/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files


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NO

Problem 1: 

(VAR v_NonEmpty:S x:S y:S)
(RULES
b -> b
f(x:S,y:S) -> g(x:S) | c(g(x:S)) ->* c(a)
f(x:S,y:S) -> h(x:S) | c(h(x:S)) ->* c(a)
g(s(x:S)) -> x:S
h(s(x:S)) -> x:S
)

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

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 B -> B
 F(x:S,y:S) -> G(x:S) | c(g(x:S)) ->* c(a)
 F(x:S,y:S) -> H(x:S) | c(h(x:S)) ->* c(a)
-> QPairs:
 Empty
-> Rules:
 b -> b
 f(x:S,y:S) -> g(x:S) | c(g(x:S)) ->* c(a)
 f(x:S,y:S) -> h(x:S) | c(h(x:S)) ->* c(a)
 g(s(x:S)) -> x:S
 h(s(x:S)) -> x:S

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

Problem 1: 

SCC Processor:
-> Pairs:
 B -> B
 F(x:S,y:S) -> G(x:S) | c(g(x:S)) ->* c(a)
 F(x:S,y:S) -> H(x:S) | c(h(x:S)) ->* c(a)
-> QPairs:
 Empty
-> Rules:
 b -> b
 f(x:S,y:S) -> g(x:S) | c(g(x:S)) ->* c(a)
 f(x:S,y:S) -> h(x:S) | c(h(x:S)) ->* c(a)
 g(s(x:S)) -> x:S
 h(s(x:S)) -> x:S
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 B -> B
-> QPairs:
 Empty
->->-> Rules:
 b -> b
 f(x:S,y:S) -> g(x:S) | c(g(x:S)) ->* c(a)
 f(x:S,y:S) -> h(x:S) | c(h(x:S)) ->* c(a)
 g(s(x:S)) -> x:S
 h(s(x:S)) -> x:S

Problem 1: 

Infinite Processor:
-> Pairs:
 B -> B
-> QPairs:
 Empty
-> Rules:
 b -> b
 f(x:S,y:S) -> g(x:S) | c(g(x:S)) ->* c(a)
 f(x:S,y:S) -> h(x:S) | c(h(x:S)) ->* c(a)
 g(s(x:S)) -> x:S
 h(s(x:S)) -> x:S
-> Pairs in cycle:
 B -> B

The problem is infinite.