TRS Standard pair #487069527

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	n186.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	19.1201 seconds
cpu usage	64.7755
user time	61.3397
system time	3.43587
max virtual memory	6969020.0
max residence set size	404328.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 active(minus(0(),Y)) -> mark(0())
 active(minus(s(X),s(Y))) -> mark(minus(X,Y))
 active(geq(X,0())) -> mark(true())
 active(geq(0(),s(Y))) -> mark(false())
 active(geq(s(X),s(Y))) -> mark(geq(X,Y))
 active(div(0(),s(Y))) -> 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(X1,X2)) -> div(active(X1),X2)
 active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
 s(mark(X)) -> mark(s(X))
 div(mark(X1),X2) -> mark(div(X1,X2))
 if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
 proper(minus(X1,X2)) -> minus(proper(X1),proper(X2))
 proper(0()) -> ok(0())
 proper(s(X)) -> s(proper(X))
 proper(geq(X1,X2)) -> geq(proper(X1),proper(X2))
 proper(true()) -> ok(true())
 proper(false()) -> ok(false())
 proper(div(X1,X2)) -> div(proper(X1),proper(X2))
 proper(if(X1,X2,X3)) -> if(proper(X1),proper(X2),proper(X3))
 minus(ok(X1),ok(X2)) -> ok(minus(X1,X2))
 s(ok(X)) -> ok(s(X))
 geq(ok(X1),ok(X2)) -> ok(geq(X1,X2))
 div(ok(X1),ok(X2)) -> ok(div(X1,X2))
 if(ok(X1),ok(X2),ok(X3)) -> ok(if(X1,X2,X3))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(minus(s(X),s(Y))) -> minus#(X,Y)
   active#(geq(s(X),s(Y))) -> geq#(X,Y)
   active#(div(s(X),s(Y))) -> minus#(X,Y)
   active#(div(s(X),s(Y))) -> div#(minus(X,Y),s(Y))
   active#(div(s(X),s(Y))) -> s#(div(minus(X,Y),s(Y)))
   active#(div(s(X),s(Y))) -> geq#(X,Y)
   active#(div(s(X),s(Y))) -> if#(geq(X,Y),s(div(minus(X,Y),s(Y))),0())
   active#(s(X)) -> active#(X)
   active#(s(X)) -> s#(active(X))
   active#(div(X1,X2)) -> active#(X1)
   active#(div(X1,X2)) -> div#(active(X1),X2)
   active#(if(X1,X2,X3)) -> active#(X1)
   active#(if(X1,X2,X3)) -> if#(active(X1),X2,X3)
   s#(mark(X)) -> s#(X)
   div#(mark(X1),X2) -> div#(X1,X2)
   if#(mark(X1),X2,X3) -> if#(X1,X2,X3)
   proper#(minus(X1,X2)) -> proper#(X2)
   proper#(minus(X1,X2)) -> proper#(X1)
   proper#(minus(X1,X2)) -> minus#(proper(X1),proper(X2))
   proper#(s(X)) -> proper#(X)
   proper#(s(X)) -> s#(proper(X))
   proper#(geq(X1,X2)) -> proper#(X2)
   proper#(geq(X1,X2)) -> proper#(X1)
   proper#(geq(X1,X2)) -> geq#(proper(X1),proper(X2))
   proper#(div(X1,X2)) -> proper#(X2)
   proper#(div(X1,X2)) -> proper#(X1)
   proper#(div(X1,X2)) -> div#(proper(X1),proper(X2))
   proper#(if(X1,X2,X3)) -> proper#(X3)
   proper#(if(X1,X2,X3)) -> proper#(X2)
   proper#(if(X1,X2,X3)) -> proper#(X1)
   proper#(if(X1,X2,X3)) -> if#(proper(X1),proper(X2),proper(X3))
   minus#(ok(X1),ok(X2)) -> minus#(X1,X2)
   s#(ok(X)) -> s#(X)
   geq#(ok(X1),ok(X2)) -> geq#(X1,X2)
   div#(ok(X1),ok(X2)) -> div#(X1,X2)
   if#(ok(X1),ok(X2),ok(X3)) -> if#(X1,X2,X3)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(minus(0(),Y)) -> mark(0())
   active(minus(s(X),s(Y))) -> mark(minus(X,Y))
   active(geq(X,0())) -> mark(true())
   active(geq(0(),s(Y))) -> mark(false())
   active(geq(s(X),s(Y))) -> mark(geq(X,Y))
   active(div(0(),s(Y))) -> 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(X1,X2)) -> div(active(X1),X2)
   active(if(X1,X2,X3)) -> if(active(X1),X2,X3)
   s(mark(X)) -> mark(s(X))
   div(mark(X1),X2) -> mark(div(X1,X2))
   if(mark(X1),X2,X3) -> mark(if(X1,X2,X3))
   proper(minus(X1,X2)) -> minus(proper(X1),proper(X2))
   proper(0()) -> ok(0())
   proper(s(X)) -> s(proper(X))
   proper(geq(X1,X2)) -> geq(proper(X1),proper(X2))
   proper(true()) -> ok(true())
   proper(false()) -> ok(false())
   proper(div(X1,X2)) -> div(proper(X1),proper(X2))

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