0.61/0.57	MAYBE
0.61/0.58	Input TRS:
0.61/0.58	    AC symbols: plus union mult
0.61/0.58	    1: union(X,empty()) -> X
0.61/0.58	    2: union(empty(),X) -> X
0.61/0.58	    3: 0(z()) -> z()
0.61/0.58	    4: U101(tt(),X,Y) -> U102(isBin(Y),X,Y)
0.61/0.58	    5: U102(tt(),X,Y) -> 0(mult(X,Y))
0.61/0.58	    6: U11(tt()) -> tt()
0.61/0.58	    7: U111(tt(),X,Y) -> U112(isBin(Y),X,Y)
0.61/0.58	    8: U112(tt(),X,Y) -> plus(0(mult(X,Y)),Y)
0.61/0.58	    9: U121(tt(),X) -> X
0.61/0.58	    10: U131(tt(),X,Y) -> U132(isBin(Y),X,Y)
0.61/0.58	    11: U132(tt(),X,Y) -> 0(plus(X,Y))
0.61/0.58	    12: U141(tt(),X,Y) -> U142(isBin(Y),X,Y)
0.61/0.58	    13: U142(tt(),X,Y) -> 1(plus(X,Y))
0.61/0.58	    14: U151(tt(),X,Y) -> U152(isBin(Y),X,Y)
0.61/0.58	    15: U152(tt(),X,Y) -> 0(plus(plus(X,Y),1(z())))
0.61/0.58	    16: U161(tt(),X) -> X
0.61/0.58	    17: U171(tt(),A,B) -> U172(isBag(B),A,B)
0.61/0.58	    18: U172(tt(),A,B) -> mult(prod(A),prod(B))
0.61/0.58	    19: U181(tt(),X) -> X
0.61/0.58	    20: U191(tt(),A,B) -> U192(isBag(B),A,B)
0.61/0.58	    21: U192(tt(),A,B) -> plus(sum(A),sum(B))
0.61/0.58	    22: U21(tt(),V2) -> U22(isBag(V2))
0.61/0.58	    23: U22(tt()) -> tt()
0.61/0.58	    24: U31(tt()) -> tt()
0.61/0.58	    25: U41(tt()) -> tt()
0.61/0.58	    26: U51(tt(),V2) -> U52(isBin(V2))
0.61/0.58	    27: U52(tt()) -> tt()
0.61/0.58	    28: U61(tt(),V2) -> U62(isBin(V2))
0.61/0.58	    29: U62(tt()) -> tt()
0.61/0.58	    30: U71(tt()) -> tt()
0.61/0.58	    31: U81(tt()) -> tt()
0.61/0.58	    32: U91(tt()) -> z()
0.61/0.58	    33: isBag(empty()) -> tt()
0.61/0.58	    34: isBag(singl(V1)) -> U11(isBin(V1))
0.61/0.58	    35: isBag(union(V1,V2)) -> U21(isBag(V1),V2)
0.61/0.58	    36: isBin(z()) -> tt()
0.61/0.58	    37: isBin(0(V1)) -> U31(isBin(V1))
0.61/0.58	    38: isBin(1(V1)) -> U41(isBin(V1))
0.61/0.58	    39: isBin(mult(V1,V2)) -> U51(isBin(V1),V2)
0.61/0.58	    40: isBin(plus(V1,V2)) -> U61(isBin(V1),V2)
0.61/0.58	    41: isBin(prod(V1)) -> U71(isBag(V1))
0.61/0.58	    42: isBin(sum(V1)) -> U81(isBag(V1))
0.61/0.58	    43: mult(z(),X) -> U91(isBin(X))
0.61/0.58	    44: mult(0(X),Y) -> U101(isBin(X),X,Y)
0.61/0.58	    45: mult(1(X),Y) -> U111(isBin(X),X,Y)
0.61/0.58	    46: plus(z(),X) -> U121(isBin(X),X)
0.61/0.58	    47: plus(0(X),0(Y)) -> U131(isBin(X),X,Y)
0.61/0.58	    48: plus(0(X),1(Y)) -> U141(isBin(X),X,Y)
0.61/0.58	    49: plus(1(X),1(Y)) -> U151(isBin(X),X,Y)
0.61/0.58	    50: prod(empty()) -> 1(z())
0.61/0.58	    51: prod(singl(X)) -> U161(isBin(X),X)
0.61/0.58	    52: prod(union(A,B)) -> U171(isBag(A),A,B)
0.61/0.58	    53: sum(empty()) -> 0(z())
0.61/0.58	    54: sum(singl(X)) -> U181(isBin(X),X)
0.61/0.58	    55: sum(union(A,B)) -> U191(isBag(A),A,B)
0.61/0.58	Number of strict rules: 55
0.61/0.58	Direct POLO(bPol) ... failed.
0.61/0.58	Uncurrying ... failed.
0.61/0.58	Dependency Pairs:
0.61/0.58	   #1: #mult(z(),X) -> #U91(isBin(X))
0.61/0.58	   #2: #mult(z(),X) -> #isBin(X)
0.61/0.58	   #3: #isBag(union(V1,V2)) -> #U21(isBag(V1),V2)
0.61/0.58	   #4: #isBag(union(V1,V2)) -> #isBag(V1)
0.61/0.58	   #5: #plus(z(),X) -> #U121(isBin(X),X)
0.61/0.58	   #6: #plus(z(),X) -> #isBin(X)
0.61/0.58	   #7: #isBin(sum(V1)) -> #U81(isBag(V1))
0.61/0.58	   #8: #isBin(sum(V1)) -> #isBag(V1)
0.61/0.58	   #9: #isBin(prod(V1)) -> #U71(isBag(V1))
0.61/0.58	   #10: #isBin(prod(V1)) -> #isBag(V1)
0.61/0.58	   #11: #isBin(0(V1)) -> #U31(isBin(V1))
0.61/0.58	   #12: #isBin(0(V1)) -> #isBin(V1)
0.61/0.58	   #13: #plus(0(X),0(Y)) -> #U131(isBin(X),X,Y)
0.61/0.58	   #14: #plus(0(X),0(Y)) -> #isBin(X)
0.61/0.58	   #15: #sum(empty()) -> #0(z())
0.61/0.58	   #16: #plus(0(X),1(Y)) -> #U141(isBin(X),X,Y)
0.61/0.58	   #17: #plus(0(X),1(Y)) -> #isBin(X)
0.61/0.58	   #18: #mult(x,mult(y,z)) ->= #mult(mult(x,y),z)
0.61/0.58	   #19: #mult(x,mult(y,z)) ->= #mult(x,y)
0.61/0.58	   #20: #isBin(1(V1)) -> #U41(isBin(V1))
0.61/0.58	   #21: #isBin(1(V1)) -> #isBin(V1)
0.61/0.58	   #22: #sum(union(A,B)) -> #U191(isBag(A),A,B)
0.61/0.58	   #23: #sum(union(A,B)) -> #isBag(A)
0.61/0.58	   #24: #isBin(plus(V1,V2)) -> #U61(isBin(V1),V2)
0.61/0.58	   #25: #isBin(plus(V1,V2)) -> #isBin(V1)
0.61/0.58	   #26: #prod(singl(X)) -> #U161(isBin(X),X)
0.61/0.58	   #27: #prod(singl(X)) -> #isBin(X)
0.61/0.58	   #28: #U142(tt(),X,Y) -> #plus(X,Y)
0.61/0.58	   #29: #U132(tt(),X,Y) -> #0(plus(X,Y))
0.61/0.58	   #30: #U132(tt(),X,Y) -> #plus(X,Y)
0.61/0.58	   #31: #union(x,union(y,z)) ->= #union(union(x,y),z)
0.61/0.58	   #32: #union(x,union(y,z)) ->= #union(x,y)
0.61/0.58	   #33: #mult(1(X),Y) -> #U111(isBin(X),X,Y)
0.61/0.58	   #34: #mult(1(X),Y) -> #isBin(X)
0.61/0.58	   #35: #U141(tt(),X,Y) -> #U142(isBin(Y),X,Y)
0.61/0.58	   #36: #U141(tt(),X,Y) -> #isBin(Y)
0.61/0.58	   #37: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
0.61/0.58	   #38: #plus(x,plus(y,z)) ->= #plus(x,y)
0.61/0.58	   #39: #U151(tt(),X,Y) -> #U152(isBin(Y),X,Y)
0.61/0.58	   #40: #U151(tt(),X,Y) -> #isBin(Y)
0.61/0.58	   #41: #prod(union(A,B)) -> #U171(isBag(A),A,B)
0.61/0.58	   #42: #prod(union(A,B)) -> #isBag(A)
0.61/0.58	   #43: #plus(1(X),1(Y)) -> #U151(isBin(X),X,Y)
0.61/0.58	   #44: #plus(1(X),1(Y)) -> #isBin(X)
0.61/0.58	   #45: #U191(tt(),A,B) -> #U192(isBag(B),A,B)
0.61/0.58	   #46: #U191(tt(),A,B) -> #isBag(B)
0.61/0.58	   #47: #U111(tt(),X,Y) -> #U112(isBin(Y),X,Y)
0.61/0.58	   #48: #U111(tt(),X,Y) -> #isBin(Y)
0.61/0.58	   #49: #isBin(mult(V1,V2)) -> #U51(isBin(V1),V2)
0.61/0.58	   #50: #isBin(mult(V1,V2)) -> #isBin(V1)
0.61/0.58	   #51: #U131(tt(),X,Y) -> #U132(isBin(Y),X,Y)
0.61/0.58	   #52: #U131(tt(),X,Y) -> #isBin(Y)
0.61/0.58	   #53: #U102(tt(),X,Y) -> #0(mult(X,Y))
0.61/0.58	   #54: #U102(tt(),X,Y) -> #mult(X,Y)
0.61/0.58	   #55: #mult(0(X),Y) -> #U101(isBin(X),X,Y)
0.61/0.58	   #56: #mult(0(X),Y) -> #isBin(X)
0.61/0.58	   #57: #U61(tt(),V2) -> #U62(isBin(V2))
0.61/0.58	   #58: #U61(tt(),V2) -> #isBin(V2)
0.61/0.58	   #59: #U21(tt(),V2) -> #U22(isBag(V2))
0.61/0.58	   #60: #U21(tt(),V2) -> #isBag(V2)
0.61/0.58	   #61: #isBag(singl(V1)) -> #U11(isBin(V1))
0.61/0.58	   #62: #isBag(singl(V1)) -> #isBin(V1)
0.61/0.58	   #63: #U171(tt(),A,B) -> #U172(isBag(B),A,B)
0.61/0.58	   #64: #U171(tt(),A,B) -> #isBag(B)
0.61/0.58	   #65: #U51(tt(),V2) -> #U52(isBin(V2))
0.61/0.58	   #66: #U51(tt(),V2) -> #isBin(V2)
0.61/0.58	   #67: #U192(tt(),A,B) -> #plus(sum(A),sum(B))
0.61/0.58	   #68: #U192(tt(),A,B) -> #sum(A)
0.61/0.58	   #69: #U192(tt(),A,B) -> #sum(B)
0.61/0.58	   #70: #sum(singl(X)) -> #U181(isBin(X),X)
0.61/0.58	   #71: #sum(singl(X)) -> #isBin(X)
0.61/0.58	   #72: #U112(tt(),X,Y) -> #plus(0(mult(X,Y)),Y)
0.61/0.58	   #73: #U112(tt(),X,Y) -> #0(mult(X,Y))
0.61/0.58	   #74: #U112(tt(),X,Y) -> #mult(X,Y)
0.61/0.58	   #75: #U152(tt(),X,Y) -> #0(plus(plus(X,Y),1(z())))
0.61/0.58	   #76: #U152(tt(),X,Y) -> #plus(plus(X,Y),1(z()))
0.61/0.58	   #77: #U152(tt(),X,Y) -> #plus(X,Y)
0.61/0.58	   #78: #U101(tt(),X,Y) -> #U102(isBin(Y),X,Y)
0.61/0.58	   #79: #U101(tt(),X,Y) -> #isBin(Y)
0.61/0.58	   #80: #U172(tt(),A,B) -> #mult(prod(A),prod(B))
0.61/0.58	   #81: #U172(tt(),A,B) -> #prod(A)
0.61/0.58	   #82: #U172(tt(),A,B) -> #prod(B)
0.61/0.58	Number of SCCs: 6, DPs: 44
0.61/0.58	  SCC { #31 #32 }
0.61/0.58	only weak rules.
0.61/0.58	Number of SCCs: 5, DPs: 42
0.61/0.58	  SCC { #22 #45 #68 #69 }
0.61/0.58	POLO(Sum)... succeeded.
0.61/0.58	      #0 	w: 0
0.61/0.58	      #isBag	w: 0
0.61/0.58	      U21	w: 3
0.61/0.58	      1 	w: x1 + 1
0.61/0.58	      prod	w: x1 + 2
0.61/0.58	      U161	w: 0
0.61/0.58	      U11	w: 3
0.61/0.58	      #U142	w: 0
0.61/0.58	      U192	w: 0
0.61/0.58	      z 	w: 1
0.61/0.58	      U142	w: 0
0.61/0.58	      #U152	w: 0
0.61/0.58	      #U181	w: 0
0.61/0.58	      #prod	w: 0
0.61/0.58	      U91	w: 0
0.61/0.58	      #U101	w: 0
0.61/0.58	      U71	w: x1
0.61/0.58	      #U81	w: 0
0.61/0.58	      U131	w: 0
0.61/0.58	      #plus	w: 0
0.61/0.58	      U101	w: 0
0.61/0.58	      U111	w: 0
0.61/0.58	      U132	w: 0
0.61/0.58	      U152	w: 0
0.61/0.58	      #U121	w: 0
0.61/0.58	      U172	w: 0
0.61/0.58	      #U131	w: 0
0.61/0.58	      #U52	w: 0
0.61/0.58	      sum	w: x1 + 2
0.61/0.58	      mult	w: x1 + x2 + 1
0.61/0.58	      isBin	w: x1 + 1
0.61/0.58	      #U141	w: 0
0.61/0.58	      U141	w: 0
0.61/0.58	      #U171	w: 0
0.61/0.58	      #U62	w: 0
0.61/0.58	      0 	w: x1 + 1
0.61/0.58	      U191	w: 0
0.61/0.58	      #isBin	w: 0
0.61/0.58	      #U102	w: 0
0.61/0.58	      U171	w: 0
0.61/0.58	      union	w: x1 + x2 + 3
0.61/0.58	      U62	w: 0
0.61/0.58	      U151	w: 0
0.61/0.58	      #U111	w: 0
0.61/0.58	      #U192	w: x1 + x2 + x3
0.61/0.58	      singl	w: 1
0.61/0.58	      U52	w: 2
0.61/0.58	      plus	w: x1 + x2 + 1
0.61/0.58	      U61	w: x1
0.61/0.58	      #U51	w: 0
0.61/0.58	      #U11	w: 0
0.61/0.58	      U31	w: x1
0.61/0.58	      U112	w: 0
0.61/0.58	      #U41	w: 0
0.61/0.58	      U102	w: 0
0.61/0.58	      #U191	w: x1 + x2 + x3 + 1
0.61/0.58	      empty	w: 1
0.61/0.58	      #U21	w: 0
0.61/0.58	      U81	w: x1
0.61/0.58	      #U22	w: 0
0.61/0.58	      #U112	w: 0
0.61/0.58	      tt	w: 3
0.61/0.58	      #U71	w: 0
0.61/0.58	      #U151	w: 0
0.61/0.58	      isBag	w: 3
0.61/0.58	      U22	w: x1
0.61/0.58	      U51	w: x1
0.61/0.58	      #U161	w: 0
0.61/0.58	      #U172	w: 0
0.61/0.58	      #sum	w: x1 + 2
0.61/0.58	      U41	w: x1
0.61/0.58	      #U31	w: 0
0.61/0.58	      #union	w: 0
0.61/0.58	      #U91	w: 0
0.61/0.58	      #mult	w: 0
0.61/0.58	      #U132	w: 0
0.61/0.58	      U121	w: 0
0.61/0.58	      #U61	w: 0
0.61/0.58	      U181	w: 0
0.61/0.58	    USABLE RULES: { 6 22 23 30 31 33..35 }
0.61/0.58	    Removed DPs: #22 #45 #68 #69
0.61/0.58	Number of SCCs: 4, DPs: 38
0.61/0.58	  SCC { #41 #63 #81 #82 }
0.61/0.58	POLO(Sum)... succeeded.
0.61/0.58	      #0 	w: 0
0.61/0.58	      #isBag	w: 0
0.61/0.58	      U21	w: 5
0.61/0.58	      1 	w: x1 + 1
0.61/0.58	      prod	w: 1
0.61/0.58	      U161	w: 0
0.61/0.58	      U11	w: x1
0.61/0.58	      #U142	w: 0
0.61/0.58	      U192	w: 0
0.61/0.58	      z 	w: 1
0.61/0.58	      U142	w: 0
0.61/0.58	      #U152	w: 0
0.61/0.58	      #U181	w: 0
0.61/0.58	      #prod	w: x1
0.61/0.58	      U91	w: 0
0.61/0.58	      #U101	w: 0
0.61/0.58	      U71	w: x1
0.61/0.58	      #U81	w: 0
0.61/0.58	      U131	w: 0
0.61/0.58	      #plus	w: 0
0.61/0.58	      U101	w: 0
0.61/0.58	      U111	w: 0
0.61/0.58	      U132	w: 0
0.61/0.58	      U152	w: 0
0.61/0.58	      #U121	w: 0
0.61/0.58	      U172	w: 0
0.61/0.58	      #U131	w: 0
0.61/0.58	      #U52	w: 0
0.61/0.58	      sum	w: x1 + 1
0.61/0.58	      mult	w: x1 + x2 + 1
0.61/0.58	      isBin	w: x1 + 1
0.61/0.58	      #U141	w: 0
0.61/0.58	      U141	w: 0
0.61/0.58	      #U171	w: x2 + x3 + 2
0.61/0.58	      #U62	w: 0
0.61/0.58	      0 	w: x1 + 1
0.61/0.58	      U191	w: 0
0.61/0.58	      #isBin	w: 0
0.61/0.58	      #U102	w: 0
0.61/0.58	      U171	w: 0
0.61/0.58	      union	w: x1 + x2 + 3
0.61/0.58	      U62	w: 0
0.61/0.58	      U151	w: 0
0.61/0.58	      #U111	w: 0
0.61/0.58	      #U192	w: 0
0.61/0.58	      singl	w: x1 + 1
0.61/0.58	      U52	w: 2
0.61/0.58	      plus	w: x1 + x2 + 1
0.61/0.58	      U61	w: x1
0.61/0.58	      #U51	w: 0
0.61/0.58	      #U11	w: 0
0.61/0.58	      U31	w: x1
0.61/0.58	      U112	w: 0
0.61/0.58	      #U41	w: 0
0.61/0.58	      U102	w: 0
0.61/0.58	      #U191	w: 1
0.61/0.58	      empty	w: 1
0.61/0.58	      #U21	w: 0
0.61/0.58	      U81	w: x1
0.61/0.58	      #U22	w: 0
0.61/0.58	      #U112	w: 0
0.61/0.58	      tt	w: 3
0.61/0.58	      #U71	w: 0
0.61/0.58	      #U151	w: 0
0.61/0.58	      isBag	w: x1 + 1
0.61/0.58	      U22	w: 6
0.61/0.58	      U51	w: x1
0.61/0.58	      #U161	w: 0
0.61/0.58	      #U172	w: x2 + x3 + 1
0.61/0.58	      #sum	w: 2
0.61/0.58	      U41	w: x1
0.61/0.58	      #U31	w: 0
0.61/0.58	      #union	w: 0
0.61/0.58	      #U91	w: 0
0.61/0.58	      #mult	w: 0
0.61/0.58	      #U132	w: 0
0.61/0.58	      U121	w: 0
0.61/0.58	      #U61	w: 0
0.61/0.58	      U181	w: 0
0.61/0.58	    USABLE RULES: { 23 30 31 }
0.61/0.58	    Removed DPs: #41 #63 #81 #82
0.61/0.58	Number of SCCs: 3, DPs: 34
0.61/0.58	  SCC { #18 #19 #33 #47 #54 #55 #74 #78 }
0.61/0.58	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
0.61/0.58	Finding a loop...  failed.
0.61/0.58	EOF