/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR x y z) (RULES ++(++(x,y),z) -> ++(x,++(y,z)) ++(nil,y) -> y ++(x,nil) -> x flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) flatten(nil) -> nil flatten(unit(x)) -> flatten(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x rev(nil) -> nil rev(unit(x)) -> unit(x) ) Problem 1: Dependency Pairs Processor: -> Pairs: ++#(++(x,y),z) -> ++#(x,++(y,z)) ++#(++(x,y),z) -> ++#(y,z) FLATTEN(++(unit(x),y)) -> ++#(flatten(x),flatten(y)) FLATTEN(++(unit(x),y)) -> FLATTEN(x) FLATTEN(++(unit(x),y)) -> FLATTEN(y) FLATTEN(++(x,y)) -> ++#(flatten(x),flatten(y)) FLATTEN(++(x,y)) -> FLATTEN(x) FLATTEN(++(x,y)) -> FLATTEN(y) FLATTEN(unit(x)) -> FLATTEN(x) REV(++(x,y)) -> ++#(rev(y),rev(x)) REV(++(x,y)) -> REV(x) REV(++(x,y)) -> REV(y) -> Rules: ++(++(x,y),z) -> ++(x,++(y,z)) ++(nil,y) -> y ++(x,nil) -> x flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) flatten(nil) -> nil flatten(unit(x)) -> flatten(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x rev(nil) -> nil rev(unit(x)) -> unit(x) Problem 1: SCC Processor: -> Pairs: ++#(++(x,y),z) -> ++#(x,++(y,z)) ++#(++(x,y),z) -> ++#(y,z) FLATTEN(++(unit(x),y)) -> ++#(flatten(x),flatten(y)) FLATTEN(++(unit(x),y)) -> FLATTEN(x) FLATTEN(++(unit(x),y)) -> FLATTEN(y) FLATTEN(++(x,y)) -> ++#(flatten(x),flatten(y)) FLATTEN(++(x,y)) -> FLATTEN(x) FLATTEN(++(x,y)) -> FLATTEN(y) FLATTEN(unit(x)) -> FLATTEN(x) REV(++(x,y)) -> ++#(rev(y),rev(x)) REV(++(x,y)) -> REV(x) REV(++(x,y)) -> REV(y) -> Rules: ++(++(x,y),z) -> ++(x,++(y,z)) ++(nil,y) -> y ++(x,nil) -> x flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) flatten(nil) -> nil flatten(unit(x)) -> flatten(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x rev(nil) -> nil rev(unit(x)) -> unit(x) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ++#(++(x,y),z) -> ++#(x,++(y,z)) ++#(++(x,y),z) -> ++#(y,z) ->->-> Rules: ++(++(x,y),z) -> ++(x,++(y,z)) ++(nil,y) -> y ++(x,nil) -> x flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) flatten(nil) -> nil flatten(unit(x)) -> flatten(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x rev(nil) -> nil rev(unit(x)) -> unit(x) ->->Cycle: ->->-> Pairs: FLATTEN(++(unit(x),y)) -> FLATTEN(x) FLATTEN(++(unit(x),y)) -> FLATTEN(y) FLATTEN(++(x,y)) -> FLATTEN(x) FLATTEN(++(x,y)) -> FLATTEN(y) FLATTEN(unit(x)) -> FLATTEN(x) ->->-> Rules: ++(++(x,y),z) -> ++(x,++(y,z)) ++(nil,y) -> y ++(x,nil) -> x flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) flatten(nil) -> nil flatten(unit(x)) -> flatten(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x rev(nil) -> nil rev(unit(x)) -> unit(x) ->->Cycle: ->->-> Pairs: REV(++(x,y)) -> REV(x) REV(++(x,y)) -> REV(y) ->->-> Rules: ++(++(x,y),z) -> ++(x,++(y,z)) ++(nil,y) -> y ++(x,nil) -> x flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) flatten(nil) -> nil flatten(unit(x)) -> flatten(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x rev(nil) -> nil rev(unit(x)) -> unit(x) The problem is decomposed in 3 subproblems. Problem 1.1: Subterm Processor: -> Pairs: ++#(++(x,y),z) -> ++#(x,++(y,z)) ++#(++(x,y),z) -> ++#(y,z) -> Rules: ++(++(x,y),z) -> ++(x,++(y,z)) ++(nil,y) -> y ++(x,nil) -> x flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) flatten(nil) -> nil flatten(unit(x)) -> flatten(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x rev(nil) -> nil rev(unit(x)) -> unit(x) ->Projection: pi(++#) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: ++(++(x,y),z) -> ++(x,++(y,z)) ++(nil,y) -> y ++(x,nil) -> x flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) flatten(nil) -> nil flatten(unit(x)) -> flatten(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x rev(nil) -> nil rev(unit(x)) -> unit(x) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Subterm Processor: -> Pairs: FLATTEN(++(unit(x),y)) -> FLATTEN(x) FLATTEN(++(unit(x),y)) -> FLATTEN(y) FLATTEN(++(x,y)) -> FLATTEN(x) FLATTEN(++(x,y)) -> FLATTEN(y) FLATTEN(unit(x)) -> FLATTEN(x) -> Rules: ++(++(x,y),z) -> ++(x,++(y,z)) ++(nil,y) -> y ++(x,nil) -> x flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) flatten(nil) -> nil flatten(unit(x)) -> flatten(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x rev(nil) -> nil rev(unit(x)) -> unit(x) ->Projection: pi(FLATTEN) = 1 Problem 1.2: SCC Processor: -> Pairs: Empty -> Rules: ++(++(x,y),z) -> ++(x,++(y,z)) ++(nil,y) -> y ++(x,nil) -> x flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) flatten(nil) -> nil flatten(unit(x)) -> flatten(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x rev(nil) -> nil rev(unit(x)) -> unit(x) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.3: Subterm Processor: -> Pairs: REV(++(x,y)) -> REV(x) REV(++(x,y)) -> REV(y) -> Rules: ++(++(x,y),z) -> ++(x,++(y,z)) ++(nil,y) -> y ++(x,nil) -> x flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) flatten(nil) -> nil flatten(unit(x)) -> flatten(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x rev(nil) -> nil rev(unit(x)) -> unit(x) ->Projection: pi(REV) = 1 Problem 1.3: SCC Processor: -> Pairs: Empty -> Rules: ++(++(x,y),z) -> ++(x,++(y,z)) ++(nil,y) -> y ++(x,nil) -> x flatten(++(unit(x),y)) -> ++(flatten(x),flatten(y)) flatten(++(x,y)) -> ++(flatten(x),flatten(y)) flatten(flatten(x)) -> flatten(x) flatten(nil) -> nil flatten(unit(x)) -> flatten(x) rev(++(x,y)) -> ++(rev(y),rev(x)) rev(rev(x)) -> x rev(nil) -> nil rev(unit(x)) -> unit(x) ->Strongly Connected Components: There is no strongly connected component The problem is finite.