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