TRS Standard pair #615301194

details

property	value
status	complete
benchmark	MYNAT_nosorts_C.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n053.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	8.30557894707 seconds
cpu usage	21.761910441
max memory	1.511985152E9

stage attributes

key	value
output-size	55581
starexec-result	"YES"

output

/export/starexec/sandbox2/solver/bin/starexec_run_ttt2 /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem:
 active(and(tt(),X)) -> mark(X)
 active(plus(N,0())) -> mark(N)
 active(plus(N,s(M))) -> mark(s(plus(N,M)))
 active(x(N,0())) -> mark(0())
 active(x(N,s(M))) -> mark(plus(x(N,M),N))
 active(and(X1,X2)) -> and(active(X1),X2)
 active(plus(X1,X2)) -> plus(active(X1),X2)
 active(plus(X1,X2)) -> plus(X1,active(X2))
 active(s(X)) -> s(active(X))
 active(x(X1,X2)) -> x(active(X1),X2)
 active(x(X1,X2)) -> x(X1,active(X2))
 and(mark(X1),X2) -> mark(and(X1,X2))
 plus(mark(X1),X2) -> mark(plus(X1,X2))
 plus(X1,mark(X2)) -> mark(plus(X1,X2))
 s(mark(X)) -> mark(s(X))
 x(mark(X1),X2) -> mark(x(X1,X2))
 x(X1,mark(X2)) -> mark(x(X1,X2))
 proper(and(X1,X2)) -> and(proper(X1),proper(X2))
 proper(tt()) -> ok(tt())
 proper(plus(X1,X2)) -> plus(proper(X1),proper(X2))
 proper(0()) -> ok(0())
 proper(s(X)) -> s(proper(X))
 proper(x(X1,X2)) -> x(proper(X1),proper(X2))
 and(ok(X1),ok(X2)) -> ok(and(X1,X2))
 plus(ok(X1),ok(X2)) -> ok(plus(X1,X2))
 s(ok(X)) -> ok(s(X))
 x(ok(X1),ok(X2)) -> ok(x(X1,X2))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(plus(N,s(M))) -> plus#(N,M)
   active#(plus(N,s(M))) -> s#(plus(N,M))
   active#(x(N,s(M))) -> x#(N,M)
   active#(x(N,s(M))) -> plus#(x(N,M),N)
   active#(and(X1,X2)) -> active#(X1)
   active#(and(X1,X2)) -> and#(active(X1),X2)
   active#(plus(X1,X2)) -> active#(X1)
   active#(plus(X1,X2)) -> plus#(active(X1),X2)
   active#(plus(X1,X2)) -> active#(X2)
   active#(plus(X1,X2)) -> plus#(X1,active(X2))
   active#(s(X)) -> active#(X)
   active#(s(X)) -> s#(active(X))
   active#(x(X1,X2)) -> active#(X1)
   active#(x(X1,X2)) -> x#(active(X1),X2)
   active#(x(X1,X2)) -> active#(X2)
   active#(x(X1,X2)) -> x#(X1,active(X2))
   and#(mark(X1),X2) -> and#(X1,X2)
   plus#(mark(X1),X2) -> plus#(X1,X2)
   plus#(X1,mark(X2)) -> plus#(X1,X2)
   s#(mark(X)) -> s#(X)
   x#(mark(X1),X2) -> x#(X1,X2)
   x#(X1,mark(X2)) -> x#(X1,X2)
   proper#(and(X1,X2)) -> proper#(X2)
   proper#(and(X1,X2)) -> proper#(X1)
   proper#(and(X1,X2)) -> and#(proper(X1),proper(X2))
   proper#(plus(X1,X2)) -> proper#(X2)
   proper#(plus(X1,X2)) -> proper#(X1)
   proper#(plus(X1,X2)) -> plus#(proper(X1),proper(X2))
   proper#(s(X)) -> proper#(X)
   proper#(s(X)) -> s#(proper(X))
   proper#(x(X1,X2)) -> proper#(X2)
   proper#(x(X1,X2)) -> proper#(X1)
   proper#(x(X1,X2)) -> x#(proper(X1),proper(X2))
   and#(ok(X1),ok(X2)) -> and#(X1,X2)
   plus#(ok(X1),ok(X2)) -> plus#(X1,X2)
   s#(ok(X)) -> s#(X)
   x#(ok(X1),ok(X2)) -> x#(X1,X2)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(and(tt(),X)) -> mark(X)
   active(plus(N,0())) -> mark(N)
   active(plus(N,s(M))) -> mark(s(plus(N,M)))
   active(x(N,0())) -> mark(0())
   active(x(N,s(M))) -> mark(plus(x(N,M),N))
   active(and(X1,X2)) -> and(active(X1),X2)
   active(plus(X1,X2)) -> plus(active(X1),X2)
   active(plus(X1,X2)) -> plus(X1,active(X2))
   active(s(X)) -> s(active(X))
   active(x(X1,X2)) -> x(active(X1),X2)
   active(x(X1,X2)) -> x(X1,active(X2))
   and(mark(X1),X2) -> mark(and(X1,X2))
   plus(mark(X1),X2) -> mark(plus(X1,X2))
   plus(X1,mark(X2)) -> mark(plus(X1,X2))
   s(mark(X)) -> mark(s(X))
   x(mark(X1),X2) -> mark(x(X1,X2))

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