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: minus(x,y) -> cond(ge(x,s(y)),x,y) cond(false,x,y) -> 0 cond(true,x,y) -> s(minus(x,s(y))) ge(u,0) -> true ge(0,s(v)) -> false ge(s(u),s(v)) -> ge(u,v) [2] TRS after applying termination preserving transformation to remove all the function symbol of arity >= 2:(1) minus(x,y) -> cond`1(ge(x,s(y)),cond`2(x,y)) (2) cond`1(false,cond`2(x,y)) -> 0 (3) cond`1(true,cond`2(x,y)) -> s(minus(x,s(y))) (4) ge(u,0) -> true (5) ge(0,s(v)) -> false (6) ge(s(u),s(v)) -> ge(u,v) /tmp/tmpyxDtoP/ex03.trs, 61.71, T Couldn't open file <60>: 60: No such file or directory