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,z) -> f(gt(x,plus(y,z)),x,s(y),z) f(true,x,y,z) -> f(gt(x,plus(y,z)),x,y,s(z)) plus(n,0) -> n plus(n,s(m)) -> s(plus(n,m)) 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,f`3(y,z))) -> f`1(gt(x,plus(y,z)),f`2(x,f`3(s(y),z))) (2) f`1(true,f`2(x,f`3(y,z))) -> f`1(gt(x,plus(y,z)),f`2(x,f`3(y,s(z)))) (3) plus(n,0) -> n (4) plus(n,s(m)) -> s(plus(n,m)) (5) gt(0,v) -> false (6) gt(s(u),0) -> true (7) gt(s(u),s(v)) -> gt(u,v) /tmp/tmpv2uCKi/ex06.trs, 62.94, T Couldn't open file <60>: 60: No such file or directory