/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 u x y z)
(RULES
a(b) -> c
f(a(x),y,s(z),u) -> f(a(b),y,z,g(x,y,s(z),u))
g(x,y,z,u) -> h(x,y,z,u)
h(b,y,z,u) -> f(y,y,z,u)
) 
(STRATEGY INNERMOST)

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(a(x),y,s(z),u) -> A(b)
 F(a(x),y,s(z),u) -> F(a(b),y,z,g(x,y,s(z),u))
 F(a(x),y,s(z),u) -> G(x,y,s(z),u)
 G(x,y,z,u) -> H(x,y,z,u)
 H(b,y,z,u) -> F(y,y,z,u)
-> Rules:
 a(b) -> c
 f(a(x),y,s(z),u) -> f(a(b),y,z,g(x,y,s(z),u))
 g(x,y,z,u) -> h(x,y,z,u)
 h(b,y,z,u) -> f(y,y,z,u)

Problem 1: 

SCC Processor:
-> Pairs:
 F(a(x),y,s(z),u) -> A(b)
 F(a(x),y,s(z),u) -> F(a(b),y,z,g(x,y,s(z),u))
 F(a(x),y,s(z),u) -> G(x,y,s(z),u)
 G(x,y,z,u) -> H(x,y,z,u)
 H(b,y,z,u) -> F(y,y,z,u)
-> Rules:
 a(b) -> c
 f(a(x),y,s(z),u) -> f(a(b),y,z,g(x,y,s(z),u))
 g(x,y,z,u) -> h(x,y,z,u)
 h(b,y,z,u) -> f(y,y,z,u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(a(x),y,s(z),u) -> F(a(b),y,z,g(x,y,s(z),u))
 F(a(x),y,s(z),u) -> G(x,y,s(z),u)
 G(x,y,z,u) -> H(x,y,z,u)
 H(b,y,z,u) -> F(y,y,z,u)
->->-> Rules:
 a(b) -> c
 f(a(x),y,s(z),u) -> f(a(b),y,z,g(x,y,s(z),u))
 g(x,y,z,u) -> h(x,y,z,u)
 h(b,y,z,u) -> f(y,y,z,u)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(a(x),y,s(z),u) -> F(a(b),y,z,g(x,y,s(z),u))
 F(a(x),y,s(z),u) -> G(x,y,s(z),u)
 G(x,y,z,u) -> H(x,y,z,u)
 H(b,y,z,u) -> F(y,y,z,u)
-> Rules:
 a(b) -> c
 f(a(x),y,s(z),u) -> f(a(b),y,z,g(x,y,s(z),u))
 g(x,y,z,u) -> h(x,y,z,u)
 h(b,y,z,u) -> f(y,y,z,u)
->Projection:
 pi(F) = 3
 pi(G) = 3
 pi(H) = 3

Problem 1: 

SCC Processor:
-> Pairs:
 F(a(x),y,s(z),u) -> G(x,y,s(z),u)
 G(x,y,z,u) -> H(x,y,z,u)
 H(b,y,z,u) -> F(y,y,z,u)
-> Rules:
 a(b) -> c
 f(a(x),y,s(z),u) -> f(a(b),y,z,g(x,y,s(z),u))
 g(x,y,z,u) -> h(x,y,z,u)
 h(b,y,z,u) -> f(y,y,z,u)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(a(x),y,s(z),u) -> G(x,y,s(z),u)
 G(x,y,z,u) -> H(x,y,z,u)
 H(b,y,z,u) -> F(y,y,z,u)
->->-> Rules:
 a(b) -> c
 f(a(x),y,s(z),u) -> f(a(b),y,z,g(x,y,s(z),u))
 g(x,y,z,u) -> h(x,y,z,u)
 h(b,y,z,u) -> f(y,y,z,u)

Problem 1: 

Forward Instantiation Processor:
-> Pairs:
 F(a(x),y,s(z),u) -> G(x,y,s(z),u)
 G(x,y,z,u) -> H(x,y,z,u)
 H(b,y,z,u) -> F(y,y,z,u)
-> Rules:
 a(b) -> c
 f(a(x),y,s(z),u) -> f(a(b),y,z,g(x,y,s(z),u))
 g(x,y,z,u) -> h(x,y,z,u)
 h(b,y,z,u) -> f(y,y,z,u)
->Instantiated Pairs:
->->Original Pair:
 G(x,y,z,u) -> H(x,y,z,u)
->-> Instantiated pairs:
 G(b,y,z,u) -> H(b,y,z,u)
->->Original Pair:
 H(b,y,z,u) -> F(y,y,z,u)
->-> Instantiated pairs:
 H(b,a(x8),s(x10),u) -> F(a(x8),a(x8),s(x10),u)

Problem 1: 

SCC Processor:
-> Pairs:
 F(a(x),y,s(z),u) -> G(x,y,s(z),u)
 G(b,y,z,u) -> H(b,y,z,u)
 H(b,a(x8),s(x10),u) -> F(a(x8),a(x8),s(x10),u)
-> Rules:
 a(b) -> c
 f(a(x),y,s(z),u) -> f(a(b),y,z,g(x,y,s(z),u))
 g(x,y,z,u) -> h(x,y,z,u)
 h(b,y,z,u) -> f(y,y,z,u)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.