TPA v.1.1 Result: Run out of time while trying to prove (non-)termination of that system. Only partial proof available. 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 as loaded from the input file: f(true,x,y) -> f(gt(x,y),x,round(s(y))) round(0) -> 0 round(s(0)) -> s(s(0)) round(s(s(x))) -> s(s(round(x))) gt(0,v) -> false gt(s(u),0) -> true gt(s(u),s(v)) -> gt(u,v) [2] TRS after applying termination preserving transformation to remove all the function symbol of arity >= 2:(1) f`1(true,f`2(x,y)) -> f`1(gt(x,y),f`2(x,round(s(y)))) (2) round(0) -> 0 (3) round(s(0)) -> s(s(0)) (4) round(s(s(x))) -> s(s(round(x))) (5) gt(0,v) -> false (6) gt(s(u),0) -> true (7) gt(s(u),s(v)) -> gt(u,v) /tmp/tmpyMa08Q/ex09.trs, 60.14, T Couldn't open file <60>: 60: No such file or directory