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,x) -> 0 minus(x,y) -> cond(equal(min(x,y),y),x,y) cond(true,x,y) -> s(minus(x,s(y))) min(0,v) -> 0 min(u,0) -> 0 min(s(u),s(v)) -> s(min(u,v)) equal(0,0) -> true equal(s(x),0) -> false equal(0,s(y)) -> false equal(s(x),s(y)) -> equal(x,y) [2] TRS after applying termination preserving transformation to remove all the function symbol of arity >= 2:(1) minus(x,x) -> 0 (2) minus(x,y) -> cond`1(equal(min(x,y),y),cond`2(x,y)) (3) cond`1(true,cond`2(x,y)) -> s(minus(x,s(y))) (4) min(0,v) -> 0 (5) min(u,0) -> 0 (6) min(s(u),s(v)) -> s(min(u,v)) (7) equal(0,0) -> true (8) equal(s(x),0) -> false (9) equal(0,s(y)) -> false (10) equal(s(x),s(y)) -> equal(x,y) /tmp/tmp33pKnA/ex05.trs, 61.2, T Couldn't open file <60>: 60: No such file or directory