0.00/0.18	YES
0.00/0.18	Input TRS:
0.00/0.18	    1: p(0(x1)) -> 0(s(s(p(x1))))
0.00/0.18	    2: p(s(x1)) -> x1
0.00/0.18	    3: p(p(s(x1))) -> p(x1)
0.00/0.18	    4: f(s(x1)) -> p(s(g(p(s(s(x1))))))
0.00/0.18	    5: g(s(x1)) -> p(p(s(s(s(j(s(p(s(p(s(x1)))))))))))
0.00/0.18	    6: j(s(x1)) -> p(s(s(p(s(f(p(s(p(p(s(x1)))))))))))
0.00/0.18	    7: half(0(x1)) -> 0(s(s(half(p(s(p(s(x1))))))))
0.00/0.18	    8: half(s(s(x1))) -> s(half(p(p(s(s(x1))))))
0.00/0.18	    9: rd(0(x1)) -> 0(s(0(0(0(0(s(0(rd(x1)))))))))
0.00/0.18	Number of strict rules: 9
0.00/0.18	Direct POLO(bPol) ... failed.
0.00/0.18	Uncurrying j p
0.00/0.18	1: p^1_0(x1) -> 0(s(s(p(x1))))
0.00/0.18	2: p^1_s(x1) -> x1
0.00/0.18	3: p(p^1_s(x1)) -> p(x1)
0.00/0.18	4: f(s(x1)) -> p^1_s(g(p^1_s(s(x1))))
0.00/0.18	5: g(s(x1)) -> p(p^1_s(s(s(j^1_s(p^1_s(p^1_s(x1)))))))
0.00/0.18	6: j^1_s(x1) -> p^1_s(s(p^1_s(f(p^1_s(p(p^1_s(x1)))))))
0.00/0.18	7: half(0(x1)) -> 0(s(s(half(p^1_s(p^1_s(x1))))))
0.00/0.18	8: half(s(s(x1))) -> s(half(p(p^1_s(s(x1)))))
0.00/0.18	9: rd(0(x1)) -> 0(s(0(0(0(0(s(0(rd(x1)))))))))
0.00/0.18	10: p(0(_1)) ->= p^1_0(_1)
0.00/0.18	11: p(s(_1)) ->= p^1_s(_1)
0.00/0.18	12: j(s(_1)) ->= j^1_s(_1)
0.00/0.18	Number of strict rules: 9
0.00/0.18	Direct POLO(bPol) ... removes: 12
0.00/0.18	      s 	w: x1
0.00/0.18	      p^1_0	w: x1
0.00/0.18	      rd	w: x1 + 1
0.00/0.18	      p^1_s	w: x1
0.00/0.18	      f 	w: x1 + 15
0.00/0.18	      half	w: x1 + 1
0.00/0.18	      p 	w: x1
0.00/0.18	      0 	w: x1
0.00/0.18	      j^1_s	w: x1 + 15
0.00/0.18	      j 	w: 2 * x1 + 16
0.00/0.18	      g 	w: x1 + 15
0.00/0.18	Number of strict rules: 9
0.00/0.18	Direct POLO(bPol) ... failed.
0.00/0.18	Dependency Pairs:
0.00/0.18	   #1: #j^1_s(x1) -> #p^1_s(s(p^1_s(f(p^1_s(p(p^1_s(x1)))))))
0.00/0.18	   #2: #j^1_s(x1) -> #p^1_s(f(p^1_s(p(p^1_s(x1)))))
0.00/0.18	   #3: #j^1_s(x1) -> #f(p^1_s(p(p^1_s(x1))))
0.00/0.18	   #4: #j^1_s(x1) -> #p^1_s(p(p^1_s(x1)))
0.00/0.18	   #5: #j^1_s(x1) -> #p(p^1_s(x1))
0.00/0.18	   #6: #j^1_s(x1) -> #p^1_s(x1)
0.00/0.18	   #7: #rd(0(x1)) -> #rd(x1)
0.00/0.18	   #8: #p(s(_1)) ->? #p^1_s(_1)
0.00/0.18	   #9: #half(0(x1)) -> #half(p^1_s(p^1_s(x1)))
0.00/0.18	   #10: #half(0(x1)) -> #p^1_s(p^1_s(x1))
0.00/0.18	   #11: #half(0(x1)) -> #p^1_s(x1)
0.00/0.18	   #12: #p(0(_1)) ->? #p^1_0(_1)
0.00/0.18	   #13: #g(s(x1)) -> #p(p^1_s(s(s(j^1_s(p^1_s(p^1_s(x1)))))))
0.00/0.18	   #14: #g(s(x1)) -> #p^1_s(s(s(j^1_s(p^1_s(p^1_s(x1))))))
0.00/0.18	   #15: #g(s(x1)) -> #j^1_s(p^1_s(p^1_s(x1)))
0.00/0.18	   #16: #g(s(x1)) -> #p^1_s(p^1_s(x1))
0.00/0.18	   #17: #g(s(x1)) -> #p^1_s(x1)
0.00/0.18	   #18: #p(p^1_s(x1)) -> #p(x1)
0.00/0.18	   #19: #p^1_0(x1) -> #p(x1)
0.00/0.18	   #20: #half(s(s(x1))) -> #half(p(p^1_s(s(x1))))
0.00/0.18	   #21: #half(s(s(x1))) -> #p(p^1_s(s(x1)))
0.00/0.18	   #22: #half(s(s(x1))) -> #p^1_s(s(x1))
0.00/0.18	   #23: #f(s(x1)) -> #p^1_s(g(p^1_s(s(x1))))
0.00/0.18	   #24: #f(s(x1)) -> #g(p^1_s(s(x1)))
0.00/0.18	   #25: #f(s(x1)) -> #p^1_s(s(x1))
0.00/0.18	Number of SCCs: 4, DPs: 9
0.00/0.18	  SCC { #7 }
0.00/0.18	POLO(Sum)... succeeded.
0.00/0.18	      s 	w: 0
0.00/0.18	      #p^1_0	w: 0
0.00/0.18	      #p^1_s	w: 0
0.00/0.18	      p^1_0	w: 0
0.00/0.18	      rd	w: 0
0.00/0.18	      p^1_s	w: 0
0.00/0.18	      #half	w: 0
0.00/0.18	      #p 	w: 0
0.00/0.18	      #rd	w: x1
0.00/0.18	      f 	w: 0
0.00/0.18	      half	w: 0
0.00/0.18	      p 	w: 0
0.00/0.18	      0 	w: x1 + 1
0.00/0.18	      #f 	w: 0
0.00/0.18	      #g 	w: 0
0.00/0.18	      j^1_s	w: 0
0.00/0.18	      j 	w: 0
0.00/0.18	      #j^1_s	w: 0
0.00/0.18	      g 	w: 0
0.00/0.18	    USABLE RULES: { }
0.00/0.18	    Removed DPs: #7
0.00/0.18	Number of SCCs: 3, DPs: 8
0.00/0.18	  SCC { #12 #18 #19 }
0.00/0.18	POLO(Sum)... succeeded.
0.00/0.18	      s 	w: 0
0.00/0.18	      #p^1_0	w: x1 + 1
0.00/0.18	      #p^1_s	w: 0
0.00/0.18	      p^1_0	w: 0
0.00/0.18	      rd	w: 0
0.00/0.18	      p^1_s	w: x1 + 1
0.00/0.18	      #half	w: 0
0.00/0.18	      #p 	w: x1
0.00/0.18	      #rd	w: 0
0.00/0.18	      f 	w: 0
0.00/0.18	      half	w: 0
0.00/0.18	      p 	w: 0
0.00/0.18	      0 	w: x1 + 2
0.00/0.18	      #f 	w: 0
0.00/0.18	      #g 	w: 0
0.00/0.18	      j^1_s	w: 0
0.00/0.18	      j 	w: 0
0.00/0.18	      #j^1_s	w: 0
0.00/0.18	      g 	w: 0
0.00/0.18	    USABLE RULES: { }
0.00/0.18	    Removed DPs: #12 #18 #19
0.00/0.18	Number of SCCs: 2, DPs: 5
0.00/0.18	  SCC { #9 #20 }
0.00/0.18	POLO(Sum)... succeeded.
0.00/0.18	      s 	w: x1
0.00/0.18	      #p^1_0	w: 1
0.00/0.18	      #p^1_s	w: 0
0.00/0.18	      p^1_0	w: x1 + 2
0.00/0.18	      rd	w: 0
0.00/0.18	      p^1_s	w: x1
0.00/0.18	      #half	w: x1
0.00/0.18	      #p 	w: 0
0.00/0.18	      #rd	w: 0
0.00/0.18	      f 	w: 0
0.00/0.18	      half	w: 0
0.00/0.18	      p 	w: x1
0.00/0.18	      0 	w: x1 + 2
0.00/0.18	      #f 	w: 0
0.00/0.18	      #g 	w: 0
0.00/0.18	      j^1_s	w: 0
0.00/0.18	      j 	w: 0
0.00/0.18	      #j^1_s	w: 0
0.00/0.18	      g 	w: 0
0.00/0.18	    USABLE RULES: { 1..3 10 11 }
0.00/0.18	    Removed DPs: #9
0.00/0.18	Number of SCCs: 2, DPs: 4
0.00/0.18	  SCC { #20 }
0.00/0.18	POLO(Sum)... succeeded.
0.00/0.18	      s 	w: x1 + 2
0.00/0.18	      #p^1_0	w: 1
0.00/0.18	      #p^1_s	w: 0
0.00/0.18	      p^1_0	w: 2
0.00/0.18	      rd	w: 0
0.00/0.18	      p^1_s	w: x1
0.00/0.18	      #half	w: x1
0.00/0.18	      #p 	w: 0
0.00/0.18	      #rd	w: 0
0.00/0.18	      f 	w: 0
0.00/0.18	      half	w: 0
0.00/0.18	      p 	w: x1 + 1
0.00/0.18	      0 	w: 2
0.00/0.18	      #f 	w: 0
0.00/0.18	      #g 	w: 0
0.00/0.18	      j^1_s	w: 0
0.00/0.18	      j 	w: 0
0.00/0.18	      #j^1_s	w: 0
0.00/0.18	      g 	w: 0
0.00/0.18	    USABLE RULES: { 1..3 10 11 }
0.00/0.18	    Removed DPs: #20
0.00/0.18	Number of SCCs: 1, DPs: 3
0.00/0.18	  SCC { #3 #15 #24 }
0.00/0.18	POLO(Sum)... succeeded.
0.00/0.18	      s 	w: x1 + 4
0.00/0.18	      #p^1_0	w: 1
0.00/0.18	      #p^1_s	w: 0
0.00/0.18	      p^1_0	w: 2
0.00/0.18	      rd	w: 0
0.00/0.18	      p^1_s	w: x1
0.00/0.18	      #half	w: x1
0.00/0.18	      #p 	w: 0
0.00/0.18	      #rd	w: 0
0.00/0.18	      f 	w: 0
0.00/0.18	      half	w: 0
0.00/0.18	      p 	w: x1 + 1
0.00/0.18	      0 	w: 2
0.00/0.18	      #f 	w: x1 + 1
0.00/0.18	      #g 	w: x1
0.00/0.18	      j^1_s	w: 0
0.00/0.18	      j 	w: 0
0.00/0.18	      #j^1_s	w: x1 + 3
0.00/0.18	      g 	w: 0
0.00/0.18	    USABLE RULES: { 1..3 10 11 }
0.00/0.18	    Removed DPs: #3 #15 #24
0.00/0.18	Number of SCCs: 0, DPs: 0
0.00/0.19	EOF