TRS Standard pair #487069219

details

property	value
status	complete
benchmark	test4.xml
ran by	Akihisa Yamada
cpu timeout	1200 seconds
wallclock timeout	300 seconds
memory limit	137438953472 bytes
execution host	n185.star.cs.uiowa.edu
space	Rubio_04

run statistics

property	value
solver	muterm 6.0.3
configuration	default
runtime (wallclock)	0.0884829 seconds
cpu usage	0.072902
user time	0.030539
system time	0.042363
max virtual memory	113188.0
max residence set size	5448.0

stage attributes

key	value
starexec-result	YES

output

YES

Problem 1: 

(VAR v_NonEmpty:S X:S)
(RULES
f(a,a) -> f(a,b)
f(a,b) -> f(s(a),c)
f(c,c) -> f(a,a)
f(s(X:S),c) -> f(X:S,c)
)

Problem 1: 

Innermost Equivalent Processor:
-> Rules:
 f(a,a) -> f(a,b)
 f(a,b) -> f(s(a),c)
 f(c,c) -> f(a,a)
 f(s(X:S),c) -> f(X:S,c)
-> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination.
 

Problem 1: 

Dependency Pairs Processor:
-> Pairs:
 F(a,a) -> F(a,b)
 F(a,b) -> F(s(a),c)
 F(c,c) -> F(a,a)
 F(s(X:S),c) -> F(X:S,c)
-> Rules:
 f(a,a) -> f(a,b)
 f(a,b) -> f(s(a),c)
 f(c,c) -> f(a,a)
 f(s(X:S),c) -> f(X:S,c)

Problem 1: 

SCC Processor:
-> Pairs:
 F(a,a) -> F(a,b)
 F(a,b) -> F(s(a),c)
 F(c,c) -> F(a,a)
 F(s(X:S),c) -> F(X:S,c)
-> Rules:
 f(a,a) -> f(a,b)
 f(a,b) -> f(s(a),c)
 f(c,c) -> f(a,a)
 f(s(X:S),c) -> f(X:S,c)
->Strongly Connected Components:
->->Cycle:
->->-> Pairs:
 F(a,a) -> F(a,b)
 F(a,b) -> F(s(a),c)
 F(c,c) -> F(a,a)
 F(s(X:S),c) -> F(X:S,c)
->->-> Rules:
 f(a,a) -> f(a,b)
 f(a,b) -> f(s(a),c)
 f(c,c) -> f(a,a)
 f(s(X:S),c) -> f(X:S,c)

Problem 1: 

Reduction Pairs Processor:
-> Pairs:
 F(a,a) -> F(a,b)
 F(a,b) -> F(s(a),c)
 F(c,c) -> F(a,a)
 F(s(X:S),c) -> F(X:S,c)
-> Rules:
 f(a,a) -> f(a,b)
 f(a,b) -> f(s(a),c)
 f(c,c) -> f(a,a)
 f(s(X:S),c) -> f(X:S,c)
-> Usable rules:
 Empty
->Interpretation type:
 Linear
->Coefficients:
 Natural Numbers
->Dimension:
 1
->Bound:
 2
->Interpretation:
 
[f](X1,X2) = 0
[a] = 0
[b] = 2
[c] = 1
[fSNonEmpty] = 0
[s](X) = X
[F](X1,X2) = 2.X1

Problem 1: 

SCC Processor:
-> Pairs:

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