TRS Standard pair #487071457

details

property	value
status	complete
benchmark	ExIntrod_GM01_iGM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n182.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	8.07081 seconds
cpu usage	25.52
user time	22.6898
system time	2.83021
max virtual memory	6862120.0
max residence set size	292560.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 active(incr(nil())) -> mark(nil())
 active(incr(cons(X,L))) -> mark(cons(s(X),incr(L)))
 active(adx(nil())) -> mark(nil())
 active(adx(cons(X,L))) -> mark(incr(cons(X,adx(L))))
 active(nats()) -> mark(adx(zeros()))
 active(zeros()) -> mark(cons(0(),zeros()))
 active(head(cons(X,L))) -> mark(X)
 active(tail(cons(X,L))) -> mark(L)
 mark(incr(X)) -> active(incr(mark(X)))
 mark(nil()) -> active(nil())
 mark(cons(X1,X2)) -> active(cons(mark(X1),X2))
 mark(s(X)) -> active(s(mark(X)))
 mark(adx(X)) -> active(adx(mark(X)))
 mark(nats()) -> active(nats())
 mark(zeros()) -> active(zeros())
 mark(0()) -> active(0())
 mark(head(X)) -> active(head(mark(X)))
 mark(tail(X)) -> active(tail(mark(X)))
 incr(mark(X)) -> incr(X)
 incr(active(X)) -> incr(X)
 cons(mark(X1),X2) -> cons(X1,X2)
 cons(X1,mark(X2)) -> cons(X1,X2)
 cons(active(X1),X2) -> cons(X1,X2)
 cons(X1,active(X2)) -> cons(X1,X2)
 s(mark(X)) -> s(X)
 s(active(X)) -> s(X)
 adx(mark(X)) -> adx(X)
 adx(active(X)) -> adx(X)
 head(mark(X)) -> head(X)
 head(active(X)) -> head(X)
 tail(mark(X)) -> tail(X)
 tail(active(X)) -> tail(X)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [cons](x0, x1) = x0 + 4x1,
   
   [zeros] = 0,
   
   [incr](x0) = x0,
   
   [mark](x0) = x0,
   
   [s](x0) = x0,
   
   [head](x0) = x0,
   
   [nil] = 4,
   
   [nats] = 4,
   
   [tail](x0) = 6x0 + 7,
   
   [0] = 0,
   
   [adx](x0) = 4x0,
   
   [active](x0) = x0
  orientation:
   active(incr(nil())) = 4 >= 4 = mark(nil())
   
   active(incr(cons(X,L))) = 4L + X >= 4L + X = mark(cons(s(X),incr(L)))
   
   active(adx(nil())) = 16 >= 4 = mark(nil())
   
   active(adx(cons(X,L))) = 16L + 4X >= 16L + X = mark(incr(cons(X,adx(L))))
   
   active(nats()) = 4 >= 0 = mark(adx(zeros()))
   
   active(zeros()) = 0 >= 0 = mark(cons(0(),zeros()))
   
   active(head(cons(X,L))) = 4L + X >= X = mark(X)
   
   active(tail(cons(X,L))) = 24L + 6X + 7 >= L = mark(L)
   
   mark(incr(X)) = X >= X = active(incr(mark(X)))
   
   mark(nil()) = 4 >= 4 = active(nil())
   
   mark(cons(X1,X2)) = X1 + 4X2 >= X1 + 4X2 = active(cons(mark(X1),X2))
   
   mark(s(X)) = X >= X = active(s(mark(X)))
   
   mark(adx(X)) = 4X >= 4X = active(adx(mark(X)))
   
   mark(nats()) = 4 >= 4 = active(nats())
   
   mark(zeros()) = 0 >= 0 = active(zeros())
   
   mark(0()) = 0 >= 0 = active(0())
   
   mark(head(X)) = X >= X = active(head(mark(X)))
   
   mark(tail(X)) = 6X + 7 >= 6X + 7 = active(tail(mark(X)))

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