/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S X:S Y:S) (RULES 0 -> n__0 activate(n__0) -> 0 activate(n__s(X:S)) -> s(X:S) activate(X:S) -> X:S div(0,n__s(Y:S)) -> 0 div(s(X:S),n__s(Y:S)) -> if(geq(X:S,activate(Y:S)),n__s(div(minus(X:S,activate(Y:S)),n__s(activate(Y:S)))),n__0) geq(n__0,n__s(Y:S)) -> ffalse geq(n__s(X:S),n__s(Y:S)) -> geq(activate(X:S),activate(Y:S)) geq(X:S,n__0) -> ttrue if(ffalse,X:S,Y:S) -> activate(Y:S) if(ttrue,X:S,Y:S) -> activate(X:S) minus(n__0,Y:S) -> 0 minus(n__s(X:S),n__s(Y:S)) -> minus(activate(X:S),activate(Y:S)) s(X:S) -> n__s(X:S) ) Problem 1: Dependency Pairs Processor: -> Pairs: ACTIVATE(n__0) -> 0# ACTIVATE(n__s(X:S)) -> S(X:S) DIV(s(X:S),n__s(Y:S)) -> ACTIVATE(Y:S) DIV(s(X:S),n__s(Y:S)) -> DIV(minus(X:S,activate(Y:S)),n__s(activate(Y:S))) DIV(s(X:S),n__s(Y:S)) -> GEQ(X:S,activate(Y:S)) DIV(s(X:S),n__s(Y:S)) -> IF(geq(X:S,activate(Y:S)),n__s(div(minus(X:S,activate(Y:S)),n__s(activate(Y:S)))),n__0) DIV(s(X:S),n__s(Y:S)) -> MINUS(X:S,activate(Y:S)) GEQ(n__s(X:S),n__s(Y:S)) -> ACTIVATE(X:S) GEQ(n__s(X:S),n__s(Y:S)) -> ACTIVATE(Y:S) GEQ(n__s(X:S),n__s(Y:S)) -> GEQ(activate(X:S),activate(Y:S)) IF(ffalse,X:S,Y:S) -> ACTIVATE(Y:S) IF(ttrue,X:S,Y:S) -> ACTIVATE(X:S) MINUS(n__0,Y:S) -> 0# MINUS(n__s(X:S),n__s(Y:S)) -> ACTIVATE(X:S) MINUS(n__s(X:S),n__s(Y:S)) -> ACTIVATE(Y:S) MINUS(n__s(X:S),n__s(Y:S)) -> MINUS(activate(X:S),activate(Y:S)) -> Rules: 0 -> n__0 activate(n__0) -> 0 activate(n__s(X:S)) -> s(X:S) activate(X:S) -> X:S div(0,n__s(Y:S)) -> 0 div(s(X:S),n__s(Y:S)) -> if(geq(X:S,activate(Y:S)),n__s(div(minus(X:S,activate(Y:S)),n__s(activate(Y:S)))),n__0) geq(n__0,n__s(Y:S)) -> ffalse geq(n__s(X:S),n__s(Y:S)) -> geq(activate(X:S),activate(Y:S)) geq(X:S,n__0) -> ttrue if(ffalse,X:S,Y:S) -> activate(Y:S) if(ttrue,X:S,Y:S) -> activate(X:S) minus(n__0,Y:S) -> 0 minus(n__s(X:S),n__s(Y:S)) -> minus(activate(X:S),activate(Y:S)) s(X:S) -> n__s(X:S) Problem 1: SCC Processor: -> Pairs: ACTIVATE(n__0) -> 0# ACTIVATE(n__s(X:S)) -> S(X:S) DIV(s(X:S),n__s(Y:S)) -> ACTIVATE(Y:S) DIV(s(X:S),n__s(Y:S)) -> DIV(minus(X:S,activate(Y:S)),n__s(activate(Y:S))) DIV(s(X:S),n__s(Y:S)) -> GEQ(X:S,activate(Y:S)) DIV(s(X:S),n__s(Y:S)) -> IF(geq(X:S,activate(Y:S)),n__s(div(minus(X:S,activate(Y:S)),n__s(activate(Y:S)))),n__0) DIV(s(X:S),n__s(Y:S)) -> MINUS(X:S,activate(Y:S)) GEQ(n__s(X:S),n__s(Y:S)) -> ACTIVATE(X:S) GEQ(n__s(X:S),n__s(Y:S)) -> ACTIVATE(Y:S) GEQ(n__s(X:S),n__s(Y:S)) -> GEQ(activate(X:S),activate(Y:S)) IF(ffalse,X:S,Y:S) -> ACTIVATE(Y:S) IF(ttrue,X:S,Y:S) -> ACTIVATE(X:S) MINUS(n__0,Y:S) -> 0# MINUS(n__s(X:S),n__s(Y:S)) -> ACTIVATE(X:S) MINUS(n__s(X:S),n__s(Y:S)) -> ACTIVATE(Y:S) MINUS(n__s(X:S),n__s(Y:S)) -> MINUS(activate(X:S),activate(Y:S)) -> Rules: 0 -> n__0 activate(n__0) -> 0 activate(n__s(X:S)) -> s(X:S) activate(X:S) -> X:S div(0,n__s(Y:S)) -> 0 div(s(X:S),n__s(Y:S)) -> if(geq(X:S,activate(Y:S)),n__s(div(minus(X:S,activate(Y:S)),n__s(activate(Y:S)))),n__0) geq(n__0,n__s(Y:S)) -> ffalse geq(n__s(X:S),n__s(Y:S)) -> geq(activate(X:S),activate(Y:S)) geq(X:S,n__0) -> ttrue if(ffalse,X:S,Y:S) -> activate(Y:S) if(ttrue,X:S,Y:S) -> activate(X:S) minus(n__0,Y:S) -> 0 minus(n__s(X:S),n__s(Y:S)) -> minus(activate(X:S),activate(Y:S)) s(X:S) -> n__s(X:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: GEQ(n__s(X:S),n__s(Y:S)) -> GEQ(activate(X:S),activate(Y:S)) ->->-> Rules: 0 -> n__0 activate(n__0) -> 0 activate(n__s(X:S)) -> s(X:S) activate(X:S) -> X:S div(0,n__s(Y:S)) -> 0 div(s(X:S),n__s(Y:S)) -> if(geq(X:S,activate(Y:S)),n__s(div(minus(X:S,activate(Y:S)),n__s(activate(Y:S)))),n__0) geq(n__0,n__s(Y:S)) -> ffalse geq(n__s(X:S),n__s(Y:S)) -> geq(activate(X:S),activate(Y:S)) geq(X:S,n__0) -> ttrue if(ffalse,X:S,Y:S) -> activate(Y:S) if(ttrue,X:S,Y:S) -> activate(X:S) minus(n__0,Y:S) -> 0 minus(n__s(X:S),n__s(Y:S)) -> minus(activate(X:S),activate(Y:S)) s(X:S) -> n__s(X:S) ->->Cycle: ->->-> Pairs: MINUS(n__s(X:S),n__s(Y:S)) -> MINUS(activate(X:S),activate(Y:S)) ->->-> Rules: 0 -> n__0 activate(n__0) -> 0 activate(n__s(X:S)) -> s(X:S) activate(X:S) -> X:S div(0,n__s(Y:S)) -> 0 div(s(X:S),n__s(Y:S)) -> if(geq(X:S,activate(Y:S)),n__s(div(minus(X:S,activate(Y:S)),n__s(activate(Y:S)))),n__0) geq(n__0,n__s(Y:S)) -> ffalse geq(n__s(X:S),n__s(Y:S)) -> geq(activate(X:S),activate(Y:S)) geq(X:S,n__0) -> ttrue if(ffalse,X:S,Y:S) -> activate(Y:S) if(ttrue,X:S,Y:S) -> activate(X:S) minus(n__0,Y:S) -> 0 minus(n__s(X:S),n__s(Y:S)) -> minus(activate(X:S),activate(Y:S)) s(X:S) -> n__s(X:S) ->->Cycle: ->->-> Pairs: DIV(s(X:S),n__s(Y:S)) -> DIV(minus(X:S,activate(Y:S)),n__s(activate(Y:S))) ->->-> Rules: 0 -> n__0 activate(n__0) -> 0 activate(n__s(X:S)) -> s(X:S) activate(X:S) -> X:S div(0,n__s(Y:S)) -> 0 div(s(X:S),n__s(Y:S)) -> if(geq(X:S,activate(Y:S)),n__s(div(minus(X:S,activate(Y:S)),n__s(activate(Y:S)))),n__0) geq(n__0,n__s(Y:S)) -> ffalse geq(n__s(X:S),n__s(Y:S)) -> geq(activate(X:S),activate(Y:S)) geq(X:S,n__0) -> ttrue if(ffalse,X:S,Y:S) -> activate(Y:S) if(ttrue,X:S,Y:S) -> activate(X:S) minus(n__0,Y:S) -> 0 minus(n__s(X:S),n__s(Y:S)) -> minus(activate(X:S),activate(Y:S)) s(X:S) -> n__s(X:S) The problem is decomposed in 3 subproblems. Problem 1.1: Reduction Pair Processor: -> Pairs: GEQ(n__s(X:S),n__s(Y:S)) -> GEQ(activate(X:S),activate(Y:S)) -> Rules: 0 -> n__0 activate(n__0) -> 0 activate(n__s(X:S)) -> s(X:S) activate(X:S) -> X:S div(0,n__s(Y:S)) -> 0 div(s(X:S),n__s(Y:S)) -> if(geq(X:S,activate(Y:S)),n__s(div(minus(X:S,activate(Y:S)),n__s(activate(Y:S)))),n__0) geq(n__0,n__s(Y:S)) -> ffalse geq(n__s(X:S),n__s(Y:S)) -> geq(activate(X:S),activate(Y:S)) geq(X:S,n__0) -> ttrue if(ffalse,X:S,Y:S) -> activate(Y:S) if(ttrue,X:S,Y:S) -> activate(X:S) minus(n__0,Y:S) -> 0 minus(n__s(X:S),n__s(Y:S)) -> minus(activate(X:S),activate(Y:S)) s(X:S) -> n__s(X:S) -> Usable rules: 0 -> n__0 activate(n__0) -> 0 activate(n__s(X:S)) -> s(X:S) activate(X:S) -> X:S s(X:S) -> n__s(X:S) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0] = 2 [activate](X) = 2.X + 1 [s](X) = 2.X + 2 [n__0] = 1 [n__s](X) = 2.X + 2 [GEQ](X1,X2) = 2.X1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: 0 -> n__0 activate(n__0) -> 0 activate(n__s(X:S)) -> s(X:S) activate(X:S) -> X:S div(0,n__s(Y:S)) -> 0 div(s(X:S),n__s(Y:S)) -> if(geq(X:S,activate(Y:S)),n__s(div(minus(X:S,activate(Y:S)),n__s(activate(Y:S)))),n__0) geq(n__0,n__s(Y:S)) -> ffalse geq(n__s(X:S),n__s(Y:S)) -> geq(activate(X:S),activate(Y:S)) geq(X:S,n__0) -> ttrue if(ffalse,X:S,Y:S) -> activate(Y:S) if(ttrue,X:S,Y:S) -> activate(X:S) minus(n__0,Y:S) -> 0 minus(n__s(X:S),n__s(Y:S)) -> minus(activate(X:S),activate(Y:S)) s(X:S) -> n__s(X:S) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Reduction Pair Processor: -> Pairs: MINUS(n__s(X:S),n__s(Y:S)) -> MINUS(activate(X:S),activate(Y:S)) -> Rules: 0 -> n__0 activate(n__0) -> 0 activate(n__s(X:S)) -> s(X:S) activate(X:S) -> X:S div(0,n__s(Y:S)) -> 0 div(s(X:S),n__s(Y:S)) -> if(geq(X:S,activate(Y:S)),n__s(div(minus(X:S,activate(Y:S)),n__s(activate(Y:S)))),n__0) geq(n__0,n__s(Y:S)) -> ffalse geq(n__s(X:S),n__s(Y:S)) -> geq(activate(X:S),activate(Y:S)) geq(X:S,n__0) -> ttrue if(ffalse,X:S,Y:S) -> activate(Y:S) if(ttrue,X:S,Y:S) -> activate(X:S) minus(n__0,Y:S) -> 0 minus(n__s(X:S),n__s(Y:S)) -> minus(activate(X:S),activate(Y:S)) s(X:S) -> n__s(X:S) -> Usable rules: 0 -> n__0 activate(n__0) -> 0 activate(n__s(X:S)) -> s(X:S) activate(X:S) -> X:S s(X:S) -> n__s(X:S) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0] = 2 [activate](X) = 2.X + 1 [s](X) = 2.X + 2 [n__0] = 1 [n__s](X) = 2.X + 2 [MINUS](X1,X2) = 2.X1 Problem 1.2: SCC Processor: -> Pairs: Empty -> Rules: 0 -> n__0 activate(n__0) -> 0 activate(n__s(X:S)) -> s(X:S) activate(X:S) -> X:S div(0,n__s(Y:S)) -> 0 div(s(X:S),n__s(Y:S)) -> if(geq(X:S,activate(Y:S)),n__s(div(minus(X:S,activate(Y:S)),n__s(activate(Y:S)))),n__0) geq(n__0,n__s(Y:S)) -> ffalse geq(n__s(X:S),n__s(Y:S)) -> geq(activate(X:S),activate(Y:S)) geq(X:S,n__0) -> ttrue if(ffalse,X:S,Y:S) -> activate(Y:S) if(ttrue,X:S,Y:S) -> activate(X:S) minus(n__0,Y:S) -> 0 minus(n__s(X:S),n__s(Y:S)) -> minus(activate(X:S),activate(Y:S)) s(X:S) -> n__s(X:S) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.3: Reduction Pair Processor: -> Pairs: DIV(s(X:S),n__s(Y:S)) -> DIV(minus(X:S,activate(Y:S)),n__s(activate(Y:S))) -> Rules: 0 -> n__0 activate(n__0) -> 0 activate(n__s(X:S)) -> s(X:S) activate(X:S) -> X:S div(0,n__s(Y:S)) -> 0 div(s(X:S),n__s(Y:S)) -> if(geq(X:S,activate(Y:S)),n__s(div(minus(X:S,activate(Y:S)),n__s(activate(Y:S)))),n__0) geq(n__0,n__s(Y:S)) -> ffalse geq(n__s(X:S),n__s(Y:S)) -> geq(activate(X:S),activate(Y:S)) geq(X:S,n__0) -> ttrue if(ffalse,X:S,Y:S) -> activate(Y:S) if(ttrue,X:S,Y:S) -> activate(X:S) minus(n__0,Y:S) -> 0 minus(n__s(X:S),n__s(Y:S)) -> minus(activate(X:S),activate(Y:S)) s(X:S) -> n__s(X:S) -> Usable rules: 0 -> n__0 activate(n__0) -> 0 activate(n__s(X:S)) -> s(X:S) activate(X:S) -> X:S minus(n__0,Y:S) -> 0 minus(n__s(X:S),n__s(Y:S)) -> minus(activate(X:S),activate(Y:S)) s(X:S) -> n__s(X:S) ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [0] = 2 [activate](X) = 2.X [minus](X1,X2) = 2.X1 + 1 [s](X) = 2.X + 2 [n__0] = 2 [n__s](X) = 2.X + 1 [DIV](X1,X2) = X1 Problem 1.3: SCC Processor: -> Pairs: Empty -> Rules: 0 -> n__0 activate(n__0) -> 0 activate(n__s(X:S)) -> s(X:S) activate(X:S) -> X:S div(0,n__s(Y:S)) -> 0 div(s(X:S),n__s(Y:S)) -> if(geq(X:S,activate(Y:S)),n__s(div(minus(X:S,activate(Y:S)),n__s(activate(Y:S)))),n__0) geq(n__0,n__s(Y:S)) -> ffalse geq(n__s(X:S),n__s(Y:S)) -> geq(activate(X:S),activate(Y:S)) geq(X:S,n__0) -> ttrue if(ffalse,X:S,Y:S) -> activate(Y:S) if(ttrue,X:S,Y:S) -> activate(X:S) minus(n__0,Y:S) -> 0 minus(n__s(X:S),n__s(Y:S)) -> minus(activate(X:S),activate(Y:S)) s(X:S) -> n__s(X:S) ->Strongly Connected Components: There is no strongly connected component The problem is finite.