TRS Standard pair #487071302

details

property	value
status	complete
benchmark	Ex1_Luc04b_GM.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n073.star.cs.uiowa.edu
space	Transformed_CSR_04

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	1.16261 seconds
cpu usage	3.40426
user time	2.66317
system time	0.741096
max virtual memory	1745764.0
max residence set size	69796.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 a__nats() -> cons(0(),incr(nats()))
 a__pairs() -> cons(0(),incr(odds()))
 a__odds() -> a__incr(a__pairs())
 a__incr(cons(X,XS)) -> cons(s(mark(X)),incr(XS))
 a__head(cons(X,XS)) -> mark(X)
 a__tail(cons(X,XS)) -> mark(XS)
 mark(nats()) -> a__nats()
 mark(incr(X)) -> a__incr(mark(X))
 mark(pairs()) -> a__pairs()
 mark(odds()) -> a__odds()
 mark(head(X)) -> a__head(mark(X))
 mark(tail(X)) -> a__tail(mark(X))
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(0()) -> 0()
 mark(s(X)) -> s(mark(X))
 a__nats() -> nats()
 a__incr(X) -> incr(X)
 a__pairs() -> pairs()
 a__odds() -> odds()
 a__head(X) -> head(X)
 a__tail(X) -> tail(X)

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [cons](x0, x1) = 4x0 + x1,
   
   [tail](x0) = x0 + 1,
   
   [a__incr](x0) = 2x0,
   
   [0] = 0,
   
   [incr](x0) = 2x0,
   
   [a__pairs] = 0,
   
   [s](x0) = 2x0,
   
   [a__nats] = 0,
   
   [a__odds] = 0,
   
   [head](x0) = 2x0,
   
   [a__tail](x0) = x0 + 1,
   
   [a__head](x0) = 2x0,
   
   [mark](x0) = x0,
   
   [pairs] = 0,
   
   [odds] = 0,
   
   [nats] = 0
  orientation:
   a__nats() = 0 >= 0 = cons(0(),incr(nats()))
   
   a__pairs() = 0 >= 0 = cons(0(),incr(odds()))
   
   a__odds() = 0 >= 0 = a__incr(a__pairs())
   
   a__incr(cons(X,XS)) = 8X + 2XS >= 8X + 2XS = cons(s(mark(X)),incr(XS))
   
   a__head(cons(X,XS)) = 8X + 2XS >= X = mark(X)
   
   a__tail(cons(X,XS)) = 4X + XS + 1 >= XS = mark(XS)
   
   mark(nats()) = 0 >= 0 = a__nats()
   
   mark(incr(X)) = 2X >= 2X = a__incr(mark(X))
   
   mark(pairs()) = 0 >= 0 = a__pairs()
   
   mark(odds()) = 0 >= 0 = a__odds()
   
   mark(head(X)) = 2X >= 2X = a__head(mark(X))
   
   mark(tail(X)) = X + 1 >= X + 1 = a__tail(mark(X))
   
   mark(cons(X1,X2)) = 4X1 + X2 >= 4X1 + X2 = cons(mark(X1),X2)
   
   mark(0()) = 0 >= 0 = 0()
   
   mark(s(X)) = 2X >= 2X = s(mark(X))
   
   a__nats() = 0 >= 0 = nats()
   
   a__incr(X) = 2X >= 2X = incr(X)
   
   a__pairs() = 0 >= 0 = pairs()
   
   a__odds() = 0 >= 0 = odds()
   
   a__head(X) = 2X >= 2X = head(X)

popout

output may be truncated. 'popout' for the full output.

job log

popout

actions all output return to TRS Standard