/export/starexec/sandbox/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


--------------------------------------------------------------------------------


MAYBE

Problem:
 prod(xs) -> prodIter(xs,s(0()))
 prodIter(xs,x) -> ifProd(isempty(xs),xs,x)
 ifProd(true(),xs,x) -> x
 ifProd(false(),xs,x) -> prodIter(tail(xs),times(x,head(xs)))
 plus(0(),y) -> y
 plus(s(x),y) -> s(plus(x,y))
 times(x,y) -> timesIter(x,y,0(),0())
 timesIter(x,y,z,u) -> ifTimes(ge(u,x),x,y,z,u)
 ifTimes(true(),x,y,z,u) -> z
 ifTimes(false(),x,y,z,u) -> timesIter(x,y,plus(y,z),s(u))
 isempty(nil()) -> true()
 isempty(cons(x,xs)) -> false()
 head(nil()) -> error()
 head(cons(x,xs)) -> x
 tail(nil()) -> nil()
 tail(cons(x,xs)) -> xs
 ge(x,0()) -> true()
 ge(0(),s(y)) -> false()
 ge(s(x),s(y)) -> ge(x,y)
 a() -> b()
 a() -> c()

Proof:
 Open