/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 y z)
(RULES
f(x,y,z) -> g(<=(x,y),x,y,z)
g(false,x,y,z) -> f(f(p(x),y,z),f(p(y),z,x),f(p(z),x,y))
g(true,x,y,z) -> z
p(0) -> 0
p(s(x)) -> x
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(x,y,z) -> g(<=(x,y),x,y,z)
 g(false,x,y,z) -> f(f(p(x),y,z),f(p(y),z,x),f(p(z),x,y))
 g(true,x,y,z) -> z
 p(0) -> 0
 p(s(x)) -> x
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 G(false,x,y,z) -> F(f(p(x),y,z),f(p(y),z,x),f(p(z),x,y))
 G(false,x,y,z) -> F(p(x),y,z)
 G(false,x,y,z) -> F(p(y),z,x)
 G(false,x,y,z) -> F(p(z),x,y)
 G(false,x,y,z) -> P(x)
 G(false,x,y,z) -> P(y)
 G(false,x,y,z) -> P(z)
-> Rules:
 f(x,y,z) -> g(<=(x,y),x,y,z)
 g(false,x,y,z) -> f(f(p(x),y,z),f(p(y),z,x),f(p(z),x,y))
 g(true,x,y,z) -> z
 p(0) -> 0
 p(s(x)) -> x

Problem 1: 

SCC Processor:
-> Pairs:
 G(false,x,y,z) -> F(f(p(x),y,z),f(p(y),z,x),f(p(z),x,y))
 G(false,x,y,z) -> F(p(x),y,z)
 G(false,x,y,z) -> F(p(y),z,x)
 G(false,x,y,z) -> F(p(z),x,y)
 G(false,x,y,z) -> P(x)
 G(false,x,y,z) -> P(y)
 G(false,x,y,z) -> P(z)
-> Rules:
 f(x,y,z) -> g(<=(x,y),x,y,z)
 g(false,x,y,z) -> f(f(p(x),y,z),f(p(y),z,x),f(p(z),x,y))
 g(true,x,y,z) -> z
 p(0) -> 0
 p(s(x)) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.