0.00/0.23 YES 0.00/0.23 Input TRS: 0.00/0.23 1: le(0(),y) -> true() 0.00/0.23 2: le(s(x),0()) -> false() 0.00/0.23 3: le(s(x),s(y)) -> le(x,y) 0.00/0.23 4: minus(0(),y) -> 0() 0.00/0.23 5: minus(s(x),y) -> if_minus(le(s(x),y),s(x),y) 0.00/0.23 6: if_minus(true(),s(x),y) -> 0() 0.00/0.23 7: if_minus(false(),s(x),y) -> s(minus(x,y)) 0.00/0.23 8: quot(0(),s(y)) -> 0() 0.00/0.23 9: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) 0.00/0.23 10: log(s(0())) -> 0() 0.00/0.23 11: log(s(s(x))) -> s(log(s(quot(x,s(s(0())))))) 0.00/0.23 12: rand(x) ->= x 0.00/0.23 13: rand(x) ->= rand(s(x)) 0.00/0.23 Number of strict rules: 11 0.00/0.23 Direct POLO(bPol) ... failed. 0.00/0.23 Uncurrying log le 0.00/0.23 1: le^1_0(y) -> true() 0.00/0.23 2: le^1_s(x,0()) -> false() 0.00/0.23 3: le^1_s(x,s(y)) -> le(x,y) 0.00/0.23 4: minus(0(),y) -> 0() 0.00/0.23 5: minus(s(x),y) -> if_minus(le^1_s(x,y),s(x),y) 0.00/0.23 6: if_minus(true(),s(x),y) -> 0() 0.00/0.23 7: if_minus(false(),s(x),y) -> s(minus(x,y)) 0.00/0.23 8: quot(0(),s(y)) -> 0() 0.00/0.23 9: quot(s(x),s(y)) -> s(quot(minus(x,y),s(y))) 0.00/0.23 10: log^1_s(0()) -> 0() 0.00/0.23 11: log^1_s(s(x)) -> s(log^1_s(quot(x,s(s(0()))))) 0.00/0.23 12: rand(x) ->= x 0.00/0.23 13: rand(x) ->= rand(s(x)) 0.00/0.23 14: le(0(),_1) ->= le^1_0(_1) 0.00/0.23 15: le(s(_1),_2) ->= le^1_s(_1,_2) 0.00/0.23 16: log(s(_1)) ->= log^1_s(_1) 0.00/0.23 Number of strict rules: 11 0.00/0.23 Direct POLO(bPol) ... failed. 0.00/0.23 Dependency Pairs: 0.00/0.23 #1: #quot(s(x),s(y)) -> #quot(minus(x,y),s(y)) 0.00/0.23 #2: #quot(s(x),s(y)) -> #minus(x,y) 0.00/0.23 #3: #log^1_s(s(x)) -> #log^1_s(quot(x,s(s(0())))) 0.00/0.23 #4: #log^1_s(s(x)) -> #quot(x,s(s(0()))) 0.00/0.23 #5: #le(0(),_1) ->? #le^1_0(_1) 0.00/0.23 #6: #if_minus(false(),s(x),y) -> #minus(x,y) 0.00/0.23 #7: #minus(s(x),y) -> #if_minus(le^1_s(x,y),s(x),y) 0.00/0.23 #8: #minus(s(x),y) -> #le^1_s(x,y) 0.00/0.23 #9: #log(s(_1)) ->? #log^1_s(_1) 0.00/0.23 #10: #le^1_s(x,s(y)) -> #le(x,y) 0.00/0.23 #11: #le(s(_1),_2) ->? #le^1_s(_1,_2) 0.00/0.23 Number of SCCs: 4, DPs: 6 0.00/0.23 SCC { #3 } 0.00/0.23 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. 0.00/0.23 #le^1_s s: [1,2] p: 0 w: max(x1 + 1, x2 + 1) 0.00/0.23 le s: [] p: 2 w: max(x2) 0.00/0.23 le^1_s s: [] p: 2 w: max(x2) 0.00/0.23 s s: [1] p: 3 w: x1 0.00/0.23 #le s: [] p: 0 w: max(x2) 0.00/0.23 #le^1_0 s: [] p: 0 w: 0 0.00/0.23 minus s: 1 0.00/0.23 false s: [] p: 1 w: 0 0.00/0.23 #log^1_s s: [1] p: 0 w: x1 0.00/0.23 #log s: [] p: 0 w: 1 0.00/0.23 true s: [] p: 1 w: 0 0.00/0.23 rand s: [] p: 0 w: x1 + 1 0.00/0.23 log s: [1] p: 4 w: x1 + 2 0.00/0.23 0 s: [] p: 1 w: 0 0.00/0.23 quot s: 1 0.00/0.23 #if_minus s: [1,2,3] p: 0 w: max(x1, x2 + 1, x3 + 1) 0.00/0.23 #minus s: [] p: 0 w: max(x2 + 1) 0.00/0.23 le^1_0 s: [] p: 2 w: 0 0.00/0.23 if_minus s: 2 0.00/0.23 #quot s: [] p: 0 w: max(x1) 0.00/0.23 log^1_s s: [1] p: 4 w: x1 + 1 0.00/0.23 Removed DPs: #3 0.00/0.23 Number of SCCs: 3, DPs: 5 0.00/0.23 SCC { #1 } 0.00/0.23 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. 0.00/0.23 #le^1_s s: [1,2] p: 0 w: max(x1 + 1, x2 + 1) 0.00/0.23 le s: [] p: 2 w: max(x2) 0.00/0.23 le^1_s s: [] p: 2 w: max(x2) 0.00/0.23 s s: [1] p: 3 w: x1 0.00/0.23 #le s: [] p: 0 w: max(x2) 0.00/0.23 #le^1_0 s: [] p: 0 w: 0 0.00/0.23 minus s: 1 0.00/0.23 false s: [] p: 1 w: 0 0.00/0.23 #log^1_s s: [1] p: 0 w: x1 0.00/0.23 #log s: [] p: 0 w: 1 0.00/0.23 true s: [] p: 1 w: 0 0.00/0.23 rand s: [] p: 0 w: x1 + 1 0.00/0.23 log s: [1] p: 4 w: x1 + 2 0.00/0.23 0 s: [] p: 1 w: 0 0.00/0.23 quot s: 1 0.00/0.23 #if_minus s: [1,2,3] p: 0 w: max(x1, x2 + 1, x3 + 1) 0.00/0.23 #minus s: [] p: 0 w: max(x2 + 1) 0.00/0.23 le^1_0 s: [] p: 2 w: 0 0.00/0.23 if_minus s: 2 0.00/0.23 #quot s: [2,1] p: 4 w: max(x1 + 2, x2 + 1) 0.00/0.23 log^1_s s: [1] p: 4 w: x1 + 1 0.00/0.23 Removed DPs: #1 0.00/0.23 Number of SCCs: 2, DPs: 4 0.00/0.23 SCC { #10 #11 } 0.00/0.23 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. 0.00/0.23 #le^1_s s: [1] p: 4 w: max(x1 + 1, x2 + 2) 0.00/0.23 le s: [] p: 2 w: max(x2) 0.00/0.23 le^1_s s: [] p: 2 w: max(x2) 0.00/0.23 s s: [1] p: 3 w: x1 0.00/0.23 #le s: [1] p: 4 w: max(x1 + 1, x2 + 2) 0.00/0.23 #le^1_0 s: [] p: 0 w: 0 0.00/0.23 minus s: 1 0.00/0.23 false s: [] p: 1 w: 0 0.00/0.23 #log^1_s s: [1] p: 0 w: x1 0.00/0.23 #log s: [] p: 0 w: 1 0.00/0.23 true s: [] p: 1 w: 0 0.00/0.23 rand s: [] p: 0 w: x1 + 1 0.00/0.23 log s: [1] p: 4 w: x1 + 2 0.00/0.23 0 s: [] p: 1 w: 0 0.00/0.23 quot s: 1 0.00/0.23 #if_minus s: [1,2,3] p: 0 w: max(x1, x2 + 1, x3 + 1) 0.00/0.23 #minus s: [] p: 0 w: max(x2 + 1) 0.00/0.23 le^1_0 s: [] p: 2 w: 0 0.00/0.23 if_minus s: 2 0.00/0.23 #quot s: [2,1] p: 4 w: max(x1 + 2, x2 + 1) 0.00/0.23 log^1_s s: [1] p: 4 w: x1 + 1 0.00/0.23 Removed DPs: #11 0.00/0.23 Number of SCCs: 1, DPs: 2 0.00/0.23 SCC { #6 #7 } 0.00/0.23 POLO(Sum)... POLO(max)... QLPOS... POLO(mSum)... QWPOpS(mSum)... succeeded. 0.00/0.23 #le^1_s s: [1] p: 4 w: max(x1 + 1, x2 + 2) 0.00/0.23 le s: [] p: 3 w: max(x2) 0.00/0.23 le^1_s s: [] p: 3 w: max(x2) 0.00/0.23 s s: [1] p: 4 w: x1 0.00/0.23 #le s: [1] p: 4 w: max(x1 + 1, x2 + 2) 0.00/0.23 #le^1_0 s: [] p: 0 w: 0 0.00/0.23 minus s: 1 0.00/0.23 false s: [] p: 3 w: 0 0.00/0.23 #log^1_s s: [1] p: 0 w: x1 0.00/0.23 #log s: [] p: 0 w: 1 0.00/0.23 true s: [] p: 1 w: 0 0.00/0.23 rand s: [] p: 0 w: x1 + 1 0.00/0.23 log s: [1] p: 5 w: x1 + 2 0.00/0.23 0 s: [] p: 1 w: 0 0.00/0.23 quot s: 1 0.00/0.23 #if_minus s: [3,2] p: 1 w: max(x1, x2 + 2, x3 + 1) 0.00/0.23 #minus s: [2,1] p: 1 w: max(x1 + 2, x2 + 1) 0.00/0.23 le^1_0 s: [] p: 2 w: 0 0.00/0.23 if_minus s: 2 0.00/0.23 #quot s: [2,1] p: 4 w: max(x1 + 2, x2 + 1) 0.00/0.23 log^1_s s: [1] p: 5 w: x1 + 1 0.00/0.23 Removed DPs: #6 0.00/0.23 Number of SCCs: 0, DPs: 0 0.00/0.23 EOF