TRS Conditional pair #516978664

details

property	value
status	complete
benchmark	403.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n168.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.062371969223 seconds
cpu usage	0.018527965
max memory	1531904.0

stage attributes

key	value
output-size	2176
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
e(0) -> ttrue
e(s(x:S)) -> ffalse | e(x:S) ->* ttrue
e(s(x:S)) -> ttrue | e(x:S) ->* ffalse
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 e(0) -> ttrue
 e(s(x:S)) -> ffalse | e(x:S) ->* ttrue
 e(s(x:S)) -> ttrue | e(x:S) ->* ffalse
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 e(0) -> ttrue
 e(s(x:S)) -> ffalse | e(x:S) ->* ttrue
 e(s(x:S)) -> ttrue | e(x:S) ->* ffalse

Conditional Termination Problem 2:
-> Pairs:
 E(s(x:S)) -> E(x:S)
-> QPairs:
 Empty
-> Rules:
 e(0) -> ttrue
 e(s(x:S)) -> ffalse | e(x:S) ->* ttrue
 e(s(x:S)) -> ttrue | e(x:S) ->* ffalse


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 e(0) -> ttrue
 e(s(x:S)) -> ffalse | e(x:S) ->* ttrue
 e(s(x:S)) -> ttrue | e(x:S) ->* ffalse
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 E(s(x:S)) -> E(x:S)
-> QPairs:
 Empty
-> Rules:
 e(0) -> ttrue
 e(s(x:S)) -> ffalse | e(x:S) ->* ttrue
 e(s(x:S)) -> ttrue | e(x:S) ->* ffalse
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 E(s(x:S)) -> E(x:S)
-> QPairs:
 Empty
->->-> Rules:
 e(0) -> ttrue
 e(s(x:S)) -> ffalse | e(x:S) ->* ttrue
 e(s(x:S)) -> ttrue | e(x:S) ->* ffalse

Problem 1.2: 

Conditional Subterm Processor:
-> Pairs:
 E(s(x:S)) -> E(x:S)
-> QPairs:
 Empty
-> Rules:
 e(0) -> ttrue
 e(s(x:S)) -> ffalse | e(x:S) ->* ttrue

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