/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 u x y z)
(RULES
f(0,y,0,u) -> true
f(0,y,s(z),u) -> false
f(s(x),0,z,u) -> f(x,u,minus(z,s(x)),u)
f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
perfectp(0) -> false
perfectp(s(x)) -> f(x,s(0),s(x),s(x))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(0,y,0,u) -> true
 f(0,y,s(z),u) -> false
 f(s(x),0,z,u) -> f(x,u,minus(z,s(x)),u)
 f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
 perfectp(0) -> false
 perfectp(s(x)) -> f(x,s(0),s(x),s(x))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(s(x),0,z,u) -> F(x,u,minus(z,s(x)),u)
 F(s(x),s(y),z,u) -> F(x,u,z,u)
 PERFECTP(s(x)) -> F(x,s(0),s(x),s(x))
-> Rules:
 f(0,y,0,u) -> true
 f(0,y,s(z),u) -> false
 f(s(x),0,z,u) -> f(x,u,minus(z,s(x)),u)
 f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
 perfectp(0) -> false
 perfectp(s(x)) -> f(x,s(0),s(x),s(x))

Problem 1: 

SCC Processor:
-> Pairs:
 F(s(x),0,z,u) -> F(x,u,minus(z,s(x)),u)
 F(s(x),s(y),z,u) -> F(x,u,z,u)
 PERFECTP(s(x)) -> F(x,s(0),s(x),s(x))
-> Rules:
 f(0,y,0,u) -> true
 f(0,y,s(z),u) -> false
 f(s(x),0,z,u) -> f(x,u,minus(z,s(x)),u)
 f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
 perfectp(0) -> false
 perfectp(s(x)) -> f(x,s(0),s(x),s(x))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(s(x),0,z,u) -> F(x,u,minus(z,s(x)),u)
 F(s(x),s(y),z,u) -> F(x,u,z,u)
->->-> Rules:
 f(0,y,0,u) -> true
 f(0,y,s(z),u) -> false
 f(s(x),0,z,u) -> f(x,u,minus(z,s(x)),u)
 f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
 perfectp(0) -> false
 perfectp(s(x)) -> f(x,s(0),s(x),s(x))

Problem 1: 

Subterm Processor:
-> Pairs:
 F(s(x),0,z,u) -> F(x,u,minus(z,s(x)),u)
 F(s(x),s(y),z,u) -> F(x,u,z,u)
-> Rules:
 f(0,y,0,u) -> true
 f(0,y,s(z),u) -> false
 f(s(x),0,z,u) -> f(x,u,minus(z,s(x)),u)
 f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
 perfectp(0) -> false
 perfectp(s(x)) -> f(x,s(0),s(x),s(x))
->Projection:
 pi(F) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 f(0,y,0,u) -> true
 f(0,y,s(z),u) -> false
 f(s(x),0,z,u) -> f(x,u,minus(z,s(x)),u)
 f(s(x),s(y),z,u) -> if(le(x,y),f(s(x),minus(y,x),z,u),f(x,u,z,u))
 perfectp(0) -> false
 perfectp(s(x)) -> f(x,s(0),s(x),s(x))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.