0.00/0.38	MAYBE
0.00/0.38	Input TRS:
0.00/0.38	    AC symbols: plus union mult
0.00/0.38	    1: union(X,empty()) -> X
0.00/0.38	    2: union(empty(),X) -> X
0.00/0.38	    3: 0(z()) -> z()
0.00/0.38	    4: U101(tt(),X) -> X
0.00/0.38	    5: U11(tt()) -> z()
0.00/0.38	    6: U111(tt(),A,B) -> plus(sum(A),sum(B))
0.00/0.38	    7: U21(tt(),X,Y) -> 0(mult(X,Y))
0.00/0.38	    8: U31(tt(),X,Y) -> plus(0(mult(X,Y)),Y)
0.00/0.38	    9: U41(tt(),X) -> X
0.00/0.38	    10: U51(tt(),X,Y) -> 0(plus(X,Y))
0.00/0.38	    11: U61(tt(),X,Y) -> 1(plus(X,Y))
0.00/0.38	    12: U71(tt(),X,Y) -> 0(plus(plus(X,Y),1(z())))
0.00/0.38	    13: U81(tt(),X) -> X
0.00/0.38	    14: U91(tt(),A,B) -> mult(prod(A),prod(B))
0.00/0.38	    15: and(tt(),X) -> X
0.00/0.38	    16: isBag(empty()) -> tt()
0.00/0.38	    17: isBag(singl(V1)) -> isBin(V1)
0.00/0.38	    18: isBag(union(V1,V2)) -> and(isBag(V1),isBag(V2))
0.00/0.38	    19: isBin(z()) -> tt()
0.00/0.38	    20: isBin(0(V1)) -> isBin(V1)
0.00/0.38	    21: isBin(1(V1)) -> isBin(V1)
0.00/0.38	    22: isBin(mult(V1,V2)) -> and(isBin(V1),isBin(V2))
0.00/0.38	    23: isBin(plus(V1,V2)) -> and(isBin(V1),isBin(V2))
0.00/0.38	    24: isBin(prod(V1)) -> isBag(V1)
0.00/0.38	    25: isBin(sum(V1)) -> isBag(V1)
0.00/0.38	    26: mult(z(),X) -> U11(isBin(X))
0.00/0.38	    27: mult(0(X),Y) -> U21(and(isBin(X),isBin(Y)),X,Y)
0.00/0.38	    28: mult(1(X),Y) -> U31(and(isBin(X),isBin(Y)),X,Y)
0.00/0.38	    29: plus(z(),X) -> U41(isBin(X),X)
0.00/0.38	    30: plus(0(X),0(Y)) -> U51(and(isBin(X),isBin(Y)),X,Y)
0.00/0.38	    31: plus(0(X),1(Y)) -> U61(and(isBin(X),isBin(Y)),X,Y)
0.00/0.38	    32: plus(1(X),1(Y)) -> U71(and(isBin(X),isBin(Y)),X,Y)
0.00/0.38	    33: prod(empty()) -> 1(z())
0.00/0.38	    34: prod(singl(X)) -> U81(isBin(X),X)
0.00/0.38	    35: prod(union(A,B)) -> U91(and(isBag(A),isBag(B)),A,B)
0.00/0.38	    36: sum(empty()) -> 0(z())
0.00/0.38	    37: sum(singl(X)) -> U101(isBin(X),X)
0.00/0.38	    38: sum(union(A,B)) -> U111(and(isBag(A),isBag(B)),A,B)
0.00/0.38	Number of strict rules: 38
0.00/0.38	Direct POLO(bPol) ... failed.
0.00/0.38	Uncurrying ... failed.
0.00/0.38	Dependency Pairs:
0.00/0.38	   #1: #plus(z(),X) -> #U41(isBin(X),X)
0.00/0.38	   #2: #plus(z(),X) -> #isBin(X)
0.00/0.38	   #3: #prod(union(A,B)) -> #U91(and(isBag(A),isBag(B)),A,B)
0.00/0.38	   #4: #prod(union(A,B)) -> #and(isBag(A),isBag(B))
0.00/0.38	   #5: #prod(union(A,B)) -> #isBag(A)
0.00/0.38	   #6: #prod(union(A,B)) -> #isBag(B)
0.00/0.38	   #7: #mult(x,mult(y,z)) ->= #mult(mult(x,y),z)
0.00/0.38	   #8: #mult(x,mult(y,z)) ->= #mult(x,y)
0.00/0.38	   #9: #sum(singl(X)) -> #U101(isBin(X),X)
0.00/0.38	   #10: #sum(singl(X)) -> #isBin(X)
0.00/0.38	   #11: #sum(union(A,B)) -> #U111(and(isBag(A),isBag(B)),A,B)
0.00/0.38	   #12: #sum(union(A,B)) -> #and(isBag(A),isBag(B))
0.00/0.38	   #13: #sum(union(A,B)) -> #isBag(A)
0.00/0.38	   #14: #sum(union(A,B)) -> #isBag(B)
0.00/0.38	   #15: #U111(tt(),A,B) -> #plus(sum(A),sum(B))
0.00/0.38	   #16: #U111(tt(),A,B) -> #sum(A)
0.00/0.38	   #17: #U111(tt(),A,B) -> #sum(B)
0.00/0.38	   #18: #union(x,union(y,z)) ->= #union(union(x,y),z)
0.00/0.38	   #19: #union(x,union(y,z)) ->= #union(x,y)
0.00/0.38	   #20: #U61(tt(),X,Y) -> #plus(X,Y)
0.00/0.38	   #21: #isBin(prod(V1)) -> #isBag(V1)
0.00/0.38	   #22: #isBin(plus(V1,V2)) -> #and(isBin(V1),isBin(V2))
0.00/0.38	   #23: #isBin(plus(V1,V2)) -> #isBin(V1)
0.00/0.38	   #24: #isBin(plus(V1,V2)) -> #isBin(V2)
0.00/0.38	   #25: #U71(tt(),X,Y) -> #0(plus(plus(X,Y),1(z())))
0.00/0.38	   #26: #U71(tt(),X,Y) -> #plus(plus(X,Y),1(z()))
0.00/0.38	   #27: #U71(tt(),X,Y) -> #plus(X,Y)
0.00/0.38	   #28: #plus(0(X),1(Y)) -> #U61(and(isBin(X),isBin(Y)),X,Y)
0.00/0.38	   #29: #plus(0(X),1(Y)) -> #and(isBin(X),isBin(Y))
0.00/0.38	   #30: #plus(0(X),1(Y)) -> #isBin(X)
0.00/0.38	   #31: #plus(0(X),1(Y)) -> #isBin(Y)
0.00/0.38	   #32: #U91(tt(),A,B) -> #mult(prod(A),prod(B))
0.00/0.38	   #33: #U91(tt(),A,B) -> #prod(A)
0.00/0.38	   #34: #U91(tt(),A,B) -> #prod(B)
0.00/0.38	   #35: #plus(0(X),0(Y)) -> #U51(and(isBin(X),isBin(Y)),X,Y)
0.00/0.38	   #36: #plus(0(X),0(Y)) -> #and(isBin(X),isBin(Y))
0.00/0.38	   #37: #plus(0(X),0(Y)) -> #isBin(X)
0.00/0.38	   #38: #plus(0(X),0(Y)) -> #isBin(Y)
0.00/0.38	   #39: #isBin(sum(V1)) -> #isBag(V1)
0.00/0.38	   #40: #isBin(0(V1)) -> #isBin(V1)
0.00/0.38	   #41: #U21(tt(),X,Y) -> #0(mult(X,Y))
0.00/0.38	   #42: #U21(tt(),X,Y) -> #mult(X,Y)
0.00/0.38	   #43: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z)
0.00/0.38	   #44: #plus(x,plus(y,z)) ->= #plus(x,y)
0.00/0.38	   #45: #U51(tt(),X,Y) -> #0(plus(X,Y))
0.00/0.38	   #46: #U51(tt(),X,Y) -> #plus(X,Y)
0.00/0.38	   #47: #mult(1(X),Y) -> #U31(and(isBin(X),isBin(Y)),X,Y)
0.00/0.38	   #48: #mult(1(X),Y) -> #and(isBin(X),isBin(Y))
0.00/0.38	   #49: #mult(1(X),Y) -> #isBin(X)
0.00/0.38	   #50: #mult(1(X),Y) -> #isBin(Y)
0.00/0.38	   #51: #isBin(mult(V1,V2)) -> #and(isBin(V1),isBin(V2))
0.00/0.38	   #52: #isBin(mult(V1,V2)) -> #isBin(V1)
0.00/0.38	   #53: #isBin(mult(V1,V2)) -> #isBin(V2)
0.00/0.38	   #54: #prod(singl(X)) -> #U81(isBin(X),X)
0.00/0.38	   #55: #prod(singl(X)) -> #isBin(X)
0.00/0.38	   #56: #mult(0(X),Y) -> #U21(and(isBin(X),isBin(Y)),X,Y)
0.00/0.38	   #57: #mult(0(X),Y) -> #and(isBin(X),isBin(Y))
0.00/0.38	   #58: #mult(0(X),Y) -> #isBin(X)
0.00/0.38	   #59: #mult(0(X),Y) -> #isBin(Y)
0.00/0.38	   #60: #isBag(singl(V1)) -> #isBin(V1)
0.00/0.38	   #61: #plus(1(X),1(Y)) -> #U71(and(isBin(X),isBin(Y)),X,Y)
0.00/0.38	   #62: #plus(1(X),1(Y)) -> #and(isBin(X),isBin(Y))
0.00/0.38	   #63: #plus(1(X),1(Y)) -> #isBin(X)
0.00/0.38	   #64: #plus(1(X),1(Y)) -> #isBin(Y)
0.00/0.38	   #65: #mult(z(),X) -> #U11(isBin(X))
0.00/0.38	   #66: #mult(z(),X) -> #isBin(X)
0.00/0.38	   #67: #sum(empty()) -> #0(z())
0.00/0.38	   #68: #isBin(1(V1)) -> #isBin(V1)
0.00/0.38	   #69: #U31(tt(),X,Y) -> #plus(0(mult(X,Y)),Y)
0.00/0.38	   #70: #U31(tt(),X,Y) -> #0(mult(X,Y))
0.00/0.38	   #71: #U31(tt(),X,Y) -> #mult(X,Y)
0.00/0.38	   #72: #isBag(union(V1,V2)) -> #and(isBag(V1),isBag(V2))
0.00/0.38	   #73: #isBag(union(V1,V2)) -> #isBag(V1)
0.00/0.38	   #74: #isBag(union(V1,V2)) -> #isBag(V2)
0.00/0.38	Number of SCCs: 6, DPs: 34
0.00/0.38	  SCC { #18 #19 }
0.00/0.38	only weak rules.
0.00/0.38	Number of SCCs: 5, DPs: 32
0.00/0.38	  SCC { #11 #16 #17 }
0.00/0.38	POLO(Sum)... succeeded.
0.00/0.38	      #0 	w: 0
0.00/0.38	      #isBag	w: 0
0.00/0.38	      U21	w: 0
0.00/0.38	      1 	w: 1
0.00/0.38	      prod	w: 1
0.00/0.38	      U11	w: 0
0.00/0.38	      z 	w: 1
0.00/0.38	      #prod	w: 0
0.00/0.38	      U91	w: 0
0.00/0.38	      #U101	w: 0
0.00/0.38	      U71	w: 0
0.00/0.38	      #U81	w: 0
0.00/0.38	      and	w: x2
0.00/0.38	      #plus	w: 0
0.00/0.38	      U101	w: 0
0.00/0.38	      U111	w: 0
0.00/0.38	      sum	w: 1
0.00/0.38	      mult	w: 1
0.00/0.38	      isBin	w: 1
0.00/0.38	      0 	w: 1
0.00/0.38	      #isBin	w: 0
0.00/0.38	      union	w: x1 + x2 + 2
0.00/0.38	      #U111	w: x1 + x2 + x3
0.00/0.38	      singl	w: 1
0.00/0.38	      plus	w: 1
0.00/0.38	      U61	w: 0
0.00/0.38	      #U51	w: 0
0.00/0.38	      #U11	w: 0
0.00/0.38	      U31	w: 0
0.00/0.38	      #U41	w: 0
0.00/0.38	      empty	w: 1
0.00/0.38	      #U21	w: 0
0.00/0.38	      U81	w: 0
0.00/0.38	      tt	w: 1
0.00/0.38	      #U71	w: 0
0.00/0.38	      isBag	w: 1
0.00/0.38	      U51	w: 0
0.00/0.38	      #sum	w: x1
0.00/0.38	      U41	w: 0
0.00/0.38	      #U31	w: 0
0.00/0.38	      #and	w: 0
0.00/0.38	      #union	w: 0
0.00/0.38	      #U91	w: 0
0.00/0.38	      #mult	w: 0
0.00/0.38	      #U61	w: 0
0.00/0.38	    USABLE RULES: { 15..25 }
0.00/0.38	    Removed DPs: #11 #16 #17
0.00/0.38	Number of SCCs: 4, DPs: 29
0.00/0.38	  SCC { #3 #33 #34 }
0.00/0.38	POLO(Sum)... succeeded.
0.00/0.38	      #0 	w: 0
0.00/0.38	      #isBag	w: 0
0.00/0.38	      U21	w: 0
0.00/0.38	      1 	w: x1 + 1
0.00/0.38	      prod	w: x1 + 1
0.00/0.38	      U11	w: 0
0.00/0.38	      z 	w: 1
0.00/0.38	      #prod	w: x1
0.00/0.38	      U91	w: 0
0.00/0.38	      #U101	w: 0
0.00/0.38	      U71	w: 0
0.00/0.38	      #U81	w: 0
0.00/0.38	      and	w: x1 + 2
0.00/0.38	      #plus	w: 0
0.00/0.38	      U101	w: 0
0.00/0.38	      U111	w: 0
0.00/0.38	      sum	w: x1 + 1
0.00/0.38	      mult	w: 1
0.00/0.38	      isBin	w: x1 + 2
0.00/0.38	      0 	w: x1 + 1
0.00/0.38	      #isBin	w: 0
0.00/0.38	      union	w: x1 + x2 + 2
0.00/0.38	      #U111	w: 0
0.00/0.38	      singl	w: x1 + 1
0.00/0.38	      plus	w: x1 + x2 + 2
0.00/0.38	      U61	w: 0
0.00/0.38	      #U51	w: 0
0.00/0.38	      #U11	w: 0
0.00/0.38	      U31	w: 0
0.00/0.38	      #U41	w: 0
0.00/0.38	      empty	w: 2
0.00/0.38	      #U21	w: 0
0.00/0.38	      U81	w: 0
0.00/0.38	      tt	w: 4
0.00/0.38	      #U71	w: 0
0.00/0.38	      isBag	w: 1
0.00/0.38	      U51	w: 0
0.00/0.38	      #sum	w: 0
0.00/0.38	      U41	w: 0
0.00/0.38	      #U31	w: 0
0.00/0.38	      #and	w: 0
0.00/0.38	      #union	w: 0
0.00/0.38	      #U91	w: x2 + x3 + 1
0.00/0.38	      #mult	w: 0
0.00/0.38	      #U61	w: 0
0.00/0.38	    USABLE RULES: { }
0.00/0.38	    Removed DPs: #3 #33 #34
0.00/0.38	Number of SCCs: 3, DPs: 26
0.00/0.38	  SCC { #7 #8 #42 #47 #56 #71 }
0.00/0.38	POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed.
0.00/0.38	Finding a loop...  failed.
0.00/0.38	EOF