TRS Standard pair #487068399

details

property	value
status	complete
benchmark	polycounter-5.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	TCT_12

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0240359 seconds
cpu usage	0.024434
user time	0.012438
system time	0.011996
max virtual memory	113188.0
max residence set size	5932.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

(VAR v_NonEmpty:S x1:S x2:S x3:S x4:S x5:S)
(RULES
f(0,0,0,0,0) -> 0
f(0,0,0,0,s(x5:S)) -> f(x5:S,x5:S,x5:S,x5:S,x5:S)
f(0,0,0,s(x4:S),x5:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S)
f(0,0,s(x3:S),x4:S,x5:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S)
f(0,s(x2:S),x3:S,x4:S,x5:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S)
f(s(x1:S),x2:S,x3:S,x4:S,x5:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(0,0,0,0,0) -> 0
 f(0,0,0,0,s(x5:S)) -> f(x5:S,x5:S,x5:S,x5:S,x5:S)
 f(0,0,0,s(x4:S),x5:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S)
 f(0,0,s(x3:S),x4:S,x5:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S)
 f(0,s(x2:S),x3:S,x4:S,x5:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S)
 f(s(x1:S),x2:S,x3:S,x4:S,x5:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S)
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(0,0,0,0,s(x5:S)) -> F(x5:S,x5:S,x5:S,x5:S,x5:S)
 F(0,0,0,s(x4:S),x5:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S)
 F(0,0,s(x3:S),x4:S,x5:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S)
 F(0,s(x2:S),x3:S,x4:S,x5:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S)
 F(s(x1:S),x2:S,x3:S,x4:S,x5:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S)
-> Rules:
 f(0,0,0,0,0) -> 0
 f(0,0,0,0,s(x5:S)) -> f(x5:S,x5:S,x5:S,x5:S,x5:S)
 f(0,0,0,s(x4:S),x5:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S)
 f(0,0,s(x3:S),x4:S,x5:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S)
 f(0,s(x2:S),x3:S,x4:S,x5:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S)
 f(s(x1:S),x2:S,x3:S,x4:S,x5:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S)

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,0,0,0,s(x5:S)) -> F(x5:S,x5:S,x5:S,x5:S,x5:S)
 F(0,0,0,s(x4:S),x5:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S)
 F(0,0,s(x3:S),x4:S,x5:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S)
 F(0,s(x2:S),x3:S,x4:S,x5:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S)
 F(s(x1:S),x2:S,x3:S,x4:S,x5:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S)
-> Rules:
 f(0,0,0,0,0) -> 0
 f(0,0,0,0,s(x5:S)) -> f(x5:S,x5:S,x5:S,x5:S,x5:S)
 f(0,0,0,s(x4:S),x5:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S)
 f(0,0,s(x3:S),x4:S,x5:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S)
 f(0,s(x2:S),x3:S,x4:S,x5:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S)
 f(s(x1:S),x2:S,x3:S,x4:S,x5:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(0,0,0,0,s(x5:S)) -> F(x5:S,x5:S,x5:S,x5:S,x5:S)
 F(0,0,0,s(x4:S),x5:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S)
 F(0,0,s(x3:S),x4:S,x5:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S)
 F(0,s(x2:S),x3:S,x4:S,x5:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S)
 F(s(x1:S),x2:S,x3:S,x4:S,x5:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S)
->->-> Rules:
 f(0,0,0,0,0) -> 0
 f(0,0,0,0,s(x5:S)) -> f(x5:S,x5:S,x5:S,x5:S,x5:S)
 f(0,0,0,s(x4:S),x5:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S)
 f(0,0,s(x3:S),x4:S,x5:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S)
 f(0,s(x2:S),x3:S,x4:S,x5:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S)
 f(s(x1:S),x2:S,x3:S,x4:S,x5:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S)

Problem 1: 

Subterm Processor:
-> Pairs:
 F(0,0,0,0,s(x5:S)) -> F(x5:S,x5:S,x5:S,x5:S,x5:S)
 F(0,0,0,s(x4:S),x5:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S)
 F(0,0,s(x3:S),x4:S,x5:S) -> F(x3:S,x3:S,x3:S,x4:S,x5:S)
 F(0,s(x2:S),x3:S,x4:S,x5:S) -> F(x2:S,x2:S,x3:S,x4:S,x5:S)
 F(s(x1:S),x2:S,x3:S,x4:S,x5:S) -> F(x1:S,x2:S,x3:S,x4:S,x5:S)
-> Rules:
 f(0,0,0,0,0) -> 0
 f(0,0,0,0,s(x5:S)) -> f(x5:S,x5:S,x5:S,x5:S,x5:S)
 f(0,0,0,s(x4:S),x5:S) -> f(x4:S,x4:S,x4:S,x4:S,x5:S)
 f(0,0,s(x3:S),x4:S,x5:S) -> f(x3:S,x3:S,x3:S,x4:S,x5:S)
 f(0,s(x2:S),x3:S,x4:S,x5:S) -> f(x2:S,x2:S,x3:S,x4:S,x5:S)
 f(s(x1:S),x2:S,x3:S,x4:S,x5:S) -> f(x1:S,x2:S,x3:S,x4:S,x5:S)
->Projection:
 pi(F) = 5

Problem 1: 

SCC Processor:
-> Pairs:
 F(0,0,0,s(x4:S),x5:S) -> F(x4:S,x4:S,x4:S,x4:S,x5:S)

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