TRS Condi 20667 pair #381733208

details

property	value
status	complete
benchmark	364.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n088.star.cs.uiowa.edu
space	COPS

run statistics

property	value
solver	muterm 5.18
configuration	default
runtime (wallclock)	0.0161828994751 seconds
cpu usage	0.012736964
max memory	1396736.0

stage attributes

key	value
output-size	2215
starexec-result	YES

output

/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 x)
(RULES
even(0) -> true
even(s(x)) -> true | odd(x) -> true
odd(s(x)) -> true | even(x) -> true
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 even(0) -> true
 even(s(x)) -> true | odd(x) -> true
 odd(s(x)) -> true | even(x) -> true
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 even(0) -> true
 even(s(x)) -> true | odd(x) -> true
 odd(s(x)) -> true | even(x) -> true

Conditional Termination Problem 2:
-> Pairs:
 EVEN(s(x)) -> ODD(x)
 ODD(s(x)) -> EVEN(x)
-> QPairs:
 Empty
-> Rules:
 even(0) -> true
 even(s(x)) -> true | odd(x) -> true
 odd(s(x)) -> true | even(x) -> true


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 even(0) -> true
 even(s(x)) -> true | odd(x) -> true
 odd(s(x)) -> true | even(x) -> true
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 EVEN(s(x)) -> ODD(x)
 ODD(s(x)) -> EVEN(x)
-> QPairs:
 Empty
-> Rules:
 even(0) -> true
 even(s(x)) -> true | odd(x) -> true
 odd(s(x)) -> true | even(x) -> true
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 EVEN(s(x)) -> ODD(x)
 ODD(s(x)) -> EVEN(x)
->->-> Rules:
 even(0) -> true
 even(s(x)) -> true | odd(x) -> true
 odd(s(x)) -> true | even(x) -> true

Problem 1.2: 

Conditional Subterm Processor:
-> Pairs:
 EVEN(s(x)) -> ODD(x)
 ODD(s(x)) -> EVEN(x)
-> QPairs:
 Empty
-> Rules:

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