Input TRS: 1: le(0(),y) -> true() 2: le(s(x),0()) -> false() 3: le(s(x),s(y)) -> le(x,y) 4: quot(x,0()) -> quotZeroErro() 5: quot(x,s(y)) -> quotIter(x,s(y),0(),0(),0()) 6: quotIter(x,s(y),z,u,v) -> if(le(x,z),x,s(y),z,u,v) 7: if(true(),x,y,z,u,v) -> v 8: if(false(),x,y,z,u,v) -> if2(le(y,s(u)),x,y,s(z),s(u),v) 9: if2(false(),x,y,z,u,v) -> quotIter(x,y,z,u,v) 10: if2(true(),x,y,z,u,v) -> quotIter(x,y,z,0(),s(v)) Number of strict rules: 10 Direct Order(PosReal,>,Poly) ... failed. Freezing ... failed. Dependency Pairs: #1: #quotIter(x,s(y),z,u,v) -> #if(le(x,z),x,s(y),z,u,v) #2: #quotIter(x,s(y),z,u,v) -> #le(x,z) #3: #if2(false(),x,y,z,u,v) -> #quotIter(x,y,z,u,v) #4: #if2(true(),x,y,z,u,v) -> #quotIter(x,y,z,0(),s(v)) #5: #quot(x,s(y)) -> #quotIter(x,s(y),0(),0(),0()) #6: #le(s(x),s(y)) -> #le(x,y) #7: #if(false(),x,y,z,u,v) -> #if2(le(y,s(u)),x,y,s(z),s(u),v) #8: #if(false(),x,y,z,u,v) -> #le(y,s(u)) Number of SCCs: 2, DPs: 5, edges: 6 SCC { #6 } Removing DPs: Order(PosReal,>,Sum)... succeeded. le(x1,x2) weight: 0 s(x1) weight: (/ 1 2) + x1 #le(x1,x2) weight: x2 quotIter(x1,x2,x3,x4,x5) weight: 0 quotZeroErro() weight: 0 false() weight: 0 true() weight: 0 if2(x1,x2,x3,x4,x5,x6) weight: 0 0() weight: 0 if(x1,x2,x3,x4,x5,x6) weight: 0 quot(x1,x2) weight: 0 #quotIter(x1,x2,x3,x4,x5) weight: 0 #if(x1,x2,x3,x4,x5,x6) weight: 0 #quot(x1,x2) weight: 0 #if2(x1,x2,x3,x4,x5,x6) weight: 0 Usable rules: { } Removed DPs: #6 Number of SCCs: 1, DPs: 4, edges: 5 SCC { #1 #3 #4 #7 } 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