0.00/0.16 MAYBE 0.00/0.16 Input TRS: 0.00/0.16 AC symbols: plus times 0.00/0.16 1: zero(S()) -> S() 0.00/0.16 2: plus(x,S()) -> x 0.00/0.16 3: plus(zero(x),zero(y)) -> zero(plus(x,y)) 0.00/0.16 4: plus(zero(x),un(y)) -> un(plus(x,y)) 0.00/0.16 5: plus(un(x),un(y)) -> zero(plus(x,plus(y,un(S())))) 0.00/0.16 6: times(x,S()) -> S() 0.00/0.16 7: times(x,times(S(),z)) -> times(S(),z) 0.00/0.16 8: times(x,zero(y)) -> zero(times(x,y)) 0.00/0.16 9: times(x,times(zero(y),z)) -> times(zero(times(x,y)),z) 0.00/0.16 10: times(x,un(y)) -> plus(x,zero(times(x,y))) 0.00/0.16 11: times(x,times(un(y),z)) -> times(plus(x,zero(times(x,y))),z) 0.00/0.16 Number of strict rules: 11 0.00/0.16 Direct POLO(bPol) ... failed. 0.00/0.16 Uncurrying ... failed. 0.00/0.16 Dependency Pairs: 0.00/0.16 #1: #times(x,times(y,z)) ->= #times(times(x,y),z) 0.00/0.16 #2: #times(x,times(y,z)) ->= #times(x,y) 0.00/0.16 #3: #times(x,times(zero(y),z)) -> #times(zero(times(x,y)),z) 0.00/0.16 #4: #times(x,times(zero(y),z)) -> #zero(times(x,y)) 0.00/0.16 #5: #times(x,times(zero(y),z)) -> #times(x,y) 0.00/0.16 #6: #times(x,times(un(y),z)) -> #times(plus(x,zero(times(x,y))),z) 0.00/0.16 #7: #times(x,times(un(y),z)) -> #plus(x,zero(times(x,y))) 0.00/0.16 #8: #times(x,times(un(y),z)) -> #zero(times(x,y)) 0.00/0.16 #9: #times(x,times(un(y),z)) -> #times(x,y) 0.00/0.16 #10: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) 0.00/0.16 #11: #plus(x,plus(y,z)) ->= #plus(x,y) 0.00/0.16 #12: #times(x,un(y)) -> #plus(x,zero(times(x,y))) 0.00/0.16 #13: #times(x,un(y)) -> #zero(times(x,y)) 0.00/0.16 #14: #times(x,un(y)) -> #times(x,y) 0.00/0.16 #15: #plus(un(x),un(y)) -> #zero(plus(x,plus(y,un(S())))) 0.00/0.16 #16: #plus(un(x),un(y)) -> #plus(x,plus(y,un(S()))) 0.00/0.16 #17: #plus(un(x),un(y)) -> #plus(y,un(S())) 0.00/0.16 #18: #plus(zero(x),zero(y)) -> #zero(plus(x,y)) 0.00/0.16 #19: #plus(zero(x),zero(y)) -> #plus(x,y) 0.00/0.16 #20: #times(x,zero(y)) -> #zero(times(x,y)) 0.00/0.16 #21: #times(x,zero(y)) -> #times(x,y) 0.00/0.16 #22: #plus(zero(x),un(y)) -> #plus(x,y) 0.00/0.16 Number of SCCs: 2, DPs: 14 0.00/0.16 SCC { #10 #11 #16 #17 #19 #22 } 0.00/0.16 POLO(Sum)... succeeded. 0.00/0.16 zero w: x1 + 1 0.00/0.16 S w: 1 0.00/0.16 #plus w: x1 + x2 0.00/0.16 #times w: 0 0.00/0.16 times w: 0 0.00/0.16 plus w: x1 + x2 + 1 0.00/0.16 #zero w: 0 0.00/0.16 un w: x1 + 3 0.00/0.16 USABLE RULES: { 1..5 12 } 0.00/0.16 Removed DPs: #11 #16 #17 #19 #22 0.00/0.16 Number of SCCs: 2, DPs: 9 0.00/0.16 SCC { #10 } 0.00/0.16 only weak rules. 0.00/0.16 Number of SCCs: 1, DPs: 8 0.00/0.16 SCC { #1..3 #5 #6 #9 #14 #21 } 0.00/0.16 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. 0.00/0.16 zero w: max(x1, 0) 0.00/0.16 S w: 0 0.00/0.16 #plus w: 0 0.00/0.16 #times w: max(x1 + x2 - 1, 0) 0.00/0.16 times w: max(x1 + x2 + 5, 0) 0.00/0.16 plus w: max(x1, x2, 0) 0.00/0.16 #zero w: 0 0.00/0.16 un w: max(x1, 0) 0.00/0.16 USABLE RULES: { 1..13 } 0.00/0.16 Removed DPs: #2 #5 #9 0.00/0.16 Number of SCCs: 1, DPs: 5 0.00/0.16 SCC { #1 #3 #6 #14 #21 } 0.00/0.16 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. 0.00/0.16 Finding a loop... failed. 0.00/0.16 EOF