/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 v_NonEmpty:S x:S y:S z:S)
(RULES
f(x:S) -> g(x:S,y:S,z:S) | h(a,x:S) ->* i(y:S), h(a,y:S) ->* i(z:S)
h(a,a) -> i(b)
h(a,b) -> i(c)
h(b,b) -> i(d)
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 f(x:S) -> g(x:S,y:S,z:S) | h(a,x:S) ->* i(y:S), h(a,y:S) ->* i(z:S)
 h(a,a) -> i(b)
 h(a,b) -> i(c)
 h(b,b) -> i(d)
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 f(x:S) -> g(x:S,y:S,z:S) | h(a,x:S) ->* i(y:S), h(a,y:S) ->* i(z:S)
 h(a,a) -> i(b)
 h(a,b) -> i(c)
 h(b,b) -> i(d)

Conditional Termination Problem 2:
-> Pairs:
 F(x:S) -> H(a,x:S)
 F(x:S) -> H(a,y:S) | h(a,x:S) ->* i(y:S)
-> QPairs:
 Empty
-> Rules:
 f(x:S) -> g(x:S,y:S,z:S) | h(a,x:S) ->* i(y:S), h(a,y:S) ->* i(z:S)
 h(a,a) -> i(b)
 h(a,b) -> i(c)
 h(b,b) -> i(d)


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 f(x:S) -> g(x:S,y:S,z:S) | h(a,x:S) ->* i(y:S), h(a,y:S) ->* i(z:S)
 h(a,a) -> i(b)
 h(a,b) -> i(c)
 h(b,b) -> i(d)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 F(x:S) -> H(a,x:S)
 F(x:S) -> H(a,y:S) | h(a,x:S) ->* i(y:S)
-> QPairs:
 Empty
-> Rules:
 f(x:S) -> g(x:S,y:S,z:S) | h(a,x:S) ->* i(y:S), h(a,y:S) ->* i(z:S)
 h(a,a) -> i(b)
 h(a,b) -> i(c)
 h(b,b) -> i(d)
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.