Input TRS: 1: msort(nil()) -> nil() 2: msort(.(x,y)) -> .(min(x,y),msort(del(min(x,y),.(x,y)))) 3: min(x,nil()) -> x 4: min(x,.(y,z)) -> if(<=(x,y),min(x,z),min(y,z)) 5: del(x,nil()) -> nil() 6: del(x,.(y,z)) -> if(=(x,y),z,.(y,del(x,z))) Number of strict rules: 6 Direct Order(PosReal,>,Poly) ... failed. Freezing ... failed. Dependency Pairs: #1: #msort(.(x,y)) -> #min(x,y) #2: #msort(.(x,y)) -> #msort(del(min(x,y),.(x,y))) #3: #msort(.(x,y)) -> #del(min(x,y),.(x,y)) #4: #msort(.(x,y)) -> #min(x,y) #5: #del(x,.(y,z)) -> #del(x,z) #6: #min(x,.(y,z)) -> #min(x,z) #7: #min(x,.(y,z)) -> #min(y,z) Number of SCCs: 2, DPs: 3, edges: 5 SCC { #5 } Removing DPs: Order(PosReal,>,Sum)... succeeded. #del(x1,x2) weight: x2 #msort(x1) weight: 0 <=(x1,x2) weight: 0 #min(x1,x2) weight: 0 msort(x1) weight: 0 if(x1,x2,x3) weight: 0 del(x1,x2) weight: 0 =(x1,x2) weight: 0 nil() weight: 0 .(x1,x2) weight: (/ 1 2) + x2 min(x1,x2) weight: 0 Usable rules: { } Removed DPs: #5 Number of SCCs: 1, DPs: 2, edges: 4 SCC { #6 #7 } Removing DPs: Order(PosReal,>,Sum)... succeeded. #del(x1,x2) weight: 0 #msort(x1) weight: 0 <=(x1,x2) weight: 0 #min(x1,x2) weight: x2 msort(x1) weight: 0 if(x1,x2,x3) weight: 0 del(x1,x2) weight: 0 =(x1,x2) weight: 0 nil() weight: 0 .(x1,x2) weight: (/ 1 2) + x2 min(x1,x2) weight: 0 Usable rules: { } Removed DPs: #6 #7 Number of SCCs: 0, DPs: 0, edges: 0 YES