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


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YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
pos(0) -> ffalse
pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse
pos(s(0)) -> ttrue
pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 pos(0) -> ffalse
 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse
 pos(s(0)) -> ttrue
 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 pos(0) -> ffalse
 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse
 pos(s(0)) -> ttrue
 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue

Conditional Termination Problem 2:
-> Pairs:
 POS(p(x:S)) -> POS(x:S)
 POS(s(x:S)) -> POS(x:S)
-> QPairs:
 Empty
-> Rules:
 pos(0) -> ffalse
 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse
 pos(s(0)) -> ttrue
 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 pos(0) -> ffalse
 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse
 pos(s(0)) -> ttrue
 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 POS(p(x:S)) -> POS(x:S)
 POS(s(x:S)) -> POS(x:S)
-> QPairs:
 Empty
-> Rules:
 pos(0) -> ffalse
 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse
 pos(s(0)) -> ttrue
 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 POS(p(x:S)) -> POS(x:S)
 POS(s(x:S)) -> POS(x:S)
-> QPairs:
 Empty
->->-> Rules:
 pos(0) -> ffalse
 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse
 pos(s(0)) -> ttrue
 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue

Problem 1.2: 

Conditional Subterm Processor:
-> Pairs:
 POS(p(x:S)) -> POS(x:S)
 POS(s(x:S)) -> POS(x:S)
-> QPairs:
 Empty
-> Rules:
 pos(0) -> ffalse
 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse
 pos(s(0)) -> ttrue
 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue
->Projection:
 pi(POS) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 pos(0) -> ffalse
 pos(p(x:S)) -> ffalse | pos(x:S) ->* ffalse
 pos(s(0)) -> ttrue
 pos(s(x:S)) -> ttrue | pos(x:S) ->* ttrue
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.