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TRS Innermost pair #487092986
details
property
value
status
complete
benchmark
#4.17.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)
36.7577 seconds
cpu usage
36.6037
user time
35.5443
system time
1.05936
max virtual memory
714904.0
max residence set size
7160.0
stage attributes
key
value
starexec-result
YES
output
YES Problem 1: (VAR v_NonEmpty:S x:S y:S) (RULES f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) g(0) -> 0 g(s(x:S)) -> s(g(x:S)) ) (STRATEGY INNERMOST) Problem 1: Dependency Pairs Processor: -> Pairs: F(g(x:S),s(0),y:S) -> F(g(s(0)),y:S,g(x:S)) F(g(x:S),s(0),y:S) -> G(s(0)) G(s(x:S)) -> G(x:S) -> Rules: f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) g(0) -> 0 g(s(x:S)) -> s(g(x:S)) Problem 1: SCC Processor: -> Pairs: F(g(x:S),s(0),y:S) -> F(g(s(0)),y:S,g(x:S)) F(g(x:S),s(0),y:S) -> G(s(0)) G(s(x:S)) -> G(x:S) -> Rules: f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) g(0) -> 0 g(s(x:S)) -> s(g(x:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: G(s(x:S)) -> G(x:S) ->->-> Rules: f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) g(0) -> 0 g(s(x:S)) -> s(g(x:S)) ->->Cycle: ->->-> Pairs: F(g(x:S),s(0),y:S) -> F(g(s(0)),y:S,g(x:S)) ->->-> Rules: f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) g(0) -> 0 g(s(x:S)) -> s(g(x:S)) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: G(s(x:S)) -> G(x:S) -> Rules: f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) g(0) -> 0 g(s(x:S)) -> s(g(x:S)) ->Projection: pi(G) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> Rules: f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) g(0) -> 0 g(s(x:S)) -> s(g(x:S)) ->Strongly Connected Components: There is no strongly connected component The problem is finite. Problem 1.2: Instantiation Processor: -> Pairs: F(g(x:S),s(0),y:S) -> F(g(s(0)),y:S,g(x:S)) -> Rules: f(g(x:S),s(0),y:S) -> f(g(s(0)),y:S,g(x:S)) g(0) -> 0 g(s(x:S)) -> s(g(x:S)) ->Instantiated Pairs: ->->Original Pair: F(g(x:S),s(0),y:S) -> F(g(s(0)),y:S,g(x:S)) ->-> Instantiated pairs: F(g(x:S),s(0),g(x4:S)) -> F(g(s(0)),g(x4:S),g(x:S)) Problem 1.2: SCC Processor: -> Pairs: F(g(x:S),s(0),g(x4:S)) -> F(g(s(0)),g(x4:S),g(x:S))
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