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