(if(false, X, Y)) => mark(Y) 
  active(s(X)) => s(active(X)) 
  active(div(X, Y)) => div(active(X), Y) 
  active(if(X, Y, Z)) => if(active(X), Y, Z) 
  s(mark(X)) => mark(s(X)) 
  div(mark(X), Y) => mark(div(X, Y)) 
  if(mark(X), Y, Z) => mark(if(X, Y, Z)) 
  proper(minus(X, Y)) => minus(proper(X), proper(Y)) 
  proper(0) => ok(0) 
  proper(s(X)) => s(proper(X)) 
  proper(geq(X, Y)) => geq(proper(X), proper(Y)) 
  proper(true) => ok(true) 
  proper(false) => ok(false) 
  proper(div(X, Y)) => div(proper(X), proper(Y)) 
  proper(if(X, Y, Z)) => if(proper(X), proper(Y), proper(Z)) 
  minus(ok(X), ok(Y)) => ok(minus(X, Y)) 
  s(ok(X)) => ok(s(X)) 
  geq(ok(X), ok(Y)) => ok(geq(X, Y)) 
  div(ok(X), ok(Y)) => ok(div(X, Y)) 
  if(ok(X), ok(Y), ok(Z)) => ok(if(X, Y, Z)) 
  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#(minus(s(X), s(Y))) =#> minus#(X, Y)   
    1] active#(geq(s(X), s(Y))) =#> geq#(X, Y)   
    2] active#(div(s(X), s(Y))) =#> if#(geq(X, Y), s(div(minus(X, Y), s(Y))), 0)   
    3] active#(div(s(X), s(Y))) =#> geq#(X, Y)   
    4] active#(div(s(X), s(Y))) =#> s#(div(minus(X, Y), s(Y)))   
    5] active#(div(s(X), s(Y))) =#> div#(minus(X, Y), s(Y))   
    6] active#(div(s(X), s(Y))) =#> minus#(X, Y)   
    7] active#(div(s(X), s(Y))) =#> s#(Y)   
    8] active#(s(X)) =#> s#(active(X))   
    9] active#(s(X)) =#> active#(X)   
    10] active#(div(X, Y)) =#> div#(active(X), Y)   
    11] active#(div(X, Y)) =#> active#(X)   
    12] active#(if(X, Y, Z)) =#> if#(active(X), Y, Z)   
    13] active#(if(X, Y, Z)) =#> active#(X)   
    14] s#(mark(X)) =#> s#(X)   
    15] div#(mark(X), Y) =#> div#(X, Y)   
    16] if#(mark(X), Y, Z) =#> if#(X, Y, Z)   
    17] proper#(minus(X, Y)) =#> minus#(proper(X), proper(Y))   
    18] proper#(minus(X, Y)) =#> proper#(X)   
    19] proper#(minus(X, Y)) =#> proper#(Y)   
    20] proper#(s(X)) =#> s#(proper(X))   
    21] proper#(s(X)) =#> proper#(X)   
    22] proper#(geq(X, Y)) =#> geq#(proper(X), proper(Y))   
    23] proper#(geq(X, Y)) =#> proper#(X)   
    24] proper#(geq(X, Y)) =#> proper#(Y)   
    25] proper#(div(X, Y)) =#> div#(proper(X), proper(Y))   
    26] proper#(div(X, Y)) =#> proper#(X)   
    27] proper#(div(X, Y)) =#> proper#(Y)   
    28] proper#(if(X, Y, Z)) =#> if#(proper(X), proper(Y), proper(Z))   
    29] proper#(if(X, Y, Z)) =#> proper#(X)   
    30] proper#(if(X, Y, Z)) =#> proper#(Y)   
    31] proper#(if(X, Y, Z)) =#> proper#(Z)   
    32] minus#(ok(X), ok(Y)) =#> minus#(X, Y)   
    33] s#(ok(X)) =#> s#(X)   
    34] geq#(ok(X), ok(Y)) =#> geq#(X, Y)   
    35] div#(ok(X), ok(Y)) =#> div#(X, Y)   
    36] if#(ok(X), ok(Y), ok(Z)) =#> if#(X, Y, Z)   
    37] top#(mark(X)) =#> top#(proper(X))

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