TRS Stand 20472 pair #381715765

details

property	value
status	complete
benchmark	Ex6_GM04_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n190.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.182799100876 seconds
cpu usage	0.171418645
max memory	4448256.0

stage attributes

key	value
output-size	7980
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.

  active : [o] --> o 
  c : [] --> o 
  f : [o] --> o 
  g : [o] --> o 
  mark : [o] --> o 
  ok : [o] --> o 
  proper : [o] --> o 
  top : [o] --> o 

  active(c) => mark(f(g(c))) 
  active(f(g(X))) => mark(g(X)) 
  proper(c) => ok(c) 
  proper(f(X)) => f(proper(X)) 
  proper(g(X)) => g(proper(X)) 
  f(ok(X)) => ok(f(X)) 
  g(ok(X)) => ok(g(X)) 
  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#(c) =#> f#(g(c))   
    1] active#(c) =#> g#(c)   
    2] active#(f(g(X))) =#> g#(X)   
    3] proper#(f(X)) =#> f#(proper(X))   
    4] proper#(f(X)) =#> proper#(X)   
    5] proper#(g(X)) =#> g#(proper(X))   
    6] proper#(g(X)) =#> proper#(X)   
    7] f#(ok(X)) =#> f#(X)   
    8] g#(ok(X)) =#> g#(X)   
    9] top#(mark(X)) =#> top#(proper(X))   
    10] top#(mark(X)) =#> proper#(X)   
    11] top#(ok(X)) =#> top#(active(X))   
    12] top#(ok(X)) =#> active#(X)   

  Rules R_0:

    active(c) => mark(f(g(c))) 
    active(f(g(X))) => mark(g(X)) 
    proper(c) => ok(c) 
    proper(f(X)) => f(proper(X)) 
    proper(g(X)) => g(proper(X)) 
    f(ok(X)) => ok(f(X)) 
    g(ok(X)) => ok(g(X)) 
    top(mark(X)) => top(proper(X)) 
    top(ok(X)) => top(active(X)) 

Thus, the original system is terminating if (P_0, R_0, minimal, formative) is finite.

We consider the dependency pair problem (P_0, R_0, minimal, formative).

We place the elements of P in a dependency graph approximation G (see e.g. [Kop12, Thm. 7.27, 7.29], as follows:

    * 0 : 7 
    * 1 :  
    * 2 : 8 
    * 3 : 7 
    * 4 : 3, 4, 5, 6 
    * 5 : 8 
    * 6 : 3, 4, 5, 6 
    * 7 : 7 
    * 8 : 8 
    * 9 : 11, 12 
    * 10 : 3, 4, 5, 6 
    * 11 : 9, 10 
    * 12 : 0, 1, 2 

This graph has the following strongly connected components:

  P_1:

    proper#(f(X)) =#> proper#(X)   
    proper#(g(X)) =#> proper#(X)   

  P_2:

    f#(ok(X)) =#> f#(X)   

  P_3:

    g#(ok(X)) =#> g#(X)   

  P_4:

    top#(mark(X)) =#> top#(proper(X))

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