TRS Stand 20472 pair #381716765

details

property	value
status	complete
benchmark	Ex15_Luc98_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n114.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	Wanda
configuration	FirstOrder
runtime (wallclock)	0.783265113831 seconds
cpu usage	0.777168216
max memory	2.439168E7

stage attributes

key	value
output-size	32406
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.

  0 : [] --> o 
  active : [o] --> o 
  add : [o * o] --> o 
  and : [o * o] --> o 
  cons : [o * o] --> o 
  false : [] --> o 
  first : [o * o] --> o 
  from : [o] --> o 
  if : [o * o * o] --> o 
  mark : [o] --> o 
  nil : [] --> o 
  ok : [o] --> o 
  proper : [o] --> o 
  s : [o] --> o 
  top : [o] --> o 
  true : [] --> o 

  active(and(true, X)) => mark(X) 
  active(and(false, X)) => mark(false) 
  active(if(true, X, Y)) => mark(X) 
  active(if(false, X, Y)) => mark(Y) 
  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(from(X)) => mark(cons(X, from(s(X)))) 
  active(and(X, Y)) => and(active(X), Y) 
  active(if(X, Y, Z)) => if(active(X), Y, Z) 
  active(add(X, Y)) => add(active(X), Y) 
  active(first(X, Y)) => first(active(X), Y) 
  active(first(X, Y)) => first(X, active(Y)) 
  and(mark(X), Y) => mark(and(X, Y)) 
  if(mark(X), Y, Z) => mark(if(X, Y, Z)) 
  add(mark(X), Y) => mark(add(X, Y)) 
  first(mark(X), Y) => mark(first(X, Y)) 
  first(X, mark(Y)) => mark(first(X, Y)) 
  proper(and(X, Y)) => and(proper(X), proper(Y)) 
  proper(true) => ok(true) 
  proper(false) => ok(false) 
  proper(if(X, Y, Z)) => if(proper(X), proper(Y), proper(Z)) 
  proper(add(X, Y)) => add(proper(X), proper(Y)) 
  proper(0) => ok(0) 
  proper(s(X)) => s(proper(X)) 
  proper(first(X, Y)) => first(proper(X), proper(Y)) 
  proper(nil) => ok(nil) 
  proper(cons(X, Y)) => cons(proper(X), proper(Y)) 
  proper(from(X)) => from(proper(X)) 
  and(ok(X), ok(Y)) => ok(and(X, Y)) 
  if(ok(X), ok(Y), ok(Z)) => ok(if(X, Y, Z)) 
  add(ok(X), ok(Y)) => ok(add(X, Y)) 
  s(ok(X)) => ok(s(X)) 
  first(ok(X), ok(Y)) => ok(first(X, Y)) 
  cons(ok(X), ok(Y)) => ok(cons(X, Y)) 
  from(ok(X)) => ok(from(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#(add(s(X), Y)) =#> s#(add(X, Y))   
    1] active#(add(s(X), Y)) =#> add#(X, Y)   
    2] active#(first(s(X), cons(Y, Z))) =#> cons#(Y, first(X, Z))   
    3] active#(first(s(X), cons(Y, Z))) =#> first#(X, Z)   
    4] active#(from(X)) =#> cons#(X, from(s(X)))   
    5] active#(from(X)) =#> from#(s(X))   
    6] active#(from(X)) =#> s#(X)   
    7] active#(and(X, Y)) =#> and#(active(X), Y)   
    8] active#(and(X, Y)) =#> active#(X)   
    9] active#(if(X, Y, Z)) =#> if#(active(X), Y, Z)   
    10] active#(if(X, Y, Z)) =#> active#(X)   
    11] active#(add(X, Y)) =#> add#(active(X), Y)   
    12] active#(add(X, Y)) =#> active#(X)   
    13] active#(first(X, Y)) =#> first#(active(X), Y)   
    14] active#(first(X, Y)) =#> active#(X)   
    15] active#(first(X, Y)) =#> first#(X, active(Y))   
    16] active#(first(X, Y)) =#> active#(Y)   
    17] and#(mark(X), Y) =#> and#(X, Y)   
    18] if#(mark(X), Y, Z) =#> if#(X, Y, Z)   
    19] add#(mark(X), Y) =#> add#(X, Y)   
    20] first#(mark(X), Y) =#> first#(X, Y)   
    21] first#(X, mark(Y)) =#> first#(X, Y)   
    22] proper#(and(X, Y)) =#> and#(proper(X), proper(Y))   
    23] proper#(and(X, Y)) =#> proper#(X)   
    24] proper#(and(X, Y)) =#> proper#(Y)   
    25] proper#(if(X, Y, Z)) =#> if#(proper(X), proper(Y), proper(Z))

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