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


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MAYBE

Problem:
 times(x,y) -> sum(generate(x,y))
 generate(x,y) -> gen(x,y,0())
 gen(x,y,z) -> if(ge(z,x),x,y,z)
 if(true(),x,y,z) -> nil()
 if(false(),x,y,z) -> cons(y,gen(x,y,s(z)))
 sum(xs) -> sum2(xs,0())
 sum2(xs,y) -> ifsum(isNil(xs),isZero(head(xs)),xs,y)
 ifsum(true(),b,xs,y) -> y
 ifsum(false(),b,xs,y) -> ifsum2(b,xs,y)
 ifsum2(true(),xs,y) -> sum2(tail(xs),y)
 ifsum2(false(),xs,y) -> sum2(cons(p(head(xs)),tail(xs)),s(y))
 isNil(nil()) -> true()
 isNil(cons(x,xs)) -> false()
 tail(nil()) -> nil()
 tail(cons(x,xs)) -> xs
 head(cons(x,xs)) -> x
 head(nil()) -> error()
 isZero(0()) -> true()
 isZero(s(0())) -> false()
 isZero(s(s(x))) -> isZero(s(x))
 p(0()) -> s(s(0()))
 p(s(0())) -> 0()
 p(s(s(x))) -> s(p(s(x)))
 ge(x,0()) -> true()
 ge(0(),s(y)) -> false()
 ge(s(x),s(y)) -> ge(x,y)
 a() -> c()
 a() -> d()

Proof:
 Open