/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S x1:S x10:S x2:S x3:S x4:S x5:S x6:S x7:S x8:S x9:S) (RULES f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ) Problem 1: Innermost Equivalent Processor: -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: F(0,0,0,0,0,0,0,0,0,s(x10:S)) -> F(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) F(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> F(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) F(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> F(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> F(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) Problem 1: SCC Processor: -> Pairs: F(0,0,0,0,0,0,0,0,0,s(x10:S)) -> F(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) F(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> F(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) F(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> F(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> F(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(0,0,0,0,0,0,0,0,0,s(x10:S)) -> F(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) F(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> F(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) F(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> F(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> F(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->->-> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) Problem 1: Subterm Processor: -> Pairs: F(0,0,0,0,0,0,0,0,0,s(x10:S)) -> F(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) F(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> F(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) F(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> F(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> F(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Projection: pi(F) = 10 Problem 1: SCC Processor: -> Pairs: F(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> F(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) F(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> F(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> F(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> F(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) F(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> F(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> F(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->->-> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) Problem 1: Subterm Processor: -> Pairs: F(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> F(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) F(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> F(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> F(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Projection: pi(F) = 9 Problem 1: SCC Processor: -> Pairs: F(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> F(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> F(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> F(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> F(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->->-> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) Problem 1: Subterm Processor: -> Pairs: F(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> F(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> F(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Projection: pi(F) = 8 Problem 1: SCC Processor: -> Pairs: F(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> F(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> F(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->->-> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) Problem 1: Subterm Processor: -> Pairs: F(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> F(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Projection: pi(F) = 7 Problem 1: SCC Processor: -> Pairs: F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->->-> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) Problem 1: Subterm Processor: -> Pairs: F(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> F(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Projection: pi(F) = 6 Problem 1: SCC Processor: -> Pairs: F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->->-> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) Problem 1: Subterm Processor: -> Pairs: F(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Projection: pi(F) = 5 Problem 1: SCC Processor: -> Pairs: F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->->-> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) Problem 1: Subterm Processor: -> Pairs: F(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Projection: pi(F) = 4 Problem 1: SCC Processor: -> Pairs: F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->->-> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) Problem 1: Subterm Processor: -> Pairs: F(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Projection: pi(F) = 3 Problem 1: SCC Processor: -> Pairs: F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->->-> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) Problem 1: Subterm Processor: -> Pairs: F(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Projection: pi(F) = 2 Problem 1: SCC Processor: -> Pairs: F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->->-> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) Problem 1: Subterm Processor: -> Pairs: F(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Projection: pi(F) = 1 Problem 1: SCC Processor: -> Pairs: Empty -> Rules: f(0,0,0,0,0,0,0,0,0,0) -> 0 f(0,0,0,0,0,0,0,0,0,s(x10:S)) -> f(x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S,x10:S) f(0,0,0,0,0,0,0,0,s(x9:S),x10:S) -> f(x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x9:S,x10:S) f(0,0,0,0,0,0,0,s(x8:S),x9:S,x10:S) -> f(x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,0,s(x7:S),x8:S,x9:S,x10:S) -> f(x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,0,s(x6:S),x7:S,x8:S,x9:S,x10:S) -> f(x6:S,x6:S,x6:S,x6:S,x6:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,0,s(x5:S),x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x5:S,x5:S,x5:S,x5:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,0,s(x4:S),x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,0,s(x3:S),x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(0,s(x2:S),x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) f(s(x1:S),x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S,x6:S,x7:S,x8:S,x9:S,x10:S) ->Strongly Connected Components: There is no strongly connected component The problem is finite.