/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR x) (RULES a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) ) Problem 1: Innermost Equivalent Processor: -> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,a(f,x))) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) A(f,a(f,a(g,a(g,x)))) -> A(f,x) A(f,a(f,a(g,a(g,x)))) -> A(g,a(f,a(f,a(f,x)))) A(f,a(f,a(g,a(g,x)))) -> A(g,a(g,a(f,a(f,a(f,x))))) A(f,a(f,a(g,a(g,x)))) -> A(g,a(g,a(g,a(f,a(f,a(f,x)))))) -> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) Problem 1: SCC Processor: -> Pairs: A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,a(f,x))) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) A(f,a(f,a(g,a(g,x)))) -> A(f,x) A(f,a(f,a(g,a(g,x)))) -> A(g,a(f,a(f,a(f,x)))) A(f,a(f,a(g,a(g,x)))) -> A(g,a(g,a(f,a(f,a(f,x))))) A(f,a(f,a(g,a(g,x)))) -> A(g,a(g,a(g,a(f,a(f,a(f,x)))))) -> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,a(f,x))) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) A(f,a(f,a(g,a(g,x)))) -> A(f,x) ->->-> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) Problem 1: Forward Instantiation Processor: -> Pairs: A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,a(f,x))) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) A(f,a(f,a(g,a(g,x)))) -> A(f,x) -> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) ->Instantiated Pairs: ->->Original Pair: A(f,a(f,a(g,a(g,x)))) -> A(f,x) ->-> Instantiated pairs: A(f,a(f,a(g,a(g,a(f,x4))))) -> A(f,a(f,x4)) A(f,a(f,a(g,a(g,a(f,x8))))) -> A(f,a(f,x8)) A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) Problem 1: SCC Processor: -> Pairs: A(f,a(f,a(g,a(g,a(f,x4))))) -> A(f,a(f,x4)) A(f,a(f,a(g,a(g,a(f,x8))))) -> A(f,a(f,x8)) A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,a(f,x))) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) -> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(f,a(f,a(g,a(g,a(f,x4))))) -> A(f,a(f,x4)) A(f,a(f,a(g,a(g,a(f,x8))))) -> A(f,a(f,x8)) A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,a(f,x))) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) ->->-> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) Problem 1: Narrowing Processor: -> Pairs: A(f,a(f,a(g,a(g,a(f,x4))))) -> A(f,a(f,x4)) A(f,a(f,a(g,a(g,a(f,x8))))) -> A(f,a(f,x8)) A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,a(f,x))) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) -> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) ->Narrowed Pairs: ->->Original Pair: A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,a(f,x))) ->-> Narrowed pairs: A(f,a(f,a(g,a(g,a(f,a(g,a(g,x))))))) -> A(f,a(f,a(g,a(g,a(g,a(f,a(f,a(f,x)))))))) A(f,a(f,a(g,a(g,a(g,a(g,x)))))) -> A(f,a(g,a(g,a(g,a(f,a(f,a(f,x))))))) Problem 1: SCC Processor: -> Pairs: A(f,a(f,a(g,a(g,a(f,a(g,a(g,x))))))) -> A(f,a(f,a(g,a(g,a(g,a(f,a(f,a(f,x)))))))) A(f,a(f,a(g,a(g,a(f,x4))))) -> A(f,a(f,x4)) A(f,a(f,a(g,a(g,a(f,x8))))) -> A(f,a(f,x8)) A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) A(f,a(f,a(g,a(g,a(g,a(g,x)))))) -> A(f,a(g,a(g,a(g,a(f,a(f,a(f,x))))))) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) -> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(f,a(f,a(g,a(g,a(f,a(g,a(g,x))))))) -> A(f,a(f,a(g,a(g,a(g,a(f,a(f,a(f,x)))))))) A(f,a(f,a(g,a(g,a(f,x4))))) -> A(f,a(f,x4)) A(f,a(f,a(g,a(g,a(f,x8))))) -> A(f,a(f,x8)) A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) ->->-> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) Problem 1: Reduction Pairs Processor: -> Pairs: A(f,a(f,a(g,a(g,a(f,a(g,a(g,x))))))) -> A(f,a(f,a(g,a(g,a(g,a(f,a(f,a(f,x)))))))) A(f,a(f,a(g,a(g,a(f,x4))))) -> A(f,a(f,x4)) A(f,a(f,a(g,a(g,a(f,x8))))) -> A(f,a(f,x8)) A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) -> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) -> Usable rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) ->Interpretation type: Simple mixed ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [a](X1,X2) = X1.X2 + 2.X1 [f] = 2 [g] = 1 [A](X1,X2) = 2.X1.X2 Problem 1: SCC Processor: -> Pairs: A(f,a(f,a(g,a(g,a(f,a(g,a(g,x))))))) -> A(f,a(f,a(g,a(g,a(g,a(f,a(f,a(f,x)))))))) A(f,a(f,a(g,a(g,a(f,x8))))) -> A(f,a(f,x8)) A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) -> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(f,a(f,a(g,a(g,a(f,a(g,a(g,x))))))) -> A(f,a(f,a(g,a(g,a(g,a(f,a(f,a(f,x)))))))) A(f,a(f,a(g,a(g,a(f,x8))))) -> A(f,a(f,x8)) A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) ->->-> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) Problem 1: Reduction Pairs Processor: -> Pairs: A(f,a(f,a(g,a(g,a(f,a(g,a(g,x))))))) -> A(f,a(f,a(g,a(g,a(g,a(f,a(f,a(f,x)))))))) A(f,a(f,a(g,a(g,a(f,x8))))) -> A(f,a(f,x8)) A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) -> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) -> Usable rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) ->Interpretation type: Simple mixed ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [a](X1,X2) = X1.X2 + 2.X1 [f] = 2 [g] = 1 [A](X1,X2) = X1.X2 Problem 1: SCC Processor: -> Pairs: A(f,a(f,a(g,a(g,a(f,a(g,a(g,x))))))) -> A(f,a(f,a(g,a(g,a(g,a(f,a(f,a(f,x)))))))) A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) -> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(f,a(f,a(g,a(g,a(f,a(g,a(g,x))))))) -> A(f,a(f,a(g,a(g,a(g,a(f,a(f,a(f,x)))))))) A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) ->->-> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) Problem 1: Reduction Pairs Processor: -> Pairs: A(f,a(f,a(g,a(g,a(f,a(g,a(g,x))))))) -> A(f,a(f,a(g,a(g,a(g,a(f,a(f,a(f,x)))))))) A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) A(f,a(f,a(g,a(g,x)))) -> A(f,a(f,x)) -> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) -> Usable rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) ->Interpretation type: Simple mixed ->Coefficients: Natural Numbers ->Dimension: 1 ->Bound: 2 ->Interpretation: [a](X1,X2) = X1.X2 + 2.X1 [f] = 2 [g] = 1 [A](X1,X2) = 2.X1.X2 Problem 1: SCC Processor: -> Pairs: A(f,a(f,a(g,a(g,a(f,a(g,a(g,x))))))) -> A(f,a(f,a(g,a(g,a(g,a(f,a(f,a(f,x)))))))) A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) -> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) ->->-> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) Problem 1: Subterm Processor: -> Pairs: A(f,a(f,a(g,a(g,a(f,x12))))) -> A(f,a(f,x12)) -> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) ->Projection: pi(A) = 2 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: a(f,a(f,a(g,a(g,x)))) -> a(g,a(g,a(g,a(f,a(f,a(f,x)))))) ->Strongly Connected Components: There is no strongly connected component The problem is finite.