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TRS Conditional pair #516978626
details
property
value
status
complete
benchmark
262.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n083.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0425570011139 seconds
cpu usage
0.019615999
max memory
1667072.0
stage attributes
key
value
output-size
2516
starexec-result
YES
output
/export/starexec/sandbox/solver/bin/starexec_run_default /export/starexec/sandbox/benchmark/theBenchmark.xml /export/starexec/sandbox/output/output_files -------------------------------------------------------------------------------- YES Problem 1: (VAR v_NonEmpty:S x:S y:S z:S z':S) (RULES f(x:S,y:S) -> z:S | plus(x:S,y:S) ->* plus(z:S,z':S) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> plus(x:S,s(y:S)) ) Problem 1: Valid CTRS Processor: -> Rules: f(x:S,y:S) -> z:S | plus(x:S,y:S) ->* plus(z:S,z':S) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> plus(x:S,s(y:S)) -> The system is a deterministic 3-CTRS. Problem 1: Dependency Pairs Processor: Conditional Termination Problem 1: -> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,s(y:S)) -> QPairs: Empty -> Rules: f(x:S,y:S) -> z:S | plus(x:S,y:S) ->* plus(z:S,z':S) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> plus(x:S,s(y:S)) Conditional Termination Problem 2: -> Pairs: F(x:S,y:S) -> PLUS(x:S,y:S) -> QPairs: PLUS(s(x:S),y:S) -> PLUS(x:S,s(y:S)) -> Rules: f(x:S,y:S) -> z:S | plus(x:S,y:S) ->* plus(z:S,z':S) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> plus(x:S,s(y:S)) The problem is decomposed in 2 subproblems. Problem 1.1: SCC Processor: -> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,s(y:S)) -> QPairs: Empty -> Rules: f(x:S,y:S) -> z:S | plus(x:S,y:S) ->* plus(z:S,z':S) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> plus(x:S,s(y:S)) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,s(y:S)) -> QPairs: Empty ->->-> Rules: f(x:S,y:S) -> z:S | plus(x:S,y:S) ->* plus(z:S,z':S) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> plus(x:S,s(y:S)) Problem 1.1: Conditional Subterm Processor: -> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,s(y:S)) -> QPairs: Empty -> Rules: f(x:S,y:S) -> z:S | plus(x:S,y:S) ->* plus(z:S,z':S) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> plus(x:S,s(y:S)) ->Projection: pi(PLUS) = 1 Problem 1.1: SCC Processor: -> Pairs: Empty -> QPairs: Empty -> Rules: f(x:S,y:S) -> z:S | plus(x:S,y:S) ->* plus(z:S,z':S) plus(0,y:S) -> y:S plus(s(x:S),y:S) -> plus(x:S,s(y:S)) ->Strongly Connected Components:
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