Input TRS: 1: f(x,y,f(z,u,v)) -> f(f(x,y,z),u,f(x,y,v)) Number of strict rules: 1 Direct Order(PosReal,>,Poly) ... failed. Freezing ... failed. Dependency Pairs: #1: #f(x,y,f(z,u,v)) -> #f(f(x,y,z),u,f(x,y,v)) #2: #f(x,y,f(z,u,v)) -> #f(x,y,z) #3: #f(x,y,f(z,u,v)) -> #f(x,y,v) Number of SCCs: 1, DPs: 3, edges: 9 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... found. #f(z_{i1},y_{i4},f(z,y_{1},f(z_{i0},u_{1},v_{i4}))) -#1-> #f(f(z_{i1},y_{i4},z),y_{1},f(z_{i1},y_{i4},f(z_{i0},u_{1},v_{i4}))) --->* #f(f(z_{i1},y_{i4},z),y_{1},f(f(f(f(f(f(z_{i1},y_{i4},z_{i0}),u_{1},z_{i1}),y_{i4},f(z_{i1},y_{i4},z_{i0})),u_{1},f(f(z_{i1},y_{i4},z_{i0}),u_{1},z_{i1})),y_{i4},f(f(f(z_{i1},y_{i4},z_{i0}),u_{1},z_{i1}),y_{i4},f(z_{i1},y_{i4},z_{i0}))),u_{1},f(f(f(f(f(z_{i1},y_{i4},z_{i0}),u_{1},z_{i1}),y_{i4},f(z_{i1},y_{i4},z_{i0})),u_{1},f(f(z_{i1},y_{i4},z_{i0}),u_{1},z_{i1})),y_{i4},v_{i4}))) Looping with: [ v_{i4} := v_{i4}; z := f(f(f(f(f(z_{i1},y_{i4},z_{i0}),u_{1},z_{i1}),y_{i4},f(z_{i1},y_{i4},z_{i0})),u_{1},f(f(z_{i1},y_{i4},z_{i0}),u_{1},z_{i1})),y_{i4},f(f(f(z_{i1},y_{i4},z_{i0}),u_{1},z_{i1}),y_{i4},f(z_{i1},y_{i4},z_{i0}))); z_{i1} := f(z_{i1},y_{i4},z); z_{i0} := f(f(f(f(z_{i1},y_{i4},z_{i0}),u_{1},z_{i1}),y_{i4},f(z_{i1},y_{i4},z_{i0})),u_{1},f(f(z_{i1},y_{i4},z_{i0}),u_{1},z_{i1})); u_{1} := y_{i4}; y_{i4} := y_{1}; y_{1} := u_{1}; ] NO