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: diff(x,y) -> cond1(equal(x,y),x,y) cond1(true,x,y) -> 0 cond1(false,x,y) -> cond2(gt(x,y),x,y) cond2(true,x,y) -> s(diff(x,s(y))) cond2(false,x,y) -> s(diff(s(x),y)) gt(0,v) -> false gt(s(u),0) -> true gt(s(u),s(v)) -> gt(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) diff(x,y) -> cond1`1(equal(x,y),cond1`2(x,y)) (2) cond1`1(true,cond1`2(x,y)) -> 0 (3) cond1`1(false,cond1`2(x,y)) -> cond2`1(gt(x,y),cond2`2(x,y)) (4) cond2`1(true,cond2`2(x,y)) -> s(diff(x,s(y))) (5) cond2`1(false,cond2`2(x,y)) -> s(diff(s(x),y)) (6) gt(0,v) -> false (7) gt(s(u),0) -> true (8) gt(s(u),s(v)) -> gt(u,v) (9) equal(0,0) -> true (10) equal(s(x),0) -> false (11) equal(0,s(y)) -> false (12) equal(s(x),s(y)) -> equal(x,y) /tmp/tmpMeM36X/ex14.trs, 60.57, T Couldn't open file <60>: 60: No such file or directory