/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES
Input TRS:
    1: times(x,plus(y,1())) -> plus(times(x,plus(y,times(1(),0()))),x)
    2: times(x,1()) -> x
    3: times(x,0()) -> 0()
    4: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
    5: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x))
    6: plus(zero(),y) -> y
    7: plus(id(x),s(y)) -> s(plus(x,if(gt(s(y),y),y,s(y))))
    8: id(x) -> x
    9: if(true(),x,y) -> x
    10: if(false(),x,y) -> y
    11: not(x) -> if(x,false(),true())
    12: gt(s(x),zero()) -> true()
    13: gt(zero(),y) -> false()
    14: gt(s(x),s(y)) -> gt(x,y)
Number of strict rules: 14
Direct poly ... failed.
Freezing gt
1: times(x,plus(y,1())) -> plus(times(x,plus(y,times(1(),0()))),x)
2: times(x,1()) -> x
3: times(x,0()) -> 0()
4: plus(s(x),s(y)) -> s(s(plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))))
5: plus(s(x),x) -> plus(if(gt(x,x),id(x),id(x)),s(x))
6: plus(zero(),y) -> y
7: plus(id(x),s(y)) -> s(plus(x,if(gt❆1_s(y,y),y,s(y))))
8: id(x) -> x
9: if(true(),x,y) -> x
10: if(false(),x,y) -> y
11: not(x) -> if(x,false(),true())
12: gt❆1_s(x,zero()) -> true()
13: gt❆1_zero(y) -> false()
14: gt❆1_s(x,s(y)) -> gt(x,y)
15: gt(zero(),_1) ->= gt❆1_zero(_1)
16: gt(s(_1),_2) ->= gt❆1_s(_1,_2)
Number of strict rules: 14
Direct poly ... failed.
Dependency Pairs:
   #1: #not(x) -> #if(x,false(),true())
   #2: #gt❆1_s(x,s(y)) -> #gt(x,y)
   #3: #plus(id(x),s(y)) -> #plus(x,if(gt❆1_s(y,y),y,s(y)))
   #4: #plus(id(x),s(y)) -> #if(gt❆1_s(y,y),y,s(y))
   #5: #plus(id(x),s(y)) -> #gt❆1_s(y,y)
   #6: #plus(s(x),x) -> #plus(if(gt(x,x),id(x),id(x)),s(x))
   #7: #plus(s(x),x) -> #if(gt(x,x),id(x),id(x))
   #8: #plus(s(x),x) -> #gt(x,x)
   #9: #plus(s(x),x) -> #id(x)
   #10: #plus(s(x),x) -> #id(x)
   #11: #gt(s(_1),_2) ->? #gt❆1_s(_1,_2)
   #12: #times(x,plus(y,1())) -> #plus(times(x,plus(y,times(1(),0()))),x)
   #13: #times(x,plus(y,1())) -> #times(x,plus(y,times(1(),0())))
   #14: #times(x,plus(y,1())) -> #plus(y,times(1(),0()))
   #15: #times(x,plus(y,1())) -> #times(1(),0())
   #16: #gt(zero(),_1) ->? #gt❆1_zero(_1)
   #17: #plus(s(x),s(y)) -> #plus(if(gt(x,y),x,y),if(not(gt(x,y)),id(x),id(y)))
   #18: #plus(s(x),s(y)) -> #if(gt(x,y),x,y)
   #19: #plus(s(x),s(y)) -> #gt(x,y)
   #20: #plus(s(x),s(y)) -> #if(not(gt(x,y)),id(x),id(y))
   #21: #plus(s(x),s(y)) -> #not(gt(x,y))
   #22: #plus(s(x),s(y)) -> #gt(x,y)
   #23: #plus(s(x),s(y)) -> #id(x)
   #24: #plus(s(x),s(y)) -> #id(y)
Number of SCCs: 3, DPs: 6
	SCC { #13 }
Sum... succeeded.
  zero()		w: (1)
  1()		w: (32287)
  s(x1)		w: (0)
  gt(x1,x2)		w: (11798 + x2 + x1)
  #plus(x1,x2)		w: (0)
  false()		w: (11801)
  #id(x1)		w: (0)
  true()		w: (11800)
  gt❆1_zero(x1)		w: (11800)
  #not(x1)		w: (0)
  #times(x1,x2)		w: (x2)
  #gt❆1_zero(x1)		w: (0)
  0()		w: (32286)
  if(x1,x2,x3)		w: (8366)
  times(x1,x2)		w: (x2)
  #gt(x1,x2)		w: (0)
  #gt❆1_s(x1,x2)		w: (0)
  plus(x1,x2)		w: (x2)
  #if(x1,x2,x3)		w: (0)
  id(x1)		w: (8856)
  gt❆1_s(x1,x2)		w: (11799 + x1)
  not(x1)		w: (x1)
    USABLE RULES: { 3..7 }
    Removed DPs: #13
Number of SCCs: 2, DPs: 5
	SCC { #2 #11 }
Sum... succeeded.
  zero()		w: (1)
  1()		w: (32287)
  s(x1)		w: (2 + x1)
  gt(x1,x2)		w: (11798 + x2)
  #plus(x1,x2)		w: (0)
  false()		w: (11801)
  #id(x1)		w: (0)
  true()		w: (20162)
  gt❆1_zero(x1)		w: (11800)
  #not(x1)		w: (0)
  #times(x1,x2)		w: (0)
  #gt❆1_zero(x1)		w: (0)
  0()		w: (32286)
  if(x1,x2,x3)		w: (0)
  times(x1,x2)		w: (x2)
  #gt(x1,x2)		w: (282 + x2)
  #gt❆1_s(x1,x2)		w: (281 + x2)
  plus(x1,x2)		w: (1 + x1)
  #if(x1,x2,x3)		w: (0)
  id(x1)		w: (0)
  gt❆1_s(x1,x2)		w: (19358 + x2 + x1)
  not(x1)		w: (20537 + x1)
    USABLE RULES: { 3 }
    Removed DPs: #2 #11
Number of SCCs: 1, DPs: 3
	SCC { #3 #6 #17 }
Sum... Max... succeeded.
  zero()		w: (0)
  1()		w: (0)
  s(x1)		w: (11300 + x1)
  gt(x1,x2)		w: (0)
  #plus(x1,x2)		w: (max{1 + x2, 11298 + x1})
  false()		w: (0)
  #id(x1)		w: (0)
  true()		w: (0)
  gt❆1_zero(x1)		w: (0)
  #not(x1)		w: (0)
  #times(x1,x2)		w: (0)
  #gt❆1_zero(x1)		w: (0)
  0()		w: (0)
  if(x1,x2,x3)		w: (max{x3, 8859 + x2, 11298 + x1})
  times(x1,x2)		w: (0)
  #gt(x1,x2)		w: (0)
  #gt❆1_s(x1,x2)		w: (0)
  plus(x1,x2)		w: (0)
  #if(x1,x2,x3)		w: (0)
  id(x1)		w: (x1)
  gt❆1_s(x1,x2)		w: (0)
  not(x1)		w: (11298 + x1)
    USABLE RULES: { 8..16 }
    Removed DPs: #6 #17
Number of SCCs: 1, DPs: 1
	SCC { #3 }
Sum... succeeded.
  zero()		w: (1)
  1()		w: (32287)
  s(x1)		w: (1 + x1)
  gt(x1,x2)		w: (1 + x2 + x1)
  #plus(x1,x2)		w: (11649 + x1)
  false()		w: (0)
  #id(x1)		w: (0)
  true()		w: (1)
  gt❆1_zero(x1)		w: (0)
  #not(x1)		w: (0)
  #times(x1,x2)		w: (0)
  #gt❆1_zero(x1)		w: (0)
  0()		w: (1)
  if(x1,x2,x3)		w: (x3 + x2 + x1)
  times(x1,x2)		w: (12329 + x2)
  #gt(x1,x2)		w: (282)
  #gt❆1_s(x1,x2)		w: (281)
  plus(x1,x2)		w: (x2)
  #if(x1,x2,x3)		w: (0)
  id(x1)		w: (4 + x1)
  gt❆1_s(x1,x2)		w: (1 + x2 + x1)
  not(x1)		w: (x1)
    USABLE RULES: { 3 8..10 12..16 }
    Removed DPs: #3
Number of SCCs: 0, DPs: 0