/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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NO

Problem 1: 

(VAR v_NonEmpty:S x:S y:S z:S)
(RULES
between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
down(s(x:S)) -> down(x:S)
down(x:S) -> x:S
up(x:S) -> up(s(x:S))
up(x:S) -> x:S
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
 down(s(x:S)) -> down(x:S)
 down(x:S) -> x:S
 up(x:S) -> up(s(x:S))
 up(x:S) -> x:S
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 DOWN(s(x:S)) -> DOWN(x:S)
 UP(x:S) -> UP(s(x:S))
-> QPairs:
 Empty
-> Rules:
 between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
 down(s(x:S)) -> down(x:S)
 down(x:S) -> x:S
 up(x:S) -> up(s(x:S))
 up(x:S) -> x:S

Conditional Termination Problem 2:
-> Pairs:
 BETWEEN(x:S,y:S,z:S) -> DOWN(z:S) | up(x:S) ->* y:S
 BETWEEN(x:S,y:S,z:S) -> UP(x:S)
-> QPairs:
 DOWN(s(x:S)) -> DOWN(x:S)
 UP(x:S) -> UP(s(x:S))
-> Rules:
 between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
 down(s(x:S)) -> down(x:S)
 down(x:S) -> x:S
 up(x:S) -> up(s(x:S))
 up(x:S) -> x:S

Problem 1: 

SCC Processor:
-> Pairs:
 DOWN(s(x:S)) -> DOWN(x:S)
 UP(x:S) -> UP(s(x:S))
-> QPairs:
 Empty
-> Rules:
 between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
 down(s(x:S)) -> down(x:S)
 down(x:S) -> x:S
 up(x:S) -> up(s(x:S))
 up(x:S) -> x:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 UP(x:S) -> UP(s(x:S))
-> QPairs:
 Empty
->->-> Rules:
 between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
 down(s(x:S)) -> down(x:S)
 down(x:S) -> x:S
 up(x:S) -> up(s(x:S))
 up(x:S) -> x:S
->->Cycle:
->->-> Pairs:
 DOWN(s(x:S)) -> DOWN(x:S)
-> QPairs:
 Empty
->->-> Rules:
 between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
 down(s(x:S)) -> down(x:S)
 down(x:S) -> x:S
 up(x:S) -> up(s(x:S))
 up(x:S) -> x:S

Problem 1: 

Infinite Processor:
-> Pairs:
 UP(x:S) -> UP(s(x:S))
-> QPairs:
 Empty
-> Rules:
 between(x:S,y:S,z:S) -> ttrue | up(x:S) ->* y:S, down(z:S) ->* y:S
 down(s(x:S)) -> down(x:S)
 down(x:S) -> x:S
 up(x:S) -> up(s(x:S))
 up(x:S) -> x:S
-> Pairs in cycle:
 UP(x:S) -> UP(s(x:S))

The problem is infinite.