TRS Standard pair #487070062

details

property	value
status	complete
benchmark	PEANO_nokinds_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n181.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	18.0387 seconds
cpu usage	65.2995
user time	59.3813
system time	5.91824
max virtual memory	6488976.0
max residence set size	202500.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 active(U11(tt(),N)) -> mark(N)
 active(U21(tt(),M,N)) -> mark(s(plus(N,M)))
 active(and(tt(),X)) -> mark(X)
 active(isNat(0())) -> mark(tt())
 active(isNat(plus(V1,V2))) -> mark(and(isNat(V1),isNat(V2)))
 active(isNat(s(V1))) -> mark(isNat(V1))
 active(plus(N,0())) -> mark(U11(isNat(N),N))
 active(plus(N,s(M))) -> mark(U21(and(isNat(M),isNat(N)),M,N))
 mark(U11(X1,X2)) -> active(U11(mark(X1),X2))
 mark(tt()) -> active(tt())
 mark(U21(X1,X2,X3)) -> active(U21(mark(X1),X2,X3))
 mark(s(X)) -> active(s(mark(X)))
 mark(plus(X1,X2)) -> active(plus(mark(X1),mark(X2)))
 mark(and(X1,X2)) -> active(and(mark(X1),X2))
 mark(isNat(X)) -> active(isNat(X))
 mark(0()) -> active(0())
 U11(mark(X1),X2) -> U11(X1,X2)
 U11(X1,mark(X2)) -> U11(X1,X2)
 U11(active(X1),X2) -> U11(X1,X2)
 U11(X1,active(X2)) -> U11(X1,X2)
 U21(mark(X1),X2,X3) -> U21(X1,X2,X3)
 U21(X1,mark(X2),X3) -> U21(X1,X2,X3)
 U21(X1,X2,mark(X3)) -> U21(X1,X2,X3)
 U21(active(X1),X2,X3) -> U21(X1,X2,X3)
 U21(X1,active(X2),X3) -> U21(X1,X2,X3)
 U21(X1,X2,active(X3)) -> U21(X1,X2,X3)
 s(mark(X)) -> s(X)
 s(active(X)) -> s(X)
 plus(mark(X1),X2) -> plus(X1,X2)
 plus(X1,mark(X2)) -> plus(X1,X2)
 plus(active(X1),X2) -> plus(X1,X2)
 plus(X1,active(X2)) -> plus(X1,X2)
 and(mark(X1),X2) -> and(X1,X2)
 and(X1,mark(X2)) -> and(X1,X2)
 and(active(X1),X2) -> and(X1,X2)
 and(X1,active(X2)) -> and(X1,X2)
 isNat(mark(X)) -> isNat(X)
 isNat(active(X)) -> isNat(X)

Proof:
 DP Processor:
  DPs:
   active#(U11(tt(),N)) -> mark#(N)
   active#(U21(tt(),M,N)) -> plus#(N,M)
   active#(U21(tt(),M,N)) -> s#(plus(N,M))
   active#(U21(tt(),M,N)) -> mark#(s(plus(N,M)))
   active#(and(tt(),X)) -> mark#(X)
   active#(isNat(0())) -> mark#(tt())
   active#(isNat(plus(V1,V2))) -> isNat#(V2)
   active#(isNat(plus(V1,V2))) -> isNat#(V1)
   active#(isNat(plus(V1,V2))) -> and#(isNat(V1),isNat(V2))
   active#(isNat(plus(V1,V2))) -> mark#(and(isNat(V1),isNat(V2)))
   active#(isNat(s(V1))) -> isNat#(V1)
   active#(isNat(s(V1))) -> mark#(isNat(V1))
   active#(plus(N,0())) -> isNat#(N)
   active#(plus(N,0())) -> U11#(isNat(N),N)
   active#(plus(N,0())) -> mark#(U11(isNat(N),N))
   active#(plus(N,s(M))) -> isNat#(N)
   active#(plus(N,s(M))) -> isNat#(M)
   active#(plus(N,s(M))) -> and#(isNat(M),isNat(N))
   active#(plus(N,s(M))) -> U21#(and(isNat(M),isNat(N)),M,N)
   active#(plus(N,s(M))) -> mark#(U21(and(isNat(M),isNat(N)),M,N))
   mark#(U11(X1,X2)) -> mark#(X1)
   mark#(U11(X1,X2)) -> U11#(mark(X1),X2)
   mark#(U11(X1,X2)) -> active#(U11(mark(X1),X2))
   mark#(tt()) -> active#(tt())
   mark#(U21(X1,X2,X3)) -> mark#(X1)
   mark#(U21(X1,X2,X3)) -> U21#(mark(X1),X2,X3)
   mark#(U21(X1,X2,X3)) -> active#(U21(mark(X1),X2,X3))
   mark#(s(X)) -> mark#(X)
   mark#(s(X)) -> s#(mark(X))
   mark#(s(X)) -> active#(s(mark(X)))
   mark#(plus(X1,X2)) -> mark#(X2)
   mark#(plus(X1,X2)) -> mark#(X1)
   mark#(plus(X1,X2)) -> plus#(mark(X1),mark(X2))
   mark#(plus(X1,X2)) -> active#(plus(mark(X1),mark(X2)))
   mark#(and(X1,X2)) -> mark#(X1)
   mark#(and(X1,X2)) -> and#(mark(X1),X2)
   mark#(and(X1,X2)) -> active#(and(mark(X1),X2))
   mark#(isNat(X)) -> active#(isNat(X))
   mark#(0()) -> active#(0())
   U11#(mark(X1),X2) -> U11#(X1,X2)
   U11#(X1,mark(X2)) -> U11#(X1,X2)
   U11#(active(X1),X2) -> U11#(X1,X2)
   U11#(X1,active(X2)) -> U11#(X1,X2)
   U21#(mark(X1),X2,X3) -> U21#(X1,X2,X3)
   U21#(X1,mark(X2),X3) -> U21#(X1,X2,X3)
   U21#(X1,X2,mark(X3)) -> U21#(X1,X2,X3)
   U21#(active(X1),X2,X3) -> U21#(X1,X2,X3)
   U21#(X1,active(X2),X3) -> U21#(X1,X2,X3)
   U21#(X1,X2,active(X3)) -> U21#(X1,X2,X3)
   s#(mark(X)) -> s#(X)
   s#(active(X)) -> s#(X)
   plus#(mark(X1),X2) -> plus#(X1,X2)
   plus#(X1,mark(X2)) -> plus#(X1,X2)
   plus#(active(X1),X2) -> plus#(X1,X2)
   plus#(X1,active(X2)) -> plus#(X1,X2)

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