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TRS Equational pair #487523275
details
property
value
status
complete
benchmark
BAG_nosorts.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n141.star.cs.uiowa.edu
space
Mixed_AC
run statistics
property
value
solver
muterm 5.18
configuration
default
runtime (wallclock)
2.84073710442 seconds
cpu usage
2.719705544
max memory
1.3172736E7
stage attributes
key
value
output-size
104540
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 A B X Y) (THEORY (AC mult plus union)) (RULES 0(z) -> z and(tt,X) -> X mult(0(X),Y) -> 0(mult(X,Y)) mult(1(X),Y) -> plus(0(mult(X,Y)),Y) mult(z,X) -> z plus(0(X),0(Y)) -> 0(plus(X,Y)) plus(0(X),1(Y)) -> 1(plus(X,Y)) plus(1(X),1(Y)) -> 0(plus(plus(X,Y),1(z))) plus(z,X) -> X prod(union(A,B)) -> mult(prod(A),prod(B)) prod(empty) -> 1(z) prod(singl(X)) -> X sum(union(A,B)) -> plus(sum(A),sum(B)) sum(empty) -> 0(z) sum(singl(X)) -> X union(empty,X) -> X union(X,empty) -> X ) Problem 1: Dependency Pairs Processor: -> FAxioms: MULT(mult(x4,x5),x6) = MULT(x4,mult(x5,x6)) MULT(x4,x5) = MULT(x5,x4) PLUS(plus(x4,x5),x6) = PLUS(x4,plus(x5,x6)) PLUS(x4,x5) = PLUS(x5,x4) UNION(union(x4,x5),x6) = UNION(x4,union(x5,x6)) UNION(x4,x5) = UNION(x5,x4) -> Pairs: MULT(0(X),Y) -> 0#(mult(X,Y)) MULT(0(X),Y) -> MULT(X,Y) MULT(mult(0(X),Y),x4) -> 0#(mult(X,Y)) MULT(mult(0(X),Y),x4) -> MULT(0(mult(X,Y)),x4) MULT(mult(0(X),Y),x4) -> MULT(X,Y) MULT(mult(1(X),Y),x4) -> 0#(mult(X,Y)) MULT(mult(1(X),Y),x4) -> MULT(plus(0(mult(X,Y)),Y),x4) MULT(mult(1(X),Y),x4) -> MULT(X,Y) MULT(mult(1(X),Y),x4) -> PLUS(0(mult(X,Y)),Y) MULT(mult(z,X),x4) -> MULT(z,x4) MULT(1(X),Y) -> 0#(mult(X,Y)) MULT(1(X),Y) -> MULT(X,Y) MULT(1(X),Y) -> PLUS(0(mult(X,Y)),Y) PLUS(0(X),0(Y)) -> 0#(plus(X,Y)) PLUS(0(X),0(Y)) -> PLUS(X,Y) PLUS(0(X),1(Y)) -> PLUS(X,Y) PLUS(plus(0(X),0(Y)),x4) -> 0#(plus(X,Y)) PLUS(plus(0(X),0(Y)),x4) -> PLUS(0(plus(X,Y)),x4) PLUS(plus(0(X),0(Y)),x4) -> PLUS(X,Y) PLUS(plus(0(X),1(Y)),x4) -> PLUS(1(plus(X,Y)),x4) PLUS(plus(0(X),1(Y)),x4) -> PLUS(X,Y) PLUS(plus(1(X),1(Y)),x4) -> 0#(plus(plus(X,Y),1(z))) PLUS(plus(1(X),1(Y)),x4) -> PLUS(0(plus(plus(X,Y),1(z))),x4) PLUS(plus(1(X),1(Y)),x4) -> PLUS(plus(X,Y),1(z)) PLUS(plus(1(X),1(Y)),x4) -> PLUS(X,Y) PLUS(plus(z,X),x4) -> PLUS(X,x4) PLUS(1(X),1(Y)) -> 0#(plus(plus(X,Y),1(z))) PLUS(1(X),1(Y)) -> PLUS(plus(X,Y),1(z)) PLUS(1(X),1(Y)) -> PLUS(X,Y) PROD(union(A,B)) -> MULT(prod(A),prod(B)) PROD(union(A,B)) -> PROD(A) PROD(union(A,B)) -> PROD(B) SUM(union(A,B)) -> PLUS(sum(A),sum(B)) SUM(union(A,B)) -> SUM(A) SUM(union(A,B)) -> SUM(B) SUM(empty) -> 0#(z) UNION(union(empty,X),x4) -> UNION(X,x4) UNION(union(X,empty),x4) -> UNION(X,x4) -> EAxioms: mult(mult(x4,x5),x6) = mult(x4,mult(x5,x6)) mult(x4,x5) = mult(x5,x4) plus(plus(x4,x5),x6) = plus(x4,plus(x5,x6)) plus(x4,x5) = plus(x5,x4) union(union(x4,x5),x6) = union(x4,union(x5,x6)) union(x4,x5) = union(x5,x4) -> Rules: 0(z) -> z and(tt,X) -> X mult(0(X),Y) -> 0(mult(X,Y)) mult(1(X),Y) -> plus(0(mult(X,Y)),Y) mult(z,X) -> z plus(0(X),0(Y)) -> 0(plus(X,Y)) plus(0(X),1(Y)) -> 1(plus(X,Y)) plus(1(X),1(Y)) -> 0(plus(plus(X,Y),1(z))) plus(z,X) -> X prod(union(A,B)) -> mult(prod(A),prod(B))
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