TRS Condi 20667 pair #381733066

details

property	value
status	complete
benchmark	plus1.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n003.star.cs.uiowa.edu
space	Mixed_CTRS_2014

run statistics

property	value
solver	muterm 5.18
configuration	default
runtime (wallclock)	0.016529083252 seconds
cpu usage	0.013257065
max memory	1495040.0

stage attributes

key	value
output-size	1958
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 x y z)
(RULES
plus(0,x) -> x
plus(s(x),y) -> s(z) | plus(x,y) -> z
plus(x,0) -> x
)

Problem 1: 
Valid CTRS Processor:
-> Rules:
 plus(0,x) -> x
 plus(s(x),y) -> s(z) | plus(x,y) -> z
 plus(x,0) -> x
-> The system is a deterministic 3-CTRS.

Problem 1: 

Dependency Pairs Processor:

Conditional Termination Problem 1:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 plus(0,x) -> x
 plus(s(x),y) -> s(z) | plus(x,y) -> z
 plus(x,0) -> x

Conditional Termination Problem 2:
-> Pairs:
 PLUS(s(x),y) -> PLUS(x,y)
-> QPairs:
 Empty
-> Rules:
 plus(0,x) -> x
 plus(s(x),y) -> s(z) | plus(x,y) -> z
 plus(x,0) -> x


The problem is decomposed in 2 subproblems.

Problem 1.1: 

SCC Processor:
-> Pairs:
 Empty
-> QPairs:
 Empty
-> Rules:
 plus(0,x) -> x
 plus(s(x),y) -> s(z) | plus(x,y) -> z
 plus(x,0) -> x
->Strongly Connected Components:
 There is no strongly connected component

The problem is finite.

Problem 1.2: 

SCC Processor:
-> Pairs:
 PLUS(s(x),y) -> PLUS(x,y)
-> QPairs:
 Empty
-> Rules:
 plus(0,x) -> x
 plus(s(x),y) -> s(z) | plus(x,y) -> z
 plus(x,0) -> x
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 PLUS(s(x),y) -> PLUS(x,y)
->->-> Rules:
 plus(0,x) -> x
 plus(s(x),y) -> s(z) | plus(x,y) -> z
 plus(x,0) -> x

Problem 1.2: 

Conditional Subterm Processor:
-> Pairs:
 PLUS(s(x),y) -> PLUS(x,y)
-> QPairs:
 Empty
-> Rules:
 plus(0,x) -> x
 plus(s(x),y) -> s(z) | plus(x,y) -> z
 plus(x,0) -> x
->Projection:

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