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TRS Innermost pair #487524026
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
n146.star.cs.uiowa.edu
space
AG01_innermost
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
36.7949888706 seconds
cpu usage
49.254981352
max memory
1.6355328E7
stage attributes
key
value
output-size
2294
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 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))
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