YES TPA v.1.0 Result: TRS is terminating Default interpretations for symbols are not printed. For polynomial interpretations and semantic labelling over N\{0,1} defaults are 2 for constants, identity for unary symbols and x+y-2 for binary symbols. For semantic labelling over {0,1} (booleans) defaults are 0 for constants, identity for unary symbols and disjunction for binary symbols. [1] TRS loaded from input file: (1) div(X,e) -> i(X) (2) i(div(X,Y)) -> div(Y,X) (3) div(div(X,Y),Z) -> div(Y,div(i(X),Z)) [2] Use following polynomial interpretation: [div(x,y)] = x + y + 1 rest default Remove rules with left hand side strictly bigger than right hand side: (1) [3] Label this TRS using following interpretation over N\{0,1}: [div(x,y)] = x + y + 1 rest default This interpretation is a model and yields following TRS: (2) i{j + i + 1}(div{i,j}(X,Y)) -> div{j,i}(Y,X) (3) div{j + i + 1,k}(div{i,j}(X,Y),Z) -> div{j,k + i + 1}(Y,div{i,k}(i{i}(X),Z)) [4] Use following polynomial interpretation: [div_{i,j}(x,y)] = x + y - 2 + i [i_{i}(x)] = x + i rest default Remove rules with left hand side strictly bigger than right hand side: (2)-(3) [5] Since there are no remaining rules, termination is proved! ../tpdb/TRS/Rubio/lescanne.trs, 0.01, Y Couldn't open file <60>: 60: No such file or directory