/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR l x y) (RULES le(0,s(x)) -> true le(s(x),s(y)) -> le(x,y) le(x,0) -> false min(cons(x,nil)) -> x min(cons(x,l)) -> min(l) | le(x,min(l)) -> false min(cons(x,l)) -> min(l) | min(l) -> x min(cons(x,l)) -> x | le(x,min(l)) -> true ) Problem 1: Valid CTRS Processor: -> Rules: le(0,s(x)) -> true le(s(x),s(y)) -> le(x,y) le(x,0) -> false min(cons(x,nil)) -> x min(cons(x,l)) -> min(l) | le(x,min(l)) -> false min(cons(x,l)) -> min(l) | min(l) -> x min(cons(x,l)) -> x | le(x,min(l)) -> true -> The system is a deterministic 3-CTRS. Problem 1: Dependency Pairs Processor: Conditional Termination Problem 1: -> Pairs: LE(s(x),s(y)) -> LE(x,y) MIN(cons(x,l)) -> MIN(l) | le(x,min(l)) -> false MIN(cons(x,l)) -> MIN(l) | min(l) -> x -> QPairs: Empty -> Rules: le(0,s(x)) -> true le(s(x),s(y)) -> le(x,y) le(x,0) -> false min(cons(x,nil)) -> x min(cons(x,l)) -> min(l) | le(x,min(l)) -> false min(cons(x,l)) -> min(l) | min(l) -> x min(cons(x,l)) -> x | le(x,min(l)) -> true Conditional Termination Problem 2: -> Pairs: MIN(cons(x,l)) -> LE(x,min(l)) MIN(cons(x,l)) -> MIN(l) -> QPairs: LE(s(x),s(y)) -> LE(x,y) MIN(cons(x,l)) -> MIN(l) | le(x,min(l)) -> false MIN(cons(x,l)) -> MIN(l) | min(l) -> x -> Rules: le(0,s(x)) -> true le(s(x),s(y)) -> le(x,y) le(x,0) -> false min(cons(x,nil)) -> x min(cons(x,l)) -> min(l) | le(x,min(l)) -> false min(cons(x,l)) -> min(l) | min(l) -> x min(cons(x,l)) -> x | le(x,min(l)) -> true The problem is decomposed in 2 subproblems. Problem 1.1: SCC Processor: -> Pairs: LE(s(x),s(y)) -> LE(x,y) MIN(cons(x,l)) -> MIN(l) | le(x,min(l)) -> false MIN(cons(x,l)) -> MIN(l) | min(l) -> x -> QPairs: Empty -> Rules: le(0,s(x)) -> true le(s(x),s(y)) -> le(x,y) le(x,0) -> false min(cons(x,nil)) -> x min(cons(x,l)) -> min(l) | le(x,min(l)) -> false min(cons(x,l)) -> min(l) | min(l) -> x min(cons(x,l)) -> x | le(x,min(l)) -> true ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: MIN(cons(x,l)) -> MIN(l) | le(x,min(l)) -> false MIN(cons(x,l)) -> MIN(l) | min(l) -> x ->->-> Rules: le(0,s(x)) -> true le(s(x),s(y)) -> le(x,y) le(x,0) -> false min(cons(x,nil)) -> x min(cons(x,l)) -> min(l) | le(x,min(l)) -> false min(cons(x,l)) -> min(l) | min(l) -> x min(cons(x,l)) -> x | le(x,min(l)) -> true ->->Cycle: ->->-> Pairs: LE(s(x),s(y)) -> LE(x,y) ->->-> Rules: le(0,s(x)) -> true le(s(x),s(y)) -> le(x,y) le(x,0) -> false min(cons(x,nil)) -> x min(cons(x,l)) -> min(l) | le(x,min(l)) -> false min(cons(x,l)) -> min(l) | min(l) -> x min(cons(x,l)) -> x | le(x,min(l)) -> true The problem is decomposed in 2 subproblems. Problem 1.1.1: Conditional Subterm Processor: -> Pairs: MIN(cons(x,l)) -> MIN(l) | le(x,min(l)) -> false MIN(cons(x,l)) -> MIN(l) | min(l) -> x -> QPairs: Empty -> Rules: le(0,s(x)) -> true le(s(x),s(y)) -> le(x,y) le(x,0) -> false min(cons(x,nil)) -> x min(cons(x,l)) -> min(l) | le(x,min(l)) -> false min(cons(x,l)) -> min(l) | min(l) -> x min(cons(x,l)) -> x | le(x,min(l)) -> true ->Projection: pi(MIN) = 1 Problem 1.1.1: SCC Processor: -> Pairs: Empty -> QPairs: Empty -> Rules: le(0,s(x)) -> true le(s(x),s(y)) -> le(x,y) le(x,0) -> false min(cons(x,nil)) -> x min(cons(x,l)) -> min(l) | le(x,min(l)) -> false min(cons(x,l)) -> min(l) | min(l) -> x min(cons(x,l)) -> x | le(x,min(l)) -> true ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.1.2: Conditional Subterm Processor: -> Pairs: LE(s(x),s(y)) -> LE(x,y) -> QPairs: Empty -> Rules: le(0,s(x)) -> true le(s(x),s(y)) -> le(x,y) le(x,0) -> false min(cons(x,nil)) -> x min(cons(x,l)) -> min(l) | le(x,min(l)) -> false min(cons(x,l)) -> min(l) | min(l) -> x min(cons(x,l)) -> x | le(x,min(l)) -> true ->Projection: pi(LE) = 1 Problem 1.1.2: SCC Processor: -> Pairs: Empty -> QPairs: Empty -> Rules: le(0,s(x)) -> true le(s(x),s(y)) -> le(x,y) le(x,0) -> false min(cons(x,nil)) -> x min(cons(x,l)) -> min(l) | le(x,min(l)) -> false min(cons(x,l)) -> min(l) | min(l) -> x min(cons(x,l)) -> x | le(x,min(l)) -> true ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: SCC Processor: -> Pairs: MIN(cons(x,l)) -> LE(x,min(l)) MIN(cons(x,l)) -> MIN(l) -> QPairs: LE(s(x),s(y)) -> LE(x,y) MIN(cons(x,l)) -> MIN(l) | le(x,min(l)) -> false MIN(cons(x,l)) -> MIN(l) | min(l) -> x -> Rules: le(0,s(x)) -> true le(s(x),s(y)) -> le(x,y) le(x,0) -> false min(cons(x,nil)) -> x min(cons(x,l)) -> min(l) | le(x,min(l)) -> false min(cons(x,l)) -> min(l) | min(l) -> x min(cons(x,l)) -> x | le(x,min(l)) -> true ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: MIN(cons(x,l)) -> LE(x,min(l)) MIN(cons(x,l)) -> MIN(l) ->->-> Rules: le(0,s(x)) -> true le(s(x),s(y)) -> le(x,y) le(x,0) -> false min(cons(x,nil)) -> x min(cons(x,l)) -> min(l) | le(x,min(l)) -> false min(cons(x,l)) -> min(l) | min(l) -> x min(cons(x,l)) -> x | le(x,min(l)) -> true Problem 1.2: Conditional Subterm Processor: -> Pairs: MIN(cons(x,l)) -> LE(x,min(l)) MIN(cons(x,l)) -> MIN(l) -> QPairs: LE(s(x),s(y)) -> LE(x,y) MIN(cons(x,l)) -> MIN(l) | le(x,min(l)) -> false MIN(cons(x,l)) -> MIN(l) | min(l) -> x -> Rules: le(0,s(x)) -> true le(s(x),s(y)) -> le(x,y) le(x,0) -> false min(cons(x,nil)) -> x min(cons(x,l)) -> min(l) | le(x,min(l)) -> false min(cons(x,l)) -> min(l) | min(l) -> x min(cons(x,l)) -> x | le(x,min(l)) -> true ->Projection: pi(LE) = 1 pi(MIN) = 1 Problem 1.2: SCC Processor: -> Pairs: Empty -> QPairs: Empty -> Rules: le(0,s(x)) -> true le(s(x),s(y)) -> le(x,y) le(x,0) -> false min(cons(x,nil)) -> x min(cons(x,l)) -> min(l) | le(x,min(l)) -> false min(cons(x,l)) -> min(l) | min(l) -> x min(cons(x,l)) -> x | le(x,min(l)) -> true ->Strongly Connected Components: There is no strongly connected component The problem is finite.