/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
quot(0,s(y),s(z)) -> 0
quot(s(x),s(y),z) -> quot(x,y,z)
quot(x,0,s(z)) -> s(quot(x,s(z),s(z)))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 quot(0,s(y),s(z)) -> 0
 quot(s(x),s(y),z) -> quot(x,y,z)
 quot(x,0,s(z)) -> s(quot(x,s(z),s(z)))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 QUOT(s(x),s(y),z) -> QUOT(x,y,z)
 QUOT(x,0,s(z)) -> QUOT(x,s(z),s(z))
-> Rules:
 quot(0,s(y),s(z)) -> 0
 quot(s(x),s(y),z) -> quot(x,y,z)
 quot(x,0,s(z)) -> s(quot(x,s(z),s(z)))

Problem 1: 

SCC Processor:
-> Pairs:
 QUOT(s(x),s(y),z) -> QUOT(x,y,z)
 QUOT(x,0,s(z)) -> QUOT(x,s(z),s(z))
-> Rules:
 quot(0,s(y),s(z)) -> 0
 quot(s(x),s(y),z) -> quot(x,y,z)
 quot(x,0,s(z)) -> s(quot(x,s(z),s(z)))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 QUOT(s(x),s(y),z) -> QUOT(x,y,z)
 QUOT(x,0,s(z)) -> QUOT(x,s(z),s(z))
->->-> Rules:
 quot(0,s(y),s(z)) -> 0
 quot(s(x),s(y),z) -> quot(x,y,z)
 quot(x,0,s(z)) -> s(quot(x,s(z),s(z)))

Problem 1: 

Subterm Processor:
-> Pairs:
 QUOT(s(x),s(y),z) -> QUOT(x,y,z)
 QUOT(x,0,s(z)) -> QUOT(x,s(z),s(z))
-> Rules:
 quot(0,s(y),s(z)) -> 0
 quot(s(x),s(y),z) -> quot(x,y,z)
 quot(x,0,s(z)) -> s(quot(x,s(z),s(z)))
->Projection:
 pi(QUOT) = 1

Problem 1: 

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

The problem is finite.