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TRS Stand 20472 pair #381716485
details
property
value
status
complete
benchmark
PEANO_complete_GM.xml
ran by
Akihisa Yamada
cpu timeout
1200 seconds
wallclock timeout
300 seconds
memory limit
137438953472 bytes
execution host
n053.star.cs.uiowa.edu
space
Transformed_CSR_04
run statistics
property
value
solver
Wanda
configuration
FirstOrder
runtime (wallclock)
3.45523500443 seconds
cpu usage
3.451350223
max memory
8.4586496E7
stage attributes
key
value
output-size
79394
starexec-result
YES
output
/export/starexec/sandbox2/solver/bin/starexec_run_FirstOrder /export/starexec/sandbox2/benchmark/theBenchmark.xml /export/starexec/sandbox2/output/output_files -------------------------------------------------------------------------------- YES We consider the system theBenchmark. We are asked to determine termination of the following first-order TRS. 0 : [] --> o U11 : [o * o * o] --> o U12 : [o * o] --> o U13 : [o] --> o U21 : [o * o] --> o U22 : [o] --> o U31 : [o * o] --> o U41 : [o * o * o] --> o a!6220!6220U11 : [o * o * o] --> o a!6220!6220U12 : [o * o] --> o a!6220!6220U13 : [o] --> o a!6220!6220U21 : [o * o] --> o a!6220!6220U22 : [o] --> o a!6220!6220U31 : [o * o] --> o a!6220!6220U41 : [o * o * o] --> o a!6220!6220and : [o * o] --> o a!6220!6220isNat : [o] --> o a!6220!6220isNatKind : [o] --> o a!6220!6220plus : [o * o] --> o and : [o * o] --> o isNat : [o] --> o isNatKind : [o] --> o mark : [o] --> o plus : [o * o] --> o s : [o] --> o tt : [] --> o a!6220!6220U11(tt, X, Y) => a!6220!6220U12(a!6220!6220isNat(X), Y) a!6220!6220U12(tt, X) => a!6220!6220U13(a!6220!6220isNat(X)) a!6220!6220U13(tt) => tt a!6220!6220U21(tt, X) => a!6220!6220U22(a!6220!6220isNat(X)) a!6220!6220U22(tt) => tt a!6220!6220U31(tt, X) => mark(X) a!6220!6220U41(tt, X, Y) => s(a!6220!6220plus(mark(Y), mark(X))) a!6220!6220and(tt, X) => mark(X) a!6220!6220isNat(0) => tt a!6220!6220isNat(plus(X, Y)) => a!6220!6220U11(a!6220!6220and(a!6220!6220isNatKind(X), isNatKind(Y)), X, Y) a!6220!6220isNat(s(X)) => a!6220!6220U21(a!6220!6220isNatKind(X), X) a!6220!6220isNatKind(0) => tt a!6220!6220isNatKind(plus(X, Y)) => a!6220!6220and(a!6220!6220isNatKind(X), isNatKind(Y)) a!6220!6220isNatKind(s(X)) => a!6220!6220isNatKind(X) a!6220!6220plus(X, 0) => a!6220!6220U31(a!6220!6220and(a!6220!6220isNat(X), isNatKind(X)), X) a!6220!6220plus(X, s(Y)) => a!6220!6220U41(a!6220!6220and(a!6220!6220and(a!6220!6220isNat(Y), isNatKind(Y)), and(isNat(X), isNatKind(X))), Y, X) mark(U11(X, Y, Z)) => a!6220!6220U11(mark(X), Y, Z) mark(U12(X, Y)) => a!6220!6220U12(mark(X), Y) mark(isNat(X)) => a!6220!6220isNat(X) mark(U13(X)) => a!6220!6220U13(mark(X)) mark(U21(X, Y)) => a!6220!6220U21(mark(X), Y) mark(U22(X)) => a!6220!6220U22(mark(X)) mark(U31(X, Y)) => a!6220!6220U31(mark(X), Y) mark(U41(X, Y, Z)) => a!6220!6220U41(mark(X), Y, Z) mark(plus(X, Y)) => a!6220!6220plus(mark(X), mark(Y)) mark(and(X, Y)) => a!6220!6220and(mark(X), Y) mark(isNatKind(X)) => a!6220!6220isNatKind(X) mark(tt) => tt mark(s(X)) => s(mark(X)) mark(0) => 0 a!6220!6220U11(X, Y, Z) => U11(X, Y, Z) a!6220!6220U12(X, Y) => U12(X, Y) a!6220!6220isNat(X) => isNat(X) a!6220!6220U13(X) => U13(X) a!6220!6220U21(X, Y) => U21(X, Y) a!6220!6220U22(X) => U22(X) a!6220!6220U31(X, Y) => U31(X, Y) a!6220!6220U41(X, Y, Z) => U41(X, Y, Z) a!6220!6220plus(X, Y) => plus(X, Y) a!6220!6220and(X, Y) => and(X, Y) a!6220!6220isNatKind(X) => isNatKind(X) We use rule removal, following [Kop12, Theorem 2.23]. This gives the following requirements (possibly using Theorems 2.25 and 2.26 in [Kop12]): a!6220!6220U11(tt, X, Y) >? a!6220!6220U12(a!6220!6220isNat(X), Y) a!6220!6220U12(tt, X) >? a!6220!6220U13(a!6220!6220isNat(X)) a!6220!6220U13(tt) >? tt a!6220!6220U21(tt, X) >? a!6220!6220U22(a!6220!6220isNat(X)) a!6220!6220U22(tt) >? tt a!6220!6220U31(tt, X) >? mark(X) a!6220!6220U41(tt, X, Y) >? s(a!6220!6220plus(mark(Y), mark(X))) a!6220!6220and(tt, X) >? mark(X) a!6220!6220isNat(0) >? tt a!6220!6220isNat(plus(X, Y)) >? a!6220!6220U11(a!6220!6220and(a!6220!6220isNatKind(X), isNatKind(Y)), X, Y) a!6220!6220isNat(s(X)) >? a!6220!6220U21(a!6220!6220isNatKind(X), X) a!6220!6220isNatKind(0) >? tt a!6220!6220isNatKind(plus(X, Y)) >? a!6220!6220and(a!6220!6220isNatKind(X), isNatKind(Y)) a!6220!6220isNatKind(s(X)) >? a!6220!6220isNatKind(X) a!6220!6220plus(X, 0) >? a!6220!6220U31(a!6220!6220and(a!6220!6220isNat(X), isNatKind(X)), X) a!6220!6220plus(X, s(Y)) >? a!6220!6220U41(a!6220!6220and(a!6220!6220and(a!6220!6220isNat(Y), isNatKind(Y)), and(isNat(X), isNatKind(X))), Y, X)
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