/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 X1 X2 Y Z) (RULES activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X ) Problem 1: Dependency Pairs Processor: -> Pairs: ACTIVATE(n__first(X1,X2)) -> ACTIVATE(X1) ACTIVATE(n__first(X1,X2)) -> ACTIVATE(X2) ACTIVATE(n__first(X1,X2)) -> FIRST(activate(X1),activate(X2)) ACTIVATE(n__from(X)) -> ACTIVATE(X) ACTIVATE(n__from(X)) -> FROM(activate(X)) ACTIVATE(n__s(X)) -> ACTIVATE(X) ACTIVATE(n__s(X)) -> S(activate(X)) FIRST(s(X),cons(Y,Z)) -> ACTIVATE(Z) SEL(s(X),cons(Y,Z)) -> ACTIVATE(Z) SEL(s(X),cons(Y,Z)) -> SEL(X,activate(Z)) -> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X Problem 1: SCC Processor: -> Pairs: ACTIVATE(n__first(X1,X2)) -> ACTIVATE(X1) ACTIVATE(n__first(X1,X2)) -> ACTIVATE(X2) ACTIVATE(n__first(X1,X2)) -> FIRST(activate(X1),activate(X2)) ACTIVATE(n__from(X)) -> ACTIVATE(X) ACTIVATE(n__from(X)) -> FROM(activate(X)) ACTIVATE(n__s(X)) -> ACTIVATE(X) ACTIVATE(n__s(X)) -> S(activate(X)) FIRST(s(X),cons(Y,Z)) -> ACTIVATE(Z) SEL(s(X),cons(Y,Z)) -> ACTIVATE(Z) SEL(s(X),cons(Y,Z)) -> SEL(X,activate(Z)) -> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVATE(n__first(X1,X2)) -> ACTIVATE(X1) ACTIVATE(n__first(X1,X2)) -> ACTIVATE(X2) ACTIVATE(n__first(X1,X2)) -> FIRST(activate(X1),activate(X2)) ACTIVATE(n__from(X)) -> ACTIVATE(X) ACTIVATE(n__s(X)) -> ACTIVATE(X) FIRST(s(X),cons(Y,Z)) -> ACTIVATE(Z) ->->-> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X ->->Cycle: ->->-> Pairs: SEL(s(X),cons(Y,Z)) -> SEL(X,activate(Z)) ->->-> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pair Processor: -> Pairs: ACTIVATE(n__first(X1,X2)) -> ACTIVATE(X1) ACTIVATE(n__first(X1,X2)) -> ACTIVATE(X2) ACTIVATE(n__first(X1,X2)) -> FIRST(activate(X1),activate(X2)) ACTIVATE(n__from(X)) -> ACTIVATE(X) ACTIVATE(n__s(X)) -> ACTIVATE(X) FIRST(s(X),cons(Y,Z)) -> ACTIVATE(Z) -> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X -> Usable rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [activate](X) = X [first](X1,X2) = 2.X1 + 2.X2 + 1 [from](X) = 2.X + 2 [s](X) = X [0] = 1 [cons](X1,X2) = X2 [n__first](X1,X2) = 2.X1 + 2.X2 + 1 [n__from](X) = 2.X + 2 [n__s](X) = X [nil] = 1 [ACTIVATE](X) = 2.X + 2 [FIRST](X1,X2) = X1 + 2.X2 + 2 Problem 1.1: SCC Processor: -> Pairs: ACTIVATE(n__first(X1,X2)) -> ACTIVATE(X2) ACTIVATE(n__first(X1,X2)) -> FIRST(activate(X1),activate(X2)) ACTIVATE(n__from(X)) -> ACTIVATE(X) ACTIVATE(n__s(X)) -> ACTIVATE(X) FIRST(s(X),cons(Y,Z)) -> ACTIVATE(Z) -> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVATE(n__first(X1,X2)) -> ACTIVATE(X2) ACTIVATE(n__first(X1,X2)) -> FIRST(activate(X1),activate(X2)) ACTIVATE(n__from(X)) -> ACTIVATE(X) ACTIVATE(n__s(X)) -> ACTIVATE(X) FIRST(s(X),cons(Y,Z)) -> ACTIVATE(Z) ->->-> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X Problem 1.1: Reduction Pair Processor: -> Pairs: ACTIVATE(n__first(X1,X2)) -> ACTIVATE(X2) ACTIVATE(n__first(X1,X2)) -> FIRST(activate(X1),activate(X2)) ACTIVATE(n__from(X)) -> ACTIVATE(X) ACTIVATE(n__s(X)) -> ACTIVATE(X) FIRST(s(X),cons(Y,Z)) -> ACTIVATE(Z) -> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X -> Usable rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [activate](X) = X [first](X1,X2) = X2 + 2 [from](X) = 2.X + 1 [s](X) = X [0] = 1 [cons](X1,X2) = X2 [n__first](X1,X2) = X2 + 2 [n__from](X) = 2.X + 1 [n__s](X) = X [nil] = 1 [ACTIVATE](X) = 2.X [FIRST](X1,X2) = 2.X2 Problem 1.1: SCC Processor: -> Pairs: ACTIVATE(n__first(X1,X2)) -> FIRST(activate(X1),activate(X2)) ACTIVATE(n__from(X)) -> ACTIVATE(X) ACTIVATE(n__s(X)) -> ACTIVATE(X) FIRST(s(X),cons(Y,Z)) -> ACTIVATE(Z) -> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVATE(n__first(X1,X2)) -> FIRST(activate(X1),activate(X2)) ACTIVATE(n__from(X)) -> ACTIVATE(X) ACTIVATE(n__s(X)) -> ACTIVATE(X) FIRST(s(X),cons(Y,Z)) -> ACTIVATE(Z) ->->-> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X Problem 1.1: Reduction Pair Processor: -> Pairs: ACTIVATE(n__first(X1,X2)) -> FIRST(activate(X1),activate(X2)) ACTIVATE(n__from(X)) -> ACTIVATE(X) ACTIVATE(n__s(X)) -> ACTIVATE(X) FIRST(s(X),cons(Y,Z)) -> ACTIVATE(Z) -> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X -> Usable rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [activate](X) = X [first](X1,X2) = X1 + X2 + 2 [from](X) = 2.X + 1 [s](X) = X [0] = 2 [cons](X1,X2) = X2 [n__first](X1,X2) = X1 + X2 + 2 [n__from](X) = 2.X + 1 [n__s](X) = X [nil] = 2 [ACTIVATE](X) = 2.X [FIRST](X1,X2) = 2.X1 + 2.X2 Problem 1.1: SCC Processor: -> Pairs: ACTIVATE(n__from(X)) -> ACTIVATE(X) ACTIVATE(n__s(X)) -> ACTIVATE(X) FIRST(s(X),cons(Y,Z)) -> ACTIVATE(Z) -> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ACTIVATE(n__from(X)) -> ACTIVATE(X) ACTIVATE(n__s(X)) -> ACTIVATE(X) ->->-> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X Problem 1.1: Subterm Processor: -> Pairs: ACTIVATE(n__from(X)) -> ACTIVATE(X) ACTIVATE(n__s(X)) -> ACTIVATE(X) -> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X ->Projection: pi(ACTIVATE) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Subterm Processor: -> Pairs: SEL(s(X),cons(Y,Z)) -> SEL(X,activate(Z)) -> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X ->Projection: pi(SEL) = 1 Problem 1.2: SCC Processor: -> Pairs: Empty -> Rules: activate(n__first(X1,X2)) -> first(activate(X1),activate(X2)) activate(n__from(X)) -> from(activate(X)) activate(n__s(X)) -> s(activate(X)) activate(X) -> X first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z))) first(0,Z) -> nil first(X1,X2) -> n__first(X1,X2) from(X) -> cons(X,n__from(n__s(X))) from(X) -> n__from(X) s(X) -> n__s(X) sel(s(X),cons(Y,Z)) -> sel(X,activate(Z)) sel(0,cons(X,Z)) -> X ->Strongly Connected Components: There is no strongly connected component The problem is finite.