0.00/0.10 MAYBE 0.00/0.10 Input TRS: 0.00/0.10 AC symbols: plus union mult 0.00/0.10 1: union(X,empty()) -> X 0.00/0.10 2: union(empty(),X) -> X 0.00/0.10 3: 0(z()) -> z() 0.00/0.10 4: and(tt(),X) -> X 0.00/0.10 5: mult(z(),X) -> z() 0.00/0.10 6: mult(0(X),Y) -> 0(mult(X,Y)) 0.00/0.10 7: mult(1(X),Y) -> plus(0(mult(X,Y)),Y) 0.00/0.10 8: plus(z(),X) -> X 0.00/0.10 9: plus(0(X),0(Y)) -> 0(plus(X,Y)) 0.00/0.10 10: plus(0(X),1(Y)) -> 1(plus(X,Y)) 0.00/0.10 11: plus(1(X),1(Y)) -> 0(plus(plus(X,Y),1(z()))) 0.00/0.10 12: prod(empty()) -> 1(z()) 0.00/0.10 13: prod(singl(X)) -> X 0.00/0.10 14: prod(union(A,B)) -> mult(prod(A),prod(B)) 0.00/0.10 15: sum(empty()) -> 0(z()) 0.00/0.10 16: sum(singl(X)) -> X 0.00/0.10 17: sum(union(A,B)) -> plus(sum(A),sum(B)) 0.00/0.10 Number of strict rules: 17 0.00/0.10 Direct POLO(bPol) ... failed. 0.00/0.10 Uncurrying ... failed. 0.00/0.10 Dependency Pairs: 0.00/0.10 #1: #mult(0(X),Y) -> #0(mult(X,Y)) 0.00/0.10 #2: #mult(0(X),Y) -> #mult(X,Y) 0.00/0.10 #3: #plus(0(X),0(Y)) -> #0(plus(X,Y)) 0.00/0.10 #4: #plus(0(X),0(Y)) -> #plus(X,Y) 0.00/0.10 #5: #plus(1(X),1(Y)) -> #0(plus(plus(X,Y),1(z()))) 0.00/0.10 #6: #plus(1(X),1(Y)) -> #plus(plus(X,Y),1(z())) 0.00/0.10 #7: #plus(1(X),1(Y)) -> #plus(X,Y) 0.00/0.10 #8: #prod(union(A,B)) -> #mult(prod(A),prod(B)) 0.00/0.10 #9: #prod(union(A,B)) -> #prod(A) 0.00/0.10 #10: #prod(union(A,B)) -> #prod(B) 0.00/0.10 #11: #mult(x,mult(y,z)) ->= #mult(mult(x,y),z) 0.00/0.10 #12: #mult(x,mult(y,z)) ->= #mult(x,y) 0.00/0.10 #13: #mult(1(X),Y) -> #plus(0(mult(X,Y)),Y) 0.00/0.10 #14: #mult(1(X),Y) -> #0(mult(X,Y)) 0.00/0.10 #15: #mult(1(X),Y) -> #mult(X,Y) 0.00/0.10 #16: #plus(0(X),1(Y)) -> #plus(X,Y) 0.00/0.10 #17: #sum(union(A,B)) -> #plus(sum(A),sum(B)) 0.00/0.10 #18: #sum(union(A,B)) -> #sum(A) 0.00/0.10 #19: #sum(union(A,B)) -> #sum(B) 0.00/0.10 #20: #union(x,union(y,z)) ->= #union(union(x,y),z) 0.00/0.10 #21: #union(x,union(y,z)) ->= #union(x,y) 0.00/0.10 #22: #sum(empty()) -> #0(z()) 0.00/0.10 #23: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) 0.00/0.10 #24: #plus(x,plus(y,z)) ->= #plus(x,y) 0.00/0.10 Number of SCCs: 5, DPs: 16 0.00/0.10 SCC { #18 #19 } 0.00/0.10 POLO(Sum)... succeeded. 0.00/0.10 #0 w: 0 0.00/0.10 1 w: 0 0.00/0.10 prod w: 0 0.00/0.10 z w: 0 0.00/0.10 #prod w: 0 0.00/0.10 and w: 0 0.00/0.10 #plus w: 0 0.00/0.10 sum w: 0 0.00/0.10 mult w: 0 0.00/0.10 0 w: 0 0.00/0.10 union w: x1 + x2 + 1 0.00/0.10 singl w: 0 0.00/0.10 plus w: 0 0.00/0.10 empty w: 0 0.00/0.10 tt w: 0 0.00/0.10 #sum w: x1 0.00/0.10 #and w: 0 0.00/0.10 #union w: 0 0.00/0.10 #mult w: 0 0.00/0.10 USABLE RULES: { } 0.00/0.10 Removed DPs: #18 #19 0.00/0.10 Number of SCCs: 4, DPs: 14 0.00/0.10 SCC { #9 #10 } 0.00/0.10 POLO(Sum)... succeeded. 0.00/0.10 #0 w: 0 0.00/0.10 1 w: 0 0.00/0.10 prod w: 0 0.00/0.10 z w: 0 0.00/0.10 #prod w: x1 0.00/0.10 and w: 0 0.00/0.10 #plus w: 0 0.00/0.10 sum w: 0 0.00/0.10 mult w: 0 0.00/0.10 0 w: 0 0.00/0.10 union w: x1 + x2 + 1 0.00/0.10 singl w: 0 0.00/0.10 plus w: 0 0.00/0.10 empty w: 0 0.00/0.10 tt w: 0 0.00/0.10 #sum w: 0 0.00/0.10 #and w: 0 0.00/0.10 #union w: 0 0.00/0.10 #mult w: 0 0.00/0.10 USABLE RULES: { } 0.00/0.10 Removed DPs: #9 #10 0.00/0.10 Number of SCCs: 3, DPs: 12 0.00/0.10 SCC { #20 #21 } 0.00/0.10 only weak rules. 0.00/0.10 Number of SCCs: 2, DPs: 10 0.00/0.10 SCC { #2 #11 #12 #15 } 0.00/0.10 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. 0.00/0.10 #0 w: 0 0.00/0.10 1 w: max(x1, 0) 0.00/0.10 prod w: 0 0.00/0.10 z w: 0 0.00/0.10 #prod w: 0 0.00/0.10 and w: 0 0.00/0.10 #plus w: 0 0.00/0.10 sum w: max(x1 - 1, 0) 0.00/0.10 mult w: max(x1 + x2 + 2, 0) 0.00/0.10 0 w: max(x1, 0) 0.00/0.10 union w: 0 0.00/0.10 singl w: max(x1 - 1, 0) 0.00/0.10 plus w: max(x1, x2, 0) 0.00/0.10 empty w: 0 0.00/0.10 tt w: 0 0.00/0.10 #sum w: max(x1 - 1, 0) 0.00/0.10 #and w: max(x1 - 1, 0) 0.00/0.10 #union w: max(x1 + x2 - 1, 0) 0.00/0.10 #mult w: max(x1 + x2 - 1, 0) 0.00/0.10 USABLE RULES: { 3 5..11 18 20 } 0.00/0.10 Removed DPs: #12 0.00/0.10 Number of SCCs: 2, DPs: 9 0.00/0.10 SCC { #2 #11 #15 } 0.00/0.10 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. 0.00/0.10 Finding a loop... failed. 0.00/0.10 EOF