/export/starexec/sandbox2/solver/bin/starexec_run_ttt2-1.17+nonreach /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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MAYBE

Problem:
 app(app(le(),0()),y) -> true()
 app(app(le(),app(s(),x)),0()) -> false()
 app(app(le(),app(s(),x)),app(s(),y)) -> app(app(le(),x),y)
 app(app(eq(),0()),0()) -> true()
 app(app(eq(),0()),app(s(),y)) -> false()
 app(app(eq(),app(s(),x)),0()) -> false()
 app(app(eq(),app(s(),x)),app(s(),y)) -> app(app(eq(),x),y)
 app(app(app(if(),true()),x),y) -> x
 app(app(app(if(),false()),x),y) -> y
 app(minsort(),nil()) -> nil()
 app(minsort(),app(app(cons(),x),y)) ->
 app(app(cons(),app(app(min(),x),y)),app(minsort(),app(app(del(),app(app(min(),x),y)),
                                                       app(app(cons(),x),y))))
 app(app(min(),x),nil()) -> x
 app(app(min(),x),app(app(cons(),y),z)) ->
 app(app(app(if(),app(app(le(),x),y)),app(app(min(),x),z)),app(app(min(),y),z))
 app(app(del(),x),nil()) -> nil()
 app(app(del(),x),app(app(cons(),y),z)) ->
 app(app(app(if(),app(app(eq(),x),y)),z),app(app(cons(),y),app(app(del(),x),z)))
 app(app(map(),f),nil()) -> nil()
 app(app(map(),f),app(app(cons(),x),xs)) -> app(app(cons(),app(f,x)),app(app(map(),f),xs))
 app(app(filter(),f),nil()) -> nil()
 app(app(filter(),f),app(app(cons(),x),xs)) -> app(app(app(app(filter2(),app(f,x)),f),x),xs)
 app(app(app(app(filter2(),true()),f),x),xs) -> app(app(cons(),x),app(app(filter(),f),xs))
 app(app(app(app(filter2(),false()),f),x),xs) -> app(app(filter(),f),xs)

Proof:
 Open