/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 x)
(RULES
e(0) -> true
e(s(x)) -> false | e(x) -> true
e(s(x)) -> true | o(x) -> true
o(0) -> true
o(s(x)) -> false | o(x) -> true
o(s(x)) -> true | e(x) -> true
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 e(0) -> true
 e(s(x)) -> false | e(x) -> true
 e(s(x)) -> true | o(x) -> true
 o(0) -> true
 o(s(x)) -> false | o(x) -> true
 o(s(x)) -> true | e(x) -> true
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 e(0) -> true
 e(s(x)) -> false | e(x) -> true
 e(s(x)) -> true | o(x) -> true
 o(0) -> true
 o(s(x)) -> false | o(x) -> true
 o(s(x)) -> true | e(x) -> true

Conditional Termination Problem 2:
-> Pairs:
 E(s(x)) -> E(x)
 E(s(x)) -> O(x)
 O(s(x)) -> E(x)
 O(s(x)) -> O(x)
-> QPairs:
 Empty
-> Rules:
 e(0) -> true
 e(s(x)) -> false | e(x) -> true
 e(s(x)) -> true | o(x) -> true
 o(0) -> true
 o(s(x)) -> false | o(x) -> true
 o(s(x)) -> true | e(x) -> true


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 e(0) -> true
 e(s(x)) -> false | e(x) -> true
 e(s(x)) -> true | o(x) -> true
 o(0) -> true
 o(s(x)) -> false | o(x) -> true
 o(s(x)) -> true | e(x) -> true
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 E(s(x)) -> E(x)
 E(s(x)) -> O(x)
 O(s(x)) -> E(x)
 O(s(x)) -> O(x)
-> QPairs:
 Empty
-> Rules:
 e(0) -> true
 e(s(x)) -> false | e(x) -> true
 e(s(x)) -> true | o(x) -> true
 o(0) -> true
 o(s(x)) -> false | o(x) -> true
 o(s(x)) -> true | e(x) -> true
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 E(s(x)) -> E(x)
 E(s(x)) -> O(x)
 O(s(x)) -> E(x)
 O(s(x)) -> O(x)
->->-> Rules:
 e(0) -> true
 e(s(x)) -> false | e(x) -> true
 e(s(x)) -> true | o(x) -> true
 o(0) -> true
 o(s(x)) -> false | o(x) -> true
 o(s(x)) -> true | e(x) -> true

Problem 1.2: 

Conditional Subterm Processor:
-> Pairs:
 E(s(x)) -> E(x)
 E(s(x)) -> O(x)
 O(s(x)) -> E(x)
 O(s(x)) -> O(x)
-> QPairs:
 Empty
-> Rules:
 e(0) -> true
 e(s(x)) -> false | e(x) -> true
 e(s(x)) -> true | o(x) -> true
 o(0) -> true
 o(s(x)) -> false | o(x) -> true
 o(s(x)) -> true | e(x) -> true
->Projection:
 pi(E) = 1
 pi(O) = 1

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 e(0) -> true
 e(s(x)) -> false | e(x) -> true
 e(s(x)) -> true | o(x) -> true
 o(0) -> true
 o(s(x)) -> false | o(x) -> true
 o(s(x)) -> true | e(x) -> true
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.