0.00/0.14 MAYBE 0.00/0.14 Input TRS: 0.00/0.14 AC symbols: plus times 0.00/0.14 1: 0(S()) -> S() 0.00/0.14 2: plus(S(),x) -> x 0.00/0.14 3: plus(0(x),0(y)) -> 0(plus(x,y)) 0.00/0.14 4: plus(0(x),1(y)) -> 1(plus(x,y)) 0.00/0.14 5: plus(0(x),j(y)) -> j(plus(x,y)) 0.00/0.14 6: plus(1(x),1(y)) -> j(plus(1(S()),plus(x,y))) 0.00/0.14 7: plus(j(x),j(y)) -> 1(plus(j(S()),plus(x,y))) 0.00/0.14 8: plus(1(x),j(y)) -> 0(plus(x,y)) 0.00/0.14 9: opp(S()) -> S() 0.00/0.14 10: opp(0(x)) -> 0(opp(x)) 0.00/0.14 11: opp(1(x)) -> j(opp(x)) 0.00/0.14 12: opp(j(x)) -> 1(opp(x)) 0.00/0.14 13: minus(x,y) -> plus(opp(y),x) 0.00/0.14 14: times(S(),x) -> S() 0.00/0.14 15: times(0(x),y) -> 0(times(x,y)) 0.00/0.14 16: times(1(x),y) -> plus(0(times(x,y)),y) 0.00/0.14 17: times(j(x),y) -> minus(0(times(x,y)),y) 0.00/0.14 Number of strict rules: 17 0.00/0.14 Direct POLO(bPol) ... failed. 0.00/0.14 Uncurrying ... failed. 0.00/0.14 Dependency Pairs: 0.00/0.14 #1: #plus(1(x),1(y)) -> #plus(1(S()),plus(x,y)) 0.00/0.14 #2: #plus(1(x),1(y)) -> #plus(x,y) 0.00/0.14 #3: #minus(x,y) -> #plus(opp(y),x) 0.00/0.14 #4: #minus(x,y) -> #opp(y) 0.00/0.14 #5: #opp(1(x)) -> #opp(x) 0.00/0.14 #6: #opp(j(x)) -> #opp(x) 0.00/0.14 #7: #plus(j(x),j(y)) -> #plus(j(S()),plus(x,y)) 0.00/0.14 #8: #plus(j(x),j(y)) -> #plus(x,y) 0.00/0.14 #9: #opp(0(x)) -> #0(opp(x)) 0.00/0.14 #10: #opp(0(x)) -> #opp(x) 0.00/0.14 #11: #plus(0(x),j(y)) -> #plus(x,y) 0.00/0.14 #12: #times(j(x),y) -> #minus(0(times(x,y)),y) 0.00/0.14 #13: #times(j(x),y) -> #0(times(x,y)) 0.00/0.14 #14: #times(j(x),y) -> #times(x,y) 0.00/0.14 #15: #times(x,times(y,z)) ->= #times(times(x,y),z) 0.00/0.14 #16: #times(x,times(y,z)) ->= #times(x,y) 0.00/0.14 #17: #times(1(x),y) -> #plus(0(times(x,y)),y) 0.00/0.14 #18: #times(1(x),y) -> #0(times(x,y)) 0.00/0.14 #19: #times(1(x),y) -> #times(x,y) 0.00/0.14 #20: #plus(0(x),0(y)) -> #0(plus(x,y)) 0.00/0.14 #21: #plus(0(x),0(y)) -> #plus(x,y) 0.00/0.14 #22: #plus(1(x),j(y)) -> #0(plus(x,y)) 0.00/0.14 #23: #plus(1(x),j(y)) -> #plus(x,y) 0.00/0.14 #24: #times(0(x),y) -> #0(times(x,y)) 0.00/0.14 #25: #times(0(x),y) -> #times(x,y) 0.00/0.14 #26: #plus(0(x),1(y)) -> #plus(x,y) 0.00/0.14 #27: #plus(x,plus(y,z)) ->= #plus(plus(x,y),z) 0.00/0.14 #28: #plus(x,plus(y,z)) ->= #plus(x,y) 0.00/0.14 Number of SCCs: 3, DPs: 18 0.00/0.14 SCC { #5 #6 #10 } 0.00/0.14 POLO(Sum)... succeeded. 0.00/0.14 #0 w: 0 0.00/0.14 1 w: x1 + 1 0.00/0.14 S w: 0 0.00/0.14 minus w: 0 0.00/0.14 #plus w: 0 0.00/0.14 #opp w: x1 0.00/0.14 #times w: 0 0.00/0.14 0 w: x1 + 1 0.00/0.14 times w: 0 0.00/0.14 j w: x1 + 1 0.00/0.14 #minus w: 0 0.00/0.14 opp w: 0 0.00/0.14 plus w: 0 0.00/0.14 USABLE RULES: { } 0.00/0.14 Removed DPs: #5 #6 #10 0.00/0.14 Number of SCCs: 2, DPs: 15 0.00/0.14 SCC { #14..16 #19 #25 } 0.00/0.14 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... succeeded. 0.00/0.14 #0 w: 0 0.00/0.14 1 w: max(x1, 0) 0.00/0.14 S w: 0 0.00/0.14 minus w: max(x1, x2 + 1, 0) 0.00/0.14 #plus w: 0 0.00/0.14 #opp w: max(x1 - 1, 0) 0.00/0.14 #times w: max(x1 + x2 + 1, 0) 0.00/0.14 0 w: max(x1, 0) 0.00/0.14 times w: max(x1 + x2 + 1, 0) 0.00/0.14 j w: max(x1, 0) 0.00/0.14 #minus w: 0 0.00/0.14 opp w: 0 0.00/0.14 plus w: max(x1, x2, 0) 0.00/0.14 USABLE RULES: { 1..19 } 0.00/0.14 Removed DPs: #16 0.00/0.14 Number of SCCs: 2, DPs: 14 0.00/0.14 SCC { #14 #15 #19 #25 } 0.00/0.14 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... Mat2b... failed. 0.00/0.14 Finding a loop... failed. 0.00/0.14 EOF