TRS Standard pair #487073157

details

property	value
status	complete
benchmark	thiemann14.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n177.star.cs.uiowa.edu
space	AProVE_07

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	3.21381 seconds
cpu usage	10.2408
user time	8.60442
system time	1.6364
max virtual memory	5798364.0
max residence set size	112476.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 empty(nil()) -> true()
 empty(cons(x,y)) -> false()
 tail(nil()) -> nil()
 tail(cons(x,y)) -> y
 head(cons(x,y)) -> x
 zero(0()) -> true()
 zero(s(x)) -> false()
 p(0()) -> 0()
 p(s(0())) -> 0()
 p(s(s(x))) -> s(p(s(x)))
 intlist(x) -> if_intlist(empty(x),x)
 if_intlist(true(),x) -> nil()
 if_intlist(false(),x) -> cons(s(head(x)),intlist(tail(x)))
 int(x,y) -> if_int(zero(x),zero(y),x,y)
 if_int(true(),b,x,y) -> if1(b,x,y)
 if_int(false(),b,x,y) -> if2(b,x,y)
 if1(true(),x,y) -> cons(0(),nil())
 if1(false(),x,y) -> cons(0(),int(s(0()),y))
 if2(true(),x,y) -> nil()
 if2(false(),x,y) -> intlist(int(p(x),p(y)))

Proof:
 DP Processor:
  DPs:
   p#(s(s(x))) -> p#(s(x))
   intlist#(x) -> empty#(x)
   intlist#(x) -> if_intlist#(empty(x),x)
   if_intlist#(false(),x) -> tail#(x)
   if_intlist#(false(),x) -> intlist#(tail(x))
   if_intlist#(false(),x) -> head#(x)
   int#(x,y) -> zero#(y)
   int#(x,y) -> zero#(x)
   int#(x,y) -> if_int#(zero(x),zero(y),x,y)
   if_int#(true(),b,x,y) -> if1#(b,x,y)
   if_int#(false(),b,x,y) -> if2#(b,x,y)
   if1#(false(),x,y) -> int#(s(0()),y)
   if2#(false(),x,y) -> p#(y)
   if2#(false(),x,y) -> p#(x)
   if2#(false(),x,y) -> int#(p(x),p(y))
   if2#(false(),x,y) -> intlist#(int(p(x),p(y)))
  TRS:
   empty(nil()) -> true()
   empty(cons(x,y)) -> false()
   tail(nil()) -> nil()
   tail(cons(x,y)) -> y
   head(cons(x,y)) -> x
   zero(0()) -> true()
   zero(s(x)) -> false()
   p(0()) -> 0()
   p(s(0())) -> 0()
   p(s(s(x))) -> s(p(s(x)))
   intlist(x) -> if_intlist(empty(x),x)
   if_intlist(true(),x) -> nil()
   if_intlist(false(),x) -> cons(s(head(x)),intlist(tail(x)))
   int(x,y) -> if_int(zero(x),zero(y),x,y)
   if_int(true(),b,x,y) -> if1(b,x,y)
   if_int(false(),b,x,y) -> if2(b,x,y)
   if1(true(),x,y) -> cons(0(),nil())
   if1(false(),x,y) -> cons(0(),int(s(0()),y))
   if2(true(),x,y) -> nil()
   if2(false(),x,y) -> intlist(int(p(x),p(y)))
  TDG Processor:
   DPs:
    p#(s(s(x))) -> p#(s(x))
    intlist#(x) -> empty#(x)
    intlist#(x) -> if_intlist#(empty(x),x)
    if_intlist#(false(),x) -> tail#(x)
    if_intlist#(false(),x) -> intlist#(tail(x))
    if_intlist#(false(),x) -> head#(x)
    int#(x,y) -> zero#(y)
    int#(x,y) -> zero#(x)
    int#(x,y) -> if_int#(zero(x),zero(y),x,y)
    if_int#(true(),b,x,y) -> if1#(b,x,y)
    if_int#(false(),b,x,y) -> if2#(b,x,y)
    if1#(false(),x,y) -> int#(s(0()),y)
    if2#(false(),x,y) -> p#(y)
    if2#(false(),x,y) -> p#(x)
    if2#(false(),x,y) -> int#(p(x),p(y))
    if2#(false(),x,y) -> intlist#(int(p(x),p(y)))
   TRS:
    empty(nil()) -> true()
    empty(cons(x,y)) -> false()
    tail(nil()) -> nil()
    tail(cons(x,y)) -> y
    head(cons(x,y)) -> x
    zero(0()) -> true()
    zero(s(x)) -> false()
    p(0()) -> 0()
    p(s(0())) -> 0()
    p(s(s(x))) -> s(p(s(x)))
    intlist(x) -> if_intlist(empty(x),x)
    if_intlist(true(),x) -> nil()
    if_intlist(false(),x) -> cons(s(head(x)),intlist(tail(x)))
    int(x,y) -> if_int(zero(x),zero(y),x,y)
    if_int(true(),b,x,y) -> if1(b,x,y)
    if_int(false(),b,x,y) -> if2(b,x,y)
    if1(true(),x,y) -> cons(0(),nil())

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