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:
div(x,s(y)) -> d(x,s(y),0)
d(x,s(y),z) -> cond(ge(x,z),x,y,z)
cond(true,x,y,z) -> s(d(x,s(y),plus(s(y),z)))
cond(false,x,y,z) -> 0
ge(u,0) -> true
ge(0,s(v)) -> false
ge(s(u),s(v)) -> ge(u,v)
plus(n,0) -> n
plus(n,s(m)) -> s(plus(n,m))
plus(plus(n,m),u) -> plus(n,plus(m,u))

[2]  TRS after applying termination preserving transformation to remove all the function symbol of arity >= 2: 
(1) div(x,s(y)) -> d`1(x,d`2(s(y),0))
(2) d`1(x,d`2(s(y),z)) -> cond`1(ge(x,z),cond`2(x,cond`3(y,z)))
(3) cond`1(true,cond`2(x,cond`3(y,z))) -> s(d`1(x,d`2(s(y),plus(s(y),z))))
(4) cond`1(false,cond`2(x,cond`3(y,z))) -> 0
(5) ge(u,0) -> true
(6) ge(0,s(v)) -> false
(7) ge(s(u),s(v)) -> ge(u,v)
(8) plus(n,0) -> n
(9) plus(n,s(m)) -> s(plus(n,m))
(10) plus(plus(n,m),u) -> plus(n,plus(m,u))


/tmp/tmpPtZw36/ex13.trs, 60.34, T
Couldn't open file <60>: 60: No such file or directory