TRS Standard pair #516966826

details

property	value
status	complete
benchmark	2.24.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n175.star.cs.uiowa.edu
space	SK90

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0947241783142 seconds
cpu usage	0.018178365
max memory	1540096.0

stage attributes

key	value
output-size	1664
starexec-result	YES

output

/export/starexec/sandbox2/solver/bin/starexec_run_default /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files


--------------------------------------------------------------------------------


YES

Problem 1: 

(VAR v_NonEmpty:S x:S)
(RULES
fib(0) -> 0
fib(s(0)) -> s(0)
fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S))
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 fib(0) -> 0
 fib(s(0)) -> s(0)
 fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S))
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 FIB(s(s(x:S))) -> FIB(s(x:S))
 FIB(s(s(x:S))) -> FIB(x:S)
-> Rules:
 fib(0) -> 0
 fib(s(0)) -> s(0)
 fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S))

Problem 1: 

SCC Processor:
-> Pairs:
 FIB(s(s(x:S))) -> FIB(s(x:S))
 FIB(s(s(x:S))) -> FIB(x:S)
-> Rules:
 fib(0) -> 0
 fib(s(0)) -> s(0)
 fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S))
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 FIB(s(s(x:S))) -> FIB(s(x:S))
 FIB(s(s(x:S))) -> FIB(x:S)
->->-> Rules:
 fib(0) -> 0
 fib(s(0)) -> s(0)
 fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S))

Problem 1: 

Subterm Processor:
-> Pairs:
 FIB(s(s(x:S))) -> FIB(s(x:S))
 FIB(s(s(x:S))) -> FIB(x:S)
-> Rules:
 fib(0) -> 0
 fib(s(0)) -> s(0)
 fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S))
->Projection:
 pi(FIB) = 1

Problem 1: 

SCC Processor:
-> Pairs:
 Empty
-> Rules:
 fib(0) -> 0
 fib(s(0)) -> s(0)
 fib(s(s(x:S))) -> +(fib(s(x:S)),fib(x:S))
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

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