0.00/0.46	YES
0.00/0.46	Input TRS:
0.00/0.46	    AC symbols: plus times
0.00/0.46	    1: s(p(x)) -> x
0.00/0.46	    2: p(s(x)) -> x
0.00/0.46	    3: plus(0(),y) -> y
0.00/0.46	    4: plus(s(x),y) -> s(plus(x,y))
0.00/0.46	    5: plus(p(x),y) -> p(plus(x,y))
0.00/0.46	    6: plus(i(x),x) -> 0()
0.00/0.46	    7: plus(x,plus(i(x),y)) -> y
0.00/0.46	    8: i(0()) -> 0()
0.00/0.46	    9: i(s(x)) -> p(i(x))
0.00/0.46	    10: i(p(x)) -> s(i(x))
0.00/0.46	    11: i(i(x)) -> x
0.00/0.46	    12: i(plus(x,y)) -> plus(i(y),i(x))
0.00/0.46	    13: times(0(),y) -> 0()
0.00/0.46	    14: times(s(x),y) -> plus(times(x,y),y)
0.00/0.46	    15: times(p(x),y) -> plus(times(x,y),i(y))
0.00/0.46	Number of strict rules: 15
0.00/0.46	Direct POLO(bPol) ... failed.
0.00/0.46	Uncurrying ... failed.
0.00/0.46	Dependency Pairs:
0.00/0.46	   #1: #i(s(x)) -> #p(i(x))
0.00/0.46	   #2: #i(s(x)) -> #i(x)
0.00/0.46	   #3: #i(plus(x,y)) -> #plus(i(y),i(x))
0.00/0.46	   #4: #i(plus(x,y)) -> #i(y)
0.00/0.46	   #5: #i(plus(x,y)) -> #i(x)
0.00/0.46	   #6: #times(s(x),y) -> #plus(times(x,y),y)
0.00/0.46	   #7: #times(s(x),y) -> #times(x,y)
0.00/0.46	   #8: #i(p(x)) -> #s(i(x))
0.00/0.46	   #9: #i(p(x)) -> #i(x)
0.00/0.46	   #10: #plus(p(x),y) -> #p(plus(x,y))
0.00/0.46	   #11: #plus(p(x),y) -> #plus(x,y)
0.00/0.46	   #12: #times(x,times(y,z)) ->= #times(times(x,y),z)
0.00/0.46	   #13: #times(x,times(y,z)) ->= #times(x,y)
0.00/0.46	   #14: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
0.00/0.46	   #15: #plus(x,plus(y,z)) ->= #plus(x,y)
0.00/0.46	   #16: #times(p(x),y) -> #plus(times(x,y),i(y))
0.00/0.46	   #17: #times(p(x),y) -> #times(x,y)
0.00/0.46	   #18: #times(p(x),y) -> #i(y)
0.00/0.46	   #19: #plus(s(x),y) -> #s(plus(x,y))
0.00/0.46	   #20: #plus(s(x),y) -> #plus(x,y)
0.00/0.46	Number of SCCs: 3, DPs: 12
0.00/0.46	  SCC { #2 #4 #5 #9 }
0.00/0.46	POLO(Sum)... succeeded.
0.00/0.46	      s 	w: x1 + 1
0.00/0.46	      #plus	w: 0
0.00/0.46	      #p 	w: 0
0.00/0.46	      p 	w: x1 + 1
0.00/0.46	      #times	w: 0
0.00/0.46	      0 	w: 0
0.00/0.46	      times	w: 0
0.00/0.46	      #s 	w: 0
0.00/0.46	      i 	w: 0
0.00/0.46	      plus	w: x1 + x2 + 1
0.00/0.46	      #i 	w: x1
0.00/0.46	    USABLE RULES: { }
0.00/0.46	    Removed DPs: #2 #4 #5 #9
0.00/0.46	Number of SCCs: 2, DPs: 8
0.00/0.46	  SCC { #7 #12 #13 #17 }
0.00/0.46	POLO(Sum)... POLO(max)... QLPOS... succeeded.
0.00/0.46	      s 	s: [1]	p: 0
0.00/0.46	      #plus	s: {}	p: 1
0.00/0.46	      #p 	s: []	p: 0
0.00/0.46	      p 	s: [1]	p: 0
0.00/0.46	      #times	s: {1,2}	p: 3
0.00/0.46	      0 	s: []	p: 0
0.00/0.46	      times	s: {1,2}	p: 3
0.00/0.46	      #s 	s: []	p: 0
0.00/0.46	      i 	s: [1]	p: 2
0.00/0.46	      plus	s: {1,2}	p: 1
0.00/0.46	      #i 	s: []	p: 0
0.00/0.46	    USABLE RULES: { 1..17 }
0.00/0.46	    Removed DPs: #7 #13 #17
0.00/0.46	Number of SCCs: 2, DPs: 5
0.00/0.46	  SCC { #12 }
0.00/0.46	only weak rules.
0.00/0.46	Number of SCCs: 1, DPs: 4
0.00/0.46	  SCC { #11 #14 #15 #20 }
0.00/0.46	POLO(Sum)... succeeded.
0.00/0.46	      s 	w: x1 + 1
0.00/0.46	      #plus	w: x1 + x2
0.00/0.46	      #p 	w: 0
0.00/0.46	      p 	w: x1 + 2
0.00/0.46	      #times	w: 0
0.00/0.46	      0 	w: 1
0.00/0.46	      times	w: x1 + x2 + 1
0.00/0.46	      #s 	w: 0
0.00/0.46	      i 	w: x1 + 1
0.00/0.46	      plus	w: x1 + x2 + 2
0.00/0.46	      #i 	w: 0
0.00/0.46	    USABLE RULES: { 1..7 16 }
0.00/0.46	    Removed DPs: #11 #15 #20
0.00/0.46	Number of SCCs: 1, DPs: 1
0.00/0.46	  SCC { #14 }
0.00/0.46	only weak rules.
0.00/0.46	Number of SCCs: 0, DPs: 0
0.00/0.46	Next Dependency Pairs:
0.00/0.46	   #21: #plus(plus(i(x),x),_1) -> #plus(0(),_1)
0.00/0.46	   #22: #times(times(0(),y),_1) -> #times(0(),_1)
0.00/0.46	   #23: #times(times(s(x),y),_1) -> #times(plus(times(x,y),y),_1)
0.00/0.46	   #24: #plus(plus(x,plus(i(x),y)),_1) -> #plus(y,_1)
0.00/0.46	   #25: #plus(plus(p(x),y),_1) -> #plus(p(plus(x,y)),_1)
0.00/0.46	   #26: #times(x,times(y,z)) ->= #times(times(x,y),z)
0.00/0.46	   #27: #times(x,times(y,z)) ->= #times(x,y)
0.00/0.46	   #28: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
0.00/0.46	   #29: #plus(x,plus(y,z)) ->= #plus(x,y)
0.00/0.46	   #30: #plus(plus(0(),y),_1) -> #plus(y,_1)
0.00/0.46	   #31: #times(times(p(x),y),_1) -> #times(plus(times(x,y),i(y)),_1)
0.00/0.46	   #32: #plus(plus(s(x),y),_1) -> #plus(s(plus(x,y)),_1)
0.00/0.46	Number of SCCs: 2, DPs: 12
0.00/0.46	  SCC { #22 #23 #26 #27 #31 }
0.00/0.46	POLO(Sum)... POLO(max)... QLPOS... succeeded.
0.00/0.46	      s 	s: [1]	p: 0
0.00/0.46	      #plus	s: {}	p: 1
0.00/0.46	      #p 	s: []	p: 0
0.00/0.46	      p 	s: [1]	p: 0
0.00/0.46	      #times	s: {1,2}	p: 3
0.00/0.46	      0 	s: []	p: 0
0.00/0.46	      times	s: {1,2}	p: 3
0.00/0.46	      #s 	s: []	p: 0
0.00/0.46	      i 	s: [1]	p: 2
0.00/0.46	      plus	s: {1,2}	p: 1
0.00/0.46	      #i 	s: []	p: 0
0.00/0.46	    USABLE RULES: { 1..17 }
0.00/0.46	    Removed DPs: #22 #23 #27 #31
0.00/0.46	Number of SCCs: 2, DPs: 8
0.00/0.46	  SCC { #26 }
0.00/0.46	only weak rules.
0.00/0.46	Number of SCCs: 1, DPs: 7
0.00/0.46	  SCC { #21 #24 #25 #28..30 #32 }
0.00/0.46	POLO(Sum)... succeeded.
0.00/0.46	      s 	w: x1 + 2
0.00/0.46	      #plus	w: x1 + x2
0.00/0.46	      #p 	w: 0
0.00/0.46	      p 	w: x1 + 1
0.00/0.46	      #times	w: 0
0.00/0.46	      0 	w: 2
0.00/0.46	      times	w: 1
0.00/0.46	      #s 	w: 0
0.00/0.46	      i 	w: x1 + 1
0.00/0.46	      plus	w: x1 + x2 + 2
0.00/0.46	      #i 	w: 0
0.00/0.46	    USABLE RULES: { 1..7 16 }
0.00/0.46	    Removed DPs: #21 #24 #29 #30
0.00/0.46	Number of SCCs: 1, DPs: 3
0.00/0.46	  SCC { #25 #28 #32 }
0.00/0.46	POLO(Sum)... POLO(max)... QLPOS... succeeded.
0.00/0.46	      s 	s: [1]	p: 0
0.00/0.46	      #plus	s: {1,2}	p: 1
0.00/0.46	      #p 	s: []	p: 0
0.00/0.46	      p 	s: [1]	p: 0
0.00/0.46	      #times	s: {1,2}	p: 3
0.00/0.46	      0 	s: []	p: 0
0.00/0.46	      times	s: {1,2}	p: 3
0.00/0.46	      #s 	s: []	p: 0
0.00/0.46	      i 	s: [1]	p: 2
0.00/0.46	      plus	s: {1,2}	p: 1
0.00/0.46	      #i 	s: []	p: 0
0.00/0.46	    USABLE RULES: { 1..17 }
0.00/0.46	    Removed DPs: #25 #32
0.00/0.46	Number of SCCs: 1, DPs: 1
0.00/0.46	  SCC { #28 }
0.00/0.46	only weak rules.
0.00/0.46	Number of SCCs: 0, DPs: 0
0.00/0.46	EOF