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(and(gt(x,y),gt(y,s(s(0)))),plus(s(0),x),double(y)) gt(0,v) -> false gt(s(u),0) -> true gt(s(u),s(v)) -> gt(u,v) and(x,true) -> x and(x,false) -> false plus(n,0) -> n plus(n,s(m)) -> s(plus(n,m)) plus(plus(n,m),u) -> plus(n,plus(m,u)) double(0) -> 0 double(s(x)) -> s(s(double(x))) [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(and(gt(x,y),gt(y,s(s(0)))),f`2(plus(s(0),x),double(y))) (2) gt(0,v) -> false (3) gt(s(u),0) -> true (4) gt(s(u),s(v)) -> gt(u,v) (5) and(x,true) -> x (6) and(x,false) -> false (7) plus(n,0) -> n (8) plus(n,s(m)) -> s(plus(n,m)) (9) plus(plus(n,m),u) -> plus(n,plus(m,u)) (10) double(0) -> 0 (11) double(s(x)) -> s(s(double(x))) /tmp/tmp81naas/ex12.trs, 64.22, T Couldn't open file <60>: 60: No such file or directory