TRS Standard pair #487068407

details

property	value
status	complete
benchmark	recursion-10.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n179.star.cs.uiowa.edu
space	TCT_12

run statistics

property	value
solver	ttt2-1.20
configuration	ttt2
runtime (wallclock)	0.788734 seconds
cpu usage	1.74416
user time	1.4799
system time	0.264266
max virtual memory	1764388.0
max residence set size	72560.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem:
 f_0(x) -> a()
 f_1(x) -> g_1(x,x)
 g_1(s(x),y) -> b(f_0(y),g_1(x,y))
 f_2(x) -> g_2(x,x)
 g_2(s(x),y) -> b(f_1(y),g_2(x,y))
 f_3(x) -> g_3(x,x)
 g_3(s(x),y) -> b(f_2(y),g_3(x,y))
 f_4(x) -> g_4(x,x)
 g_4(s(x),y) -> b(f_3(y),g_4(x,y))
 f_5(x) -> g_5(x,x)
 g_5(s(x),y) -> b(f_4(y),g_5(x,y))
 f_6(x) -> g_6(x,x)
 g_6(s(x),y) -> b(f_5(y),g_6(x,y))
 f_7(x) -> g_7(x,x)
 g_7(s(x),y) -> b(f_6(y),g_7(x,y))
 f_8(x) -> g_8(x,x)
 g_8(s(x),y) -> b(f_7(y),g_8(x,y))
 f_9(x) -> g_9(x,x)
 g_9(s(x),y) -> b(f_8(y),g_9(x,y))
 f_10(x) -> g_10(x,x)
 g_10(s(x),y) -> b(f_9(y),g_10(x,y))

Proof:
 DP Processor:
  DPs:
   f_1#(x) -> g_1#(x,x)
   g_1#(s(x),y) -> g_1#(x,y)
   g_1#(s(x),y) -> f_0#(y)
   f_2#(x) -> g_2#(x,x)
   g_2#(s(x),y) -> g_2#(x,y)
   g_2#(s(x),y) -> f_1#(y)
   f_3#(x) -> g_3#(x,x)
   g_3#(s(x),y) -> g_3#(x,y)
   g_3#(s(x),y) -> f_2#(y)
   f_4#(x) -> g_4#(x,x)
   g_4#(s(x),y) -> g_4#(x,y)
   g_4#(s(x),y) -> f_3#(y)
   f_5#(x) -> g_5#(x,x)
   g_5#(s(x),y) -> g_5#(x,y)
   g_5#(s(x),y) -> f_4#(y)
   f_6#(x) -> g_6#(x,x)
   g_6#(s(x),y) -> g_6#(x,y)
   g_6#(s(x),y) -> f_5#(y)
   f_7#(x) -> g_7#(x,x)
   g_7#(s(x),y) -> g_7#(x,y)
   g_7#(s(x),y) -> f_6#(y)
   f_8#(x) -> g_8#(x,x)
   g_8#(s(x),y) -> g_8#(x,y)
   g_8#(s(x),y) -> f_7#(y)
   f_9#(x) -> g_9#(x,x)
   g_9#(s(x),y) -> g_9#(x,y)
   g_9#(s(x),y) -> f_8#(y)
   f_10#(x) -> g_10#(x,x)
   g_10#(s(x),y) -> g_10#(x,y)
   g_10#(s(x),y) -> f_9#(y)
  TRS:
   f_0(x) -> a()
   f_1(x) -> g_1(x,x)
   g_1(s(x),y) -> b(f_0(y),g_1(x,y))
   f_2(x) -> g_2(x,x)
   g_2(s(x),y) -> b(f_1(y),g_2(x,y))
   f_3(x) -> g_3(x,x)
   g_3(s(x),y) -> b(f_2(y),g_3(x,y))
   f_4(x) -> g_4(x,x)
   g_4(s(x),y) -> b(f_3(y),g_4(x,y))
   f_5(x) -> g_5(x,x)
   g_5(s(x),y) -> b(f_4(y),g_5(x,y))
   f_6(x) -> g_6(x,x)
   g_6(s(x),y) -> b(f_5(y),g_6(x,y))
   f_7(x) -> g_7(x,x)
   g_7(s(x),y) -> b(f_6(y),g_7(x,y))
   f_8(x) -> g_8(x,x)
   g_8(s(x),y) -> b(f_7(y),g_8(x,y))
   f_9(x) -> g_9(x,x)
   g_9(s(x),y) -> b(f_8(y),g_9(x,y))
   f_10(x) -> g_10(x,x)
   g_10(s(x),y) -> b(f_9(y),g_10(x,y))
  TDG Processor:
   DPs:
    f_1#(x) -> g_1#(x,x)
    g_1#(s(x),y) -> g_1#(x,y)
    g_1#(s(x),y) -> f_0#(y)
    f_2#(x) -> g_2#(x,x)
    g_2#(s(x),y) -> g_2#(x,y)
    g_2#(s(x),y) -> f_1#(y)
    f_3#(x) -> g_3#(x,x)
    g_3#(s(x),y) -> g_3#(x,y)
    g_3#(s(x),y) -> f_2#(y)
    f_4#(x) -> g_4#(x,x)
    g_4#(s(x),y) -> g_4#(x,y)
    g_4#(s(x),y) -> f_3#(y)
    f_5#(x) -> g_5#(x,x)
    g_5#(s(x),y) -> g_5#(x,y)
    g_5#(s(x),y) -> f_4#(y)
    f_6#(x) -> g_6#(x,x)
    g_6#(s(x),y) -> g_6#(x,y)
    g_6#(s(x),y) -> f_5#(y)

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