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TRS Standard pair #516967766
details
property
value
status
complete
benchmark
#4.23.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n136.star.cs.uiowa.edu
space
Strategy_removed_AG01
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.0810379981995 seconds
cpu usage
0.039605935
max memory
3358720.0
stage attributes
key
value
output-size
4989
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 z:S) (RULES plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) ) Problem 1: Innermost Equivalent Processor: -> Rules: plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) -> The term rewriting system is non-overlaping or locally confluent overlay system. Therefore, innermost termination implies termination. Problem 1: Dependency Pairs Processor: -> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S) QUOT(x:S,0,s(z:S)) -> PLUS(z:S,s(0)) QUOT(x:S,0,s(z:S)) -> QUOT(x:S,plus(z:S,s(0)),s(z:S)) -> Rules: plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) Problem 1: SCC Processor: -> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S) QUOT(x:S,0,s(z:S)) -> PLUS(z:S,s(0)) QUOT(x:S,0,s(z:S)) -> QUOT(x:S,plus(z:S,s(0)),s(z:S)) -> Rules: plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) ->->-> Rules: plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) ->->Cycle: ->->-> Pairs: QUOT(s(x:S),s(y:S),z:S) -> QUOT(x:S,y:S,z:S) QUOT(x:S,0,s(z:S)) -> QUOT(x:S,plus(z:S,s(0)),s(z:S)) ->->-> Rules: plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) The problem is decomposed in 2 subproblems. Problem 1.1: Subterm Processor: -> Pairs: PLUS(s(x:S),y:S) -> PLUS(x:S,y:S) -> Rules: plus(0,y:S) -> y:S plus(s(x:S),y:S) -> s(plus(x:S,y:S)) quot(0,s(y:S),s(z:S)) -> 0 quot(s(x:S),s(y:S),z:S) -> quot(x:S,y:S,z:S) quot(x:S,0,s(z:S)) -> s(quot(x:S,plus(z:S,s(0)),s(z:S))) ->Projection: pi(PLUS) = 1 Problem 1.1:
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