/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


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YES

Problem 1: 

(VAR x y z)
(RULES
minus(x,0) -> x
minus(x,s(y)) -> z | minus(x,y) -> s(z)
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 minus(x,0) -> x
 minus(x,s(y)) -> z | minus(x,y) -> s(z)
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 minus(x,0) -> x
 minus(x,s(y)) -> z | minus(x,y) -> s(z)

Conditional Termination Problem 2:
-> Pairs:
 MINUS(x,s(y)) -> MINUS(x,y)
-> QPairs:
 Empty
-> Rules:
 minus(x,0) -> x
 minus(x,s(y)) -> z | minus(x,y) -> s(z)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 minus(x,0) -> x
 minus(x,s(y)) -> z | minus(x,y) -> s(z)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 MINUS(x,s(y)) -> MINUS(x,y)
-> QPairs:
 Empty
-> Rules:
 minus(x,0) -> x
 minus(x,s(y)) -> z | minus(x,y) -> s(z)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 MINUS(x,s(y)) -> MINUS(x,y)
->->-> Rules:
 minus(x,0) -> x
 minus(x,s(y)) -> z | minus(x,y) -> s(z)

Problem 1.2: 

Conditional Subterm Processor:
-> Pairs:
 MINUS(x,s(y)) -> MINUS(x,y)
-> QPairs:
 Empty
-> Rules:
 minus(x,0) -> x
 minus(x,s(y)) -> z | minus(x,y) -> s(z)
->Projection:
 pi(MINUS) = 2

Problem 1.2: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 minus(x,0) -> x
 minus(x,s(y)) -> z | minus(x,y) -> s(z)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.