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TRS Innermost pair #487092992
details
property
value
status
complete
benchmark
#4.19.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n142.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0176409 seconds
cpu usage
0.018099
user time
0.006846
system time
0.011253
max virtual memory
113188.0
max residence set size
5192.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S z:S) (RULES f(c(x:S),x:S,y:S) -> c(y:S) f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S)) f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S)) g(x:S,y:S) -> x:S g(x:S,y:S) -> y:S ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: F(s(x:S),y:S,z:S) -> F(x:S,s(c(y:S)),c(z:S)) F(x:S,c(x:S),c(y:S)) -> F(y:S,x:S,y:S) F(x:S,c(x:S),c(y:S)) -> F(y:S,y:S,f(y:S,x:S,y:S)) -> Rules: f(c(x:S),x:S,y:S) -> c(y:S) f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S)) f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S)) g(x:S,y:S) -> x:S g(x:S,y:S) -> y:S Problem 1: SCC Processor: -> Pairs: F(s(x:S),y:S,z:S) -> F(x:S,s(c(y:S)),c(z:S)) F(x:S,c(x:S),c(y:S)) -> F(y:S,x:S,y:S) F(x:S,c(x:S),c(y:S)) -> F(y:S,y:S,f(y:S,x:S,y:S)) -> Rules: f(c(x:S),x:S,y:S) -> c(y:S) f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S)) f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S)) g(x:S,y:S) -> x:S g(x:S,y:S) -> y:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: F(s(x:S),y:S,z:S) -> F(x:S,s(c(y:S)),c(z:S)) ->->-> Rules: f(c(x:S),x:S,y:S) -> c(y:S) f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S)) f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S)) g(x:S,y:S) -> x:S g(x:S,y:S) -> y:S ->->Cycle: ->->-> Pairs: F(x:S,c(x:S),c(y:S)) -> F(y:S,x:S,y:S) ->->-> Rules: f(c(x:S),x:S,y:S) -> c(y:S) f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S)) f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S)) g(x:S,y:S) -> x:S g(x:S,y:S) -> y:S The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: F(s(x:S),y:S,z:S) -> F(x:S,s(c(y:S)),c(z:S)) -> Rules: f(c(x:S),x:S,y:S) -> c(y:S) f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S)) f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S)) g(x:S,y:S) -> x:S g(x:S,y:S) -> y:S ->Projection: pi(F) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: f(c(x:S),x:S,y:S) -> c(y:S) f(s(x:S),y:S,z:S) -> f(x:S,s(c(y:S)),c(z:S)) f(x:S,c(x:S),c(y:S)) -> f(y:S,y:S,f(y:S,x:S,y:S)) g(x:S,y:S) -> x:S g(x:S,y:S) -> y:S ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Subterm Processor: -> Pairs: F(x:S,c(x:S),c(y:S)) -> F(y:S,x:S,y:S) -> Rules:
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