Input TRS: 1: lt(0(),s(x)) -> true() 2: lt(x,0()) -> false() 3: lt(s(x),s(y)) -> lt(x,y) 4: minus(x,y) -> help(lt(y,x),x,y) 5: help(true(),x,y) -> s(minus(x,s(y))) 6: help(false(),x,y) -> 0() Number of strict rules: 6 Direct Order(PosReal,>,Poly) ... failed. Freezing ... failed. Dependency Pairs: #1: #help(true(),x,y) -> #minus(x,s(y)) #2: #lt(s(x),s(y)) -> #lt(x,y) #3: #minus(x,y) -> #help(lt(y,x),x,y) #4: #minus(x,y) -> #lt(y,x) Number of SCCs: 2, DPs: 3, edges: 3 SCC { #2 } Removing DPs: Order(PosReal,>,Sum)... succeeded. s(x1) weight: (/ 1 2) + x1 #lt(x1,x2) weight: x2 minus(x1,x2) weight: 0 #help(x1,x2,x3) weight: 0 false() weight: 0 true() weight: 0 0() weight: 0 #minus(x1,x2) weight: 0 help(x1,x2,x3) weight: 0 lt(x1,x2) weight: 0 Usable rules: { } Removed DPs: #2 Number of SCCs: 1, DPs: 2, edges: 2 SCC { #1 #3 } Removing DPs: Order(PosReal,>,Sum)... Order(PosReal,>,Max)... QLPOpS... Order(PosReal,>,MaxSum)... QWPOpS(PosReal,>,MaxSum)... Order(PosReal,>,Sum-Sum; PosReal,≥,Sum-Sum)... Order(PosReal,>,Sum-Sum; NegReal,≥,Sum)... Order(PosReal,>,MaxSum-Sum; NegReal,≥,Sum)... failed. Removing edges: failed. Finding a loop... failed. MAYBE