/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR M N X) (RULES U11(tt,M,N) -> U12(tt,activate(M),activate(N)) U12(tt,M,N) -> s(plus(activate(N),activate(M))) U21(tt,M,N) -> U22(tt,activate(M),activate(N)) U22(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N)) activate(X) -> X plus(N,0) -> N plus(N,s(M)) -> U11(tt,M,N) x(N,0) -> 0 x(N,s(M)) -> U21(tt,M,N) ) Problem 1: Innermost Equivalent Processor: -> Rules: U11(tt,M,N) -> U12(tt,activate(M),activate(N)) U12(tt,M,N) -> s(plus(activate(N),activate(M))) U21(tt,M,N) -> U22(tt,activate(M),activate(N)) U22(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N)) activate(X) -> X plus(N,0) -> N plus(N,s(M)) -> U11(tt,M,N) x(N,0) -> 0 x(N,s(M)) -> U21(tt,M,N) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: U11#(tt,M,N) -> U12#(tt,activate(M),activate(N)) U11#(tt,M,N) -> ACTIVATE(M) U11#(tt,M,N) -> ACTIVATE(N) U12#(tt,M,N) -> ACTIVATE(M) U12#(tt,M,N) -> ACTIVATE(N) U12#(tt,M,N) -> PLUS(activate(N),activate(M)) U21#(tt,M,N) -> U22#(tt,activate(M),activate(N)) U21#(tt,M,N) -> ACTIVATE(M) U21#(tt,M,N) -> ACTIVATE(N) U22#(tt,M,N) -> ACTIVATE(M) U22#(tt,M,N) -> ACTIVATE(N) U22#(tt,M,N) -> PLUS(x(activate(N),activate(M)),activate(N)) U22#(tt,M,N) -> X(activate(N),activate(M)) PLUS(N,s(M)) -> U11#(tt,M,N) X(N,s(M)) -> U21#(tt,M,N) -> Rules: U11(tt,M,N) -> U12(tt,activate(M),activate(N)) U12(tt,M,N) -> s(plus(activate(N),activate(M))) U21(tt,M,N) -> U22(tt,activate(M),activate(N)) U22(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N)) activate(X) -> X plus(N,0) -> N plus(N,s(M)) -> U11(tt,M,N) x(N,0) -> 0 x(N,s(M)) -> U21(tt,M,N) Problem 1: SCC Processor: -> Pairs: U11#(tt,M,N) -> U12#(tt,activate(M),activate(N)) U11#(tt,M,N) -> ACTIVATE(M) U11#(tt,M,N) -> ACTIVATE(N) U12#(tt,M,N) -> ACTIVATE(M) U12#(tt,M,N) -> ACTIVATE(N) U12#(tt,M,N) -> PLUS(activate(N),activate(M)) U21#(tt,M,N) -> U22#(tt,activate(M),activate(N)) U21#(tt,M,N) -> ACTIVATE(M) U21#(tt,M,N) -> ACTIVATE(N) U22#(tt,M,N) -> ACTIVATE(M) U22#(tt,M,N) -> ACTIVATE(N) U22#(tt,M,N) -> PLUS(x(activate(N),activate(M)),activate(N)) U22#(tt,M,N) -> X(activate(N),activate(M)) PLUS(N,s(M)) -> U11#(tt,M,N) X(N,s(M)) -> U21#(tt,M,N) -> Rules: U11(tt,M,N) -> U12(tt,activate(M),activate(N)) U12(tt,M,N) -> s(plus(activate(N),activate(M))) U21(tt,M,N) -> U22(tt,activate(M),activate(N)) U22(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N)) activate(X) -> X plus(N,0) -> N plus(N,s(M)) -> U11(tt,M,N) x(N,0) -> 0 x(N,s(M)) -> U21(tt,M,N) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: U11#(tt,M,N) -> U12#(tt,activate(M),activate(N)) U12#(tt,M,N) -> PLUS(activate(N),activate(M)) PLUS(N,s(M)) -> U11#(tt,M,N) ->->-> Rules: U11(tt,M,N) -> U12(tt,activate(M),activate(N)) U12(tt,M,N) -> s(plus(activate(N),activate(M))) U21(tt,M,N) -> U22(tt,activate(M),activate(N)) U22(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N)) activate(X) -> X plus(N,0) -> N plus(N,s(M)) -> U11(tt,M,N) x(N,0) -> 0 x(N,s(M)) -> U21(tt,M,N) ->->Cycle: ->->-> Pairs: U21#(tt,M,N) -> U22#(tt,activate(M),activate(N)) U22#(tt,M,N) -> X(activate(N),activate(M)) X(N,s(M)) -> U21#(tt,M,N) ->->-> Rules: U11(tt,M,N) -> U12(tt,activate(M),activate(N)) U12(tt,M,N) -> s(plus(activate(N),activate(M))) U21(tt,M,N) -> U22(tt,activate(M),activate(N)) U22(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N)) activate(X) -> X plus(N,0) -> N plus(N,s(M)) -> U11(tt,M,N) x(N,0) -> 0 x(N,s(M)) -> U21(tt,M,N) The problem is decomposed in 2 subproblems. Problem 1.1: Reduction Pairs Processor: -> Pairs: U11#(tt,M,N) -> U12#(tt,activate(M),activate(N)) U12#(tt,M,N) -> PLUS(activate(N),activate(M)) PLUS(N,s(M)) -> U11#(tt,M,N) -> Rules: U11(tt,M,N) -> U12(tt,activate(M),activate(N)) U12(tt,M,N) -> s(plus(activate(N),activate(M))) U21(tt,M,N) -> U22(tt,activate(M),activate(N)) U22(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N)) activate(X) -> X plus(N,0) -> N plus(N,s(M)) -> U11(tt,M,N) x(N,0) -> 0 x(N,s(M)) -> U21(tt,M,N) -> Usable rules: activate(X) -> X ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [activate](X) = X [s](X) = 2.X + 2 [tt] = 2 [U11#](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U12#](X1,X2,X3) = 2.X2 + 2.X3 + 2 [PLUS](X1,X2) = 2.X1 + 2.X2 + 2 Problem 1.1: SCC Processor: -> Pairs: U12#(tt,M,N) -> PLUS(activate(N),activate(M)) PLUS(N,s(M)) -> U11#(tt,M,N) -> Rules: U11(tt,M,N) -> U12(tt,activate(M),activate(N)) U12(tt,M,N) -> s(plus(activate(N),activate(M))) U21(tt,M,N) -> U22(tt,activate(M),activate(N)) U22(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N)) activate(X) -> X plus(N,0) -> N plus(N,s(M)) -> U11(tt,M,N) x(N,0) -> 0 x(N,s(M)) -> U21(tt,M,N) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Reduction Pairs Processor: -> Pairs: U21#(tt,M,N) -> U22#(tt,activate(M),activate(N)) U22#(tt,M,N) -> X(activate(N),activate(M)) X(N,s(M)) -> U21#(tt,M,N) -> Rules: U11(tt,M,N) -> U12(tt,activate(M),activate(N)) U12(tt,M,N) -> s(plus(activate(N),activate(M))) U21(tt,M,N) -> U22(tt,activate(M),activate(N)) U22(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N)) activate(X) -> X plus(N,0) -> N plus(N,s(M)) -> U11(tt,M,N) x(N,0) -> 0 x(N,s(M)) -> U21(tt,M,N) -> Usable rules: activate(X) -> X ->Interpretation type: Linear ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [activate](X) = X [s](X) = 2.X + 2 [tt] = 2 [U21#](X1,X2,X3) = 2.X1 + 2.X2 + 2.X3 + 2 [U22#](X1,X2,X3) = 2.X2 + 2.X3 + 2 [X](X1,X2) = 2.X1 + 2.X2 + 2 Problem 1.2: SCC Processor: -> Pairs: U22#(tt,M,N) -> X(activate(N),activate(M)) X(N,s(M)) -> U21#(tt,M,N) -> Rules: U11(tt,M,N) -> U12(tt,activate(M),activate(N)) U12(tt,M,N) -> s(plus(activate(N),activate(M))) U21(tt,M,N) -> U22(tt,activate(M),activate(N)) U22(tt,M,N) -> plus(x(activate(N),activate(M)),activate(N)) activate(X) -> X plus(N,0) -> N plus(N,s(M)) -> U11(tt,M,N) x(N,0) -> 0 x(N,s(M)) -> U21(tt,M,N) ->Strongly Connected Components: There is no strongly connected component The problem is finite.