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TRS Conditional pair #487562819
details
property
value
status
complete
benchmark
388.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n149.star.cs.uiowa.edu
space
COPS
run statistics
property
value
solver
muterm 6.0.3
configuration
default
runtime (wallclock)
0.050726890564 seconds
cpu usage
0.018929006
max memory
1654784.0
stage attributes
key
value
output-size
2630
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) (RULES add(x:S,0) -> x:S add(x:S,s(y:S)) -> s(add(x:S,y:S)) quad(x:S) -> z:S | add(x:S,x:S) ->* y:S, add(y:S,y:S) ->* z:S ) Problem 1: Valid CTRS Processor: -> Rules: add(x:S,0) -> x:S add(x:S,s(y:S)) -> s(add(x:S,y:S)) quad(x:S) -> z:S | add(x:S,x:S) ->* y:S, add(y:S,y:S) ->* z:S -> The system is a deterministic 3-CTRS. Problem 1: Dependency Pairs Processor: Conditional Termination Problem 1: -> Pairs: ADD(x:S,s(y:S)) -> ADD(x:S,y:S) -> QPairs: Empty -> Rules: add(x:S,0) -> x:S add(x:S,s(y:S)) -> s(add(x:S,y:S)) quad(x:S) -> z:S | add(x:S,x:S) ->* y:S, add(y:S,y:S) ->* z:S Conditional Termination Problem 2: -> Pairs: QUAD(x:S) -> ADD(x:S,x:S) QUAD(x:S) -> ADD(y:S,y:S) | add(x:S,x:S) ->* y:S -> QPairs: ADD(x:S,s(y:S)) -> ADD(x:S,y:S) -> Rules: add(x:S,0) -> x:S add(x:S,s(y:S)) -> s(add(x:S,y:S)) quad(x:S) -> z:S | add(x:S,x:S) ->* y:S, add(y:S,y:S) ->* z:S The problem is decomposed in 2 subproblems. Problem 1.1: SCC Processor: -> Pairs: ADD(x:S,s(y:S)) -> ADD(x:S,y:S) -> QPairs: Empty -> Rules: add(x:S,0) -> x:S add(x:S,s(y:S)) -> s(add(x:S,y:S)) quad(x:S) -> z:S | add(x:S,x:S) ->* y:S, add(y:S,y:S) ->* z:S ->Strongly Connected Components: ->->Cycle: ->->-> Pairs: ADD(x:S,s(y:S)) -> ADD(x:S,y:S) -> QPairs: Empty ->->-> Rules: add(x:S,0) -> x:S add(x:S,s(y:S)) -> s(add(x:S,y:S)) quad(x:S) -> z:S | add(x:S,x:S) ->* y:S, add(y:S,y:S) ->* z:S Problem 1.1: Conditional Subterm Processor: -> Pairs: ADD(x:S,s(y:S)) -> ADD(x:S,y:S) -> QPairs: Empty -> Rules: add(x:S,0) -> x:S add(x:S,s(y:S)) -> s(add(x:S,y:S)) quad(x:S) -> z:S | add(x:S,x:S) ->* y:S, add(y:S,y:S) ->* z:S ->Projection: pi(ADD) = 2 Problem 1.1: SCC Processor: -> Pairs: Empty -> QPairs: Empty -> Rules: add(x:S,0) -> x:S add(x:S,s(y:S)) -> s(add(x:S,y:S)) quad(x:S) -> z:S | add(x:S,x:S) ->* y:S, add(y:S,y:S) ->* z:S
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